uk: Комп'ютерні науки

description: Some 70% of Earth's surface is covered by clouds at any given time, according to NASA. The existence of clouds in optical satellite imagery limits its usefulness, blocking features of interest on the ground. We have developed a machine learning-based approach for detection and segmentation of clouds, and for production of cloud-free mosaics. Our efforts include development of an open dataset consisting of Sentinel-2 imagery and labeled clouds, creation of a lightweight ML architecture for cloud segmentation, and creation of open source tools for inexpensive production of cloud-free mosaics at continent scale. Our dataset and methods are applicable to many types of optical satellite imagery, not just Sentinel-2.

uk: вхід без авторизації

name: A Dataset and Tools for Detection and Segmentation of Clouds in Optical Satellite Imagery


Harris Hudson

type: Person

cs: Informatika

de: Informatik

fi: tietojenkäsittelytiede

uk: Комп'ютерні науки

en: Computer Science

fr: Informatique

da: Datalogi

es: Ciencias de la Computación

nl: Informatica

cs: Technické vědy

de: Ingenieurwissenschaften

fi: tekniikka

uk: Інженерія

en: Engineering Sciences

fr: Ingénierie

da: Ingeniørvidenskab

es: Ingeniería

nl: Engineering

description: Visual Field is essentially a single HTML file - with some internal links to various CDN CSS and Javascript component resources. Visual Field can be loaded as a web accessible resource, offline web resource, installed as a PWA, or as a stand alone file. It's an Open Source Application that builds upon other Open Source components and allows you to import, process and visualize your data, or other remote CORS enabled datasets. It has a potential broad audience and broad set of use cases. Visual Field isn't about solving all GIS problems but it is about empowering both the end users and designers of your data driven visualizations and workflows alike. This presentation will briefly introduce the capabilities of Visual Field, run a quick demonstration, and then lead in to a general discussion on what you can do going forward should a standards based, text and spatially enabled, SQL engine become available in the browser. My name is Harris Hudson and I am the author of Visual Field. There is both a lot of set precedence and also a lot of continuing ongoing change in the web ecosystem - and should the WebSQL database (which is at the very core of Visual Field) still have broad browser support come September 2021 - I would be delighted to present in FOSS4G 2021 BA. Whether you are technical or non-technical, I hope you might find this presentation useful in some way.

TIB AV-Portal

type: Service

type: WebContent

type: MediaObject

@language: en

cs: přihlášení není vyžadováno

de: keine Anmeldung erforderlich

uk: вхід без авторизації

en: no login required

nl: geen login vereist

name: A look beyond the edge with Visual Field

type: Organization

name: Open Source Geospatial Foundation (OSGeo)

cs: Video

de: Video

fi: Video

uk: Відео

en: Video

fr: Vidéo

da: Video

nl: Video

es: Video


uk: Комп'ютерні науки

description: The Argentinian Space Agency - CONAE along with the Brazilian Space Agency (AEB) are currently carrying out the ocean color satellite mission SABIA-Mar in the context of the National Space Plan. SABIA-Mar is planned to be a constellation of two satellites oriented to the support of blue economy. The first of them, SABIA-Mar 1, is the one currently being developed by CONAE. The main objective of this mission is to provide information and products for the study of marine ecosystems, carbon cycle, coastal dynamics and marine habitats, according to UN Sustainable Development Goals and the national initiative Pampa Azul. With a scheduled launch in 2023, SABIA-Mar 1 will perform in the visible and infrared bands of the electromagnetic spectrum. This will provide valuable information for a wide community of users within scientific, productive and decision making areas.

uk: вхід без авторизації

name: A view into the SABIA-MAR satellite mission


keywords:
tensors
tensor networks
high dimension
approximation
learning
algorithms

cs: Matematika

de: Mathematik

fi: matematiikka

uk: Математика

en: Mathematics

fr: Mathématiques

da: Matematik

es: Matemáticas

nl: Wiskunde

de: Mathematik, Naturwissenschaften

uk: Математика, природничі науки

en: Mathematics, Natural Sciences

description: Many problems in computational and data science require the approximation of high-dimensional functions. Examples of such problems can be found in physics, stochastic analysis, statistics, machine learning or uncertainty quantification. The approximation of high-dimensional functions requires the introduction of approximation tools that capture specific features of these functions. In this lecture, we will give an introduction to tree tensor networks (TNs), or tree-based tensor formats. In part I, we will present some general notions about tensors, tensor ranks, tensor formats and tensorization of vectors and functions. Then in part II, we will introduce approximation tools based on TNs, present results on the approximation power (or expressivity) of TNs and discuss the role of tensorization and architecture of TNs. Finally in part III, we will present algorithms for computing with TNs. This includes algorithms for tensor truncation, for the solution of optimization problems, for learning functions from samples...

uk: вхід без авторизації

name: Approximation and learning with tree tensor networks - lecture 2

name: Centre International de Rencontres Mathématiques (CIRM)

addressCountry: FR

addressLocality: Marseille

addressRegion: Provence-Alpes-Côte d'Azur


uk: Математика, природничі науки

uk: вхід без авторизації

name: Approximation and learning with tree tensor networks - lecture 1


uk: Математика, природничі науки

description: We consider the inverse problem of recovering an unknown parameter from a finite set of indirect measurements. We start with reviewing the formulation of the Bayesian approach to inverse problems. In this approach the data and the unknown parameter are modelled as random variables; the distribution of the data is given and the unknown is assumed to be drawn from a given prior distribution. The solution, called the posterior distribution, is the probability distribution of the unknown given the data, obtained through the Bayes rule. We will talk about the conditions under which this formulation leads to well-posedness of the inverse problem at the level of probability distributions. We then discuss the connection of the Bayesian approach to inverse problems with the variational regularization. This will also help us to study the properties of the modes of the posterior distribution as point estimators for the unknown parameter. We will also briefly talk about the Markov chain Monte Carlo methods in this context.

uk: вхід без авторизації

name: Lecture 2: Introduction to Data Assimilation - Methods


uk: Математика, природничі науки

description: Recently a lot of progress has been made regarding the theoretical understanding of machine learning methods in particular deep learning. One of the very promising directions is the statistical approach, which interprets machine learning as a collection of statistical methods and builds on existing techniques in mathematical statistics to derive theoretical error bounds and to understand phenomena such as overparametrization. The lecture series surveys this field and describes future challenges.

uk: вхід без авторизації

name: Statistical theory for deep neural networks - lecture 1


uk: Математика, природничі науки

uk: вхід без авторизації

name: Statistical theory for deep neural networks - lecture 2


uk: Математика, природничі науки

description: Coupling models or coupling codes: two examples where the coupled model has better properties than each model. In a simple setting (1d in space), a model of porous media (which is characterized by a degenerate parabolic equation) is coupled with the behavior of the medium, the resulting system is a non degenerate heat equation. Similarly, the diffusion equation of neutronics, which coefficients depend on the local temperature of the nuclear core, is (classically) an eigenvalue problem, with infinitely many eigenvalues. Coupled with the equation for the local temperature yields a unique solution.

uk: вхід без авторизації

name: Coupling models instead of coupling codes: two toy examples


How to compute transition times?

keywords:
Metastable dynamics
Hill relation
rare event

uk: Математика, природничі науки

description: We illustrate how the Hill relation and the notion of quasi-stationary distribution can be used to analyse the error introduced by many algorithms that have been proposed in the literature, in particular in molecular dynamics, to compute mean reaction times between metastable states for Markov processes. We present in particular how this analysis gives rigorous foundations to methods using splitting algorithms to sample the reactive trajectories.

uk: вхід без авторизації


Nearshore hydrodynamics - Lecture 1

keywords: hydrology PDE geophysics

uk: Математика, природничі науки

uk: вхід без авторизації


keywords:
PDEs in connection with geophysics
geophysics
finite volume methods
applications to physics

uk: Математика, природничі науки

uk: вхід без авторизації

name: Finite volume methods, dissipative problems and long time behavior - Part 1 : Introduction to the finite volume method


uk: Математика, природничі науки

description: geophysics PDE seismology earthquake problems glaciology geological problems

uk: вхід без авторизації

name: How to extract information on geophysical mass movements from generated seismic waves? - Lecture 1


Nearshore hydrodynamics - Lecture 2

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Finite volume methods, dissipative problems and long time behavior - Part 2 : Dissipative problems and long time behavior


Scales in geophysical flows - Lecture 1

keywords:
atmospheric physics
PDEs in connection with geophysics

uk: Математика, природничі науки

description: Earth's atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation. Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology. Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations. Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem. Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.

uk: вхід без авторизації


keywords:
geophysics
PDE
seismology
earthquake problems
glaciology
geological problems

uk: Математика, природничі науки

uk: вхід без авторизації

name: How to extract information on geophysical mass movements from generated seismic waves? - Lecture 2


uk: Математика, природничі науки

uk: вхід без авторизації

name: How to extract information on geophysical mass movements from generated seismic waves? - Lecture 3


Nearshore hydrodynamics - Lecture 3

uk: Математика, природничі науки

uk: вхід без авторизації


keywords:
oceanography
multiple scale methods
Navier-Stokes equations
elliptic equations and systems

uk: Математика, природничі науки

description: In these lectures, we will focus on the analysis of oceanographic models. These models involve several small parameters: Mach number, Froude number, Rossby number... We will present a hierarchy of models, and explain how they can formally be derived from one another. We will also present different mathematical tools to address the asymptotic analysis of these models (filtering methods, boundary layer techniques).

uk: вхід без авторизації

name: Asymptotic methods for the study of oceanographic models - Lecture 1: model hierarchy


uk: Математика, природничі науки

uk: вхід без авторизації

name: Internal wave dynamics in the atmosphere - Lecture 2


keywords:
PDEs in connection with geophysics
water wave

uk: Математика, природничі науки

description: A good understanding of waves in shallow water, typically in coastal regions, is important for several environmental and societal issues: submersion risks, protection of harbors, erosion, offshore structures, wave energies, etc. The goal of this serie of lectures is to show how efficient asymptotic models can be derived from the full fluid equations (Navier-Stokes and Euler) and to point out several modelling, numerical and mathematical challenges that one still has to understand in order to describe correctly and efficiently such complex phenomena as wave breaking, overtopping, wave-structures interactions, etc. I Derivation of several shallow water models We will show how to derive several shallow water models (nonlinear shallow water equations, Boussinesq and Serre-Green-Naghdi systems) from the free surface Euler equations. We will consider first the case of an idealized configuration where no breaking waves are involved, where the water height does not vanish (no beach!), and where the flow is irrotational – this is the only configuration for which a rigorous justification of the asymptotic models can be justified. II Brief analysis of these models. We will briefly comment the mathematical structure of these equations, with a particular focus on the properties that are of interest for their numerical implementation. We will also discuss how these models behave in when the water height vanishes, since they are typically used in such configurations (see the lecture by P. Bonneton). III Vorticity and turbulent effects. We will propose a generalization of the derivation of the main shallow water models in the presence of vorticity, and show that the standard irrotational shallow water models must be coupled with an equation for a ”turbulent” tensor. We will also make the link with a modelling of wave breaking proposed by Gavrilyuk and Richard in which wave breaking is taken into account as a source term in this additional equation. IV Floating objects. This last section will be devoted to the description of a new approach to describe the interaction of waves in shallow water with floating objects, which leads to several interesting mathematical and numerical issues.

uk: вхід без авторизації

name: Modelling shallow water waves - Lecture 1


uk: Математика, природничі науки

uk: вхід без авторизації

name: Finite volume methods, dissipative problems and long time behavior - Part 3 : Finite volume methods and long time behavior


uk: Математика, природничі науки

uk: вхід без авторизації

name: Asymptotic methods for the study of oceanographic models - Lecture 2: filtering methods


uk: Математика, природничі науки

uk: вхід без авторизації

name: Internal wave dynamics in the atmosphere, take-home messages - Lecture 3


uk: Математика, природничі науки

uk: вхід без авторизації

name: Modelling shallow water waves - Lecture 2

name: Centre International de Rencontres Mathématiques (CIRM)


uk: Математика, природничі науки

uk: вхід без авторизації

name: Asymptotic methods for the study of oceanographic models - Lecture 3: boundary layer methods


uk: Математика, природничі науки

uk: вхід без авторизації

name: Modelling shallow water waves - Lecture 3


TotBlocks Video Abstract

keywords:
modular mineralogy
biopyriboles
palysepioles
rock forming

de: Geowissenschaften (ohne Geographie)

uk: Науки про Землю(крім географії)

en: Geosciences (excl. Geography)

uk: Математика, природничі науки

description: Many rock-forming chain and sheet silicate minerals, i.e., pyroxenes, amphiboles, micas, and clay minerals, are built from shared chemical building blocks known as T-O-T modules. Each module consists of two opposing chains of vertex-sharing silica tetrahedra (T), which vertically sandwich a ribbon of edge-sharing metal-oxygen octahedra (O) in a T-O-T configuration. These minerals are both abundant (26 % of the crust) and diverse (~23 % of silicate species) in the lithosphere because T-O-T modules are chemically and structurally versatile over a wide range of chemical and physical conditions. Chemically, T-O-T modules can incorporate a multitude of common crustal elements, e.g., O, Si, Al, Fe, and Mg. Structurally, T-O-T modules can be configured in many ways, as a function of the module width and linkage type. Therefore, these minerals lie at the center of understanding geological processes. However, their diversity leads to the minerals developing complex, three-dimensional crystal structures, which are challenging to communicate to general audiences, students, and geoscientists. Current methods for communicating the crystal structures of minerals are limited to ball-and-stick models and computer visualization software, but both methods have limitations in communicating the relationships between these complex crystal structures. Here, we apply 3D printing, modular mineralogy, and pedagogical theory to communicate mineral structures in an accessible, interactive, and versatile manner. The open-source TotBlocks project consists of 3D-printed, T-O-T interlocking bricks, based on ideal polyhedral representations of T and O modules, which are linked by hexagonal pegs and slots. Using TotBlocks, we explore the relationships between modular minerals within the biopyribole (biotite-pyroxene-amphibole) and palysepiole (palygorskite-sepiolite) series, as well as other layered minerals (brucite, kaolinite-serpentine, and chlorite groups). TotBlocks can be used in geoscience outreach settings to show the relationships between different mineral structures in a fun and interactive manner. As for geoscience education, the T-O-T modules within these minerals can be used to visually derive many mineral properties by first principles, e.g., habit, cleavage angles, and symmetry/polytypism. Distinct crystallographic sites can be highlighted for geoscience research. With respect to pedagogical theory, TotBlocks are physical manipulatives that align well with experiential learning theory and constructionism. In conclusion, the TotBlocks project provides an accessible (open-source models, low overhead printing cost), interactive (physical manipulatives allowing students to construct and manipulate mineral structures), and versatile (applications in geoscience outreach, education, and research) way to communicate the crystal structures of common rock-forming minerals.

uk: вхід без авторизації


Assembly of TotBlocks

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains the components of TotBlocks, a series of 3D-printed building blocks used to construct the crystal structures of minerals, how to build chains from them, and how these chains can be linked together. The main pieces of TotBlocks are the T (tetrahedral) and O (octahedral) modules and each of these modules can have a positive or negative orientation based on the direction the apices (up versus down). In some minerals, single octahedron pieces and vertical stacking pegs are also used in their structures. To construct a T-O-T module, an O module is stacked on a T⁺ module and a T⁻ module is stacked on the O module. This pattern can be repeated for different chain widths and for both O⁺ and O⁻ modules. These T-O-T modules can be connected widthwise into phyllosilicate-type, pyribole-type, or palysepiole type linkages. Equipped with these different sizes of chains and the different ways we can connect them, we can build a multitude of minerals that can come in many shapes and sizes.

uk: вхід без авторизації


2:1 Phyllosilicates

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structure of the 2:1 phyllosilicates (i.e., the mica and pyrophyllite-talc groups) using TotBlocks, a series of 3D-printed building blocks. The structure of the 2:1 phyllosilicates at the atomic scale, that is, their infinite sheets of T-O-T modules, influences their macroscopic mineral properties. In particular, the weak vertical bonds lead to platy habits and a perfect basal cleavage. The 2:1 phyllosilicates structure can be thought of as a protostructure for rock-forming minerals that are made of T and O modules.

uk: вхід без авторизації


Pyroxene Group

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy
pyroxene

uk: Комп'ютерні науки

description: This video explains how to construct the crystal structures of the three polytypes of the pyroxene group (clinopyroxene, orthopyroxene, and protopyroxene) using TotBlocks, a series of 3D-printed building blocks. The pyroxene group structure consists of single-chain-width modules connected by pyribole type linkages. The stacking of the O modules within the specific polytype observed influences whether the crystal structure is monoclinic or orthorhombic. These different structures affect the mineral’s optical properties, like extinction, when examined in thin section.

uk: вхід без авторизації


Amphibole Supergroup

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy
amphiboles

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structure of the amphibole supergroup using TotBlocks, a series of 3D-printed building blocks. The amphibole supergroup structure consists of double-chain-width modules connected by pyribole-type linkages. This crystal structure leads to an elongate, fibrous to acicular, or asbestiform habit within the supergroup. As a result of their modular crystal structures, the dominant cleavage angles of amphiboles, pyroxenes, and micas allow for these mineral groups to be distinguished from each other in hand specimen.

uk: вхід без авторизації


Clinojimthompsonite and Chesterite

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy
clinojimthompsonite
chesterite

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structures of clinojimthompsonite and chesterite using TotBlocks, a series of 3D-printed building blocks. These non-classical biopyriboles were discovered as a result of the predictions made by modular mineralogical theory, proposed by Jim Thompson. Clinojimthompsonite’s structure consists of triple-chain-width T-O-T modules connected by pyribole-type linkages while chesterite’s structure consists of alternating double- and triple-chain-width T-O-T modules connected by pyribole-type linkages.

uk: вхід без авторизації


Palygorskite Group

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structure of the palygorskite group using TotBlocks, a series of 3D-printed building blocks. The palygorskite group’s structure consists of double-chain-width T-O-T modules connected by palysepiole-type linkages. The resulting crystal structure contains wide channel spaces that can be occupied by water and other molecules like indigo.

uk: вхід без авторизації


Sepiolite Group

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy
sepiolite

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structure of the sepiolite group using TotBlocks, a series of 3D-printed building blocks. The structure of the sepiolite group consists of triple-chain-width T-O-T modules connected by palysepiole-type linkages. As a result of strain in the linkages, the growth of small fibrous crystals is favored, and minerals commonly exhibit clay-like properties.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Robotic design involves modeling the behavior of a robot mechanism when it moves along potential paths set by the users. In this lecture, we will first give an overview of different approaches to design a set of kinematic equations associated with a robot mechanism. In particular, these equations can be used to solve the forward and the backward kinematics problems associated with a robot mechanism or to model its singularity locus. Then we will review methods to solve those equations, and notably methods to draw with guarantees the real solutions of an under-constrained system of equations modeling the singularities of a robot.

uk: вхід без авторизації

name: Computational real algebraic geometry and applications to robotics - lecture 2


Kalifersite

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy
kalifersite

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structure of kalifersite using TotBlocks, a series of 3D-printed building blocks. Kalifersite’s structure consists of alternating double- and triple-chain-width T-O-T modules connected by palysepiole-type linkages. Essentially, it consists of both palygorskite-like and sepiolite-like modules. Compared to palygorskite and sepiolite, kalifersite is missing octahedral sites and will require the use of specific Z₃ and Z₆ O modules in its construction.

uk: вхід без авторизації


Brucite Group

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy
brucite

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structure of the brucite group using TotBlocks, a series of 3D-printed building blocks. The structure of the brucite group consists of O layer modules joined together widthwise to form infinite sheets. Based on the charge of the component cations of the O layer, the modules can be either dioctahedral or trioctahedral. Other layered minerals with O modules display similar patterns between dioctahedral and trioctahedral modules. The sheeted nature of the O modules leads to a platy habit and basal cleavage within this mineral group.

uk: вхід без авторизації


Kaolinite-Serpentine Group

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy
kaolinite
serpentine

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structure of the kaolinite-serpentine group (the 1:1 phyllosilicates) using TotBlocks, a series of 3D-printed building blocks. The kaolinite-serpentine group structures consists of infinite sheets of T-O modules as seen in lizardite, one of the three serpentine polymorphs.The unique T-O configuration of these minerals leads to structural deformations in their modules and the development of these polymorphs.

uk: вхід без авторизації


Chlorite Group

keywords:
mineralogy
biopyriboles
palysepioles
rock-forming minerals
3d printing
pedagogy
chlorite

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to construct the crystal structure of the chlorite group using TotBlocks, a series of 3D-printed building blocks. The chlorite group’s crystal structure consists of T-O-T layer modules which alternate with O layer modules. Essentially, the chlorite group can be thought of as a 2:1 phyllosilicate with an added brucite layer as the interlayer. Subtle differences in the interlayer bonds of chlorites and micas lead to their different physical properties of brittleness and elasticity.

uk: вхід без авторизації


How to 3D Print TotBlocks

uk: Науки про Землю(крім географії)

uk: Математика, природничі науки

description: This video explains how to download the 3D models and how to 3D print TotBlocks, a series of mineral building blocks. After accessing the files on Printables, the component 3D models will be passed through a slicer to generate a 3D printable .gcode file. While in the slicing program, pay careful attention to using supports when printing the O modules and make sure that print settings, filament settings, and printer settings are all adjusted based on the specifics of the 3D printer available. The source code for TotBlocks and a discussion forum for construction issues are available at the TotBlocks repository on GitHub. When you’ve successfully 3D printed TotBlocks, you’re ready to build the foundational building blocks of the earth!

uk: вхід без авторизації


uk: Математика, природничі науки

description: Cell-extracellular matrix interaction and the mechanical properties of cell nucleus have been demonstrated to play a fundamental role in cell movement across fibre networks and micro-channels and then in the spread of cancer metastases. The lectures will be aimed at presenting several mathematical models dealing with such a problem, starting from modelling cell adhesion mechanics to the inclusion of influence of nucleus stiffness in the motion of cells, through continuum mechanics, kinetic models and individual cell-based models.

uk: вхід без авторизації

name: Multi-level mathematical models for cell migration in dense fibrous environments


keywords:
cell membrane
irreversible electroporation
tissue ablation
hepatocellular carcinoma

uk: Математика, природничі науки

description: Irreversible electroporation (IRE) is the sole physical ablative technology inducing tumorous cell death by process unrelated to thermal effect. This characteristic makes the technique suitable for the treatment of subtypes of liver tumors especially hepatocellular carcinoma (HCC) located next to critical structures leading to contraindications to thermal ablation like radiofrequency, microwave or cryotherapy. However, while IRE appears safe in such assumed challenging cases for thermal techniques, several issues remain to be addressed to make its use easier and more effective in clinical practice. First of all, tissue changes induced by IRE must be assessed keeping in mind that conversely to thermal techniques its efficacy is not limited to observable coagulative necrotic component of treatment zone. In addition, IRE which is multibipolar ablative technology requires meticulous demanding electrodes positioning to ensure proper magnitude of electric fields between each dipole. Finally, numerical simulations of IRE are mandatory to ease the setting of electrical pulses parameters to improve predictability of treatment in each individual case. In this setting of continue efforts to improve practicability of IRE the technique is routinely used in our institution since several years for the treatment of patients bearing early and locally advanced HCC not amenable to resection or thermal ablation. All along our experience with IRE, imaging appeared as a key point for addressing the specific issues listed above. For the 58 first patients 92% of complete ablation were achieved while the one-year local tumor progression free survival was 70% (95% CI: 56%, 81%). Indeed, despite the need of improvements IRE appears right now as a unique opportunity to achieve complete sustained local tumor control for patient bearing early or locally advanced HCC not amenable to other curative treatments.

uk: вхід без авторизації

name: Irreversible electroporation of liver malignancy: a new opportunity of curative treatment for patients not amenable to resection and thermal ablation


keywords:
fluid-structure interaction
added-mass effect
finite-elements methods
Nitsche's method
time discretization
loosely coupled schemes

uk: Математика, природничі науки

description: I will introduce the topic of computational cardiac electrophysiology and electrocardiograms simulation. Then I will address some questions of general interest, like the modeling of variability and the extraction of features from biomedical signals, relevant for identification and classification. I will illustrate this research with an example of application to the pharmaceutical industry.

uk: вхід без авторизації

name: Fluid-structure interaction in the cardiovascular system. Lecture 1: Forward problems


uk: Математика, природничі науки

description: This minicourse aims at providing tentative explanations of some specific phenomena observed in the motion of crowds, or more generally collections of living entities. The first lecture shall focus on the so-called Stop and Go Waves, which sometimes spontaneously emerge and persist in crowds in motion. We shall present a general class of dynamical systems which are likely to exhibit this type of instabilities, and emphasize the critical role of two basic ingredients: the asymmetry of interactions, and any sort of delay in the transmission of information through the network of entities. The second lecture will address the Capacity Drop Phenomenon (decrease of the flux though a bottleneck when the upstream density becomes too high), and the more paradoxical Faster is Slower Effect (in some regimes, attempts to go quicker may slow down the overall process). We shall in particular detail how an accurate description of the relative position of entities (at the microscopic level) is crucial to recover and understand those effects.

uk: вхід без авторизації

name: Mathematics behind some phenomena in crowd motion : Stop and Go waves and Capacity Drop


uk: Математика, природничі науки

description: The question of using the available measurements to retrieve mathematical models characteristics (parameters, boundary conditions, initial conditions) is a key aspect of the modeling objective in biology or medicine. In a stochastic/statistical framework this question is seen as an estimation problems. From a deterministic point of view, we classical talk about inverse problems as we recover classical model inputs from outputs. When considering evolution problems,this question falls in the realm of data assimilation that can be seen from a deterministic of statistical point of view. Our objective in this course is to introduce the mathematical principles and numerical aspects behind data assimilation strategies with an emphasis on the deterministic formalism allowing to understand why data assimilation is a specific inverse problem. Our presentation will include considerations on finite dimensional problems but also on infinite dimensional problems such as the ones arising from PDE models. And we will illustrate the course with numerous examples coming from cardiovascular applications and biology.

uk: вхід без авторизації

name: Data Assimilation: a deterministic vision, theory and applications. Lecture 1: Least-square estimation


keywords:
packing
non-overlapping constraint
minimization
level sets
continuity equation
domain velocity
Dirichlet energy
Laplace-Beltrami

uk: Математика, природничі науки

description: Emergence is a process by which coherent structures arise through interactions among elementary entities without being directly encoded in these interactions. In this course, we will address some of the key questions of emergence such as the deciphering of the hidden relation between individual behavior and emergent structures. We will start with presenting biologically relevant examples of microscopic individual-based models (IBM). Then, we will develop a systematic coarse-graining approach and derive corresponding coarse-grained models (CGM) using mathematical kinetic theory as the key methodology. We will highlight that novel kinetic theory concepts need to be developed as new mathematical problems arise with emergent systems such as the lack of conservations, the build-up of correlations, or the presence of phase transitions (or bifurcations). Our goal is to show how kinetic theory can be used to provide better understanding of emergence phenomena taking place in a wide variety of biological contexts.

uk: вхід без авторизації

name: A new continuum theory for incompressible swelling materials


keywords:
cardiac biomechanics
image-based modeling
computational fluid dynamics
finite element method
heart modeling
filtering
data assimilation
biomechanics

uk: Математика, природничі науки

uk: вхід без авторизації

name: Fluid-structure interaction in the cardiovascular system. Lecture 2: Cardiac valves


uk: Математика, природничі науки

uk: вхід без авторизації

name: Data Assimilation: a deterministic vision, theory and applications. Lecture 2: Asymptotic observers


uk: Математика, природничі науки

uk: вхід без авторизації

name: Macroscopic limit from a structured population model to the Kirkpatrick-Barton model


keywords:
cell population
cell kinetic
cell dynamic
neurogenesis
neural progenitor
multiscale model

uk: Математика, природничі науки

uk: вхід без авторизації

name: Mathematical model of cortical neurogenesis


keywords:
dynamical networks
microscopic model
kinetic equation
phase transition
Fourier analysis
bifurcation
Hookean spring

uk: Математика, природничі науки

uk: вхід без авторизації

name: Modelling of complex dynamical networks: from agent-based to continuum models


keywords:
Willmore flow
level set framework
numerical simulation
diffusion-truncature scheme
diffusion-redistancing scheme
mean curvature flow
numerical examples

uk: Математика, природничі науки

uk: вхід без авторизації

name: Diffusion redistanciation schemes, Willmore problem and red blood cells


keywords:
discrepancy
energy minimization
positive-definite functions

uk: Математика, природничі науки

description: Discrepancy and discrete energy are two of the most standard ways to measure the quality of the distribution of a finite point set, and it is very well known that there is strong interplay between these concepts. One particular important example of such interplay is the classical Stolarsky principle which ties together the pairwise sum of distances and the spherical cap discrepancy. In the current talk we shall survey various manifestations of this connection between discrepancy and energy minimization.

uk: вхід без авторизації

name: On the interplay between uniform distribution, discrepancy, and energy minimization


keywords:
Feynman checkerboard
quantum walk
Ising model
Young diagram
Dirac equation
stationary phase method

uk: Математика, природничі науки

description: In the 40s R. Feynman invented a simple model of electron motion, which is now known as Feynman's checkers. This model is also known as the one-dimensional quantum walk or the imaginary temperature Ising model. In Feynman's checkers, a checker moves on a checkerboard by simple rules, and the result describes the quantum-mechanical behavior of an electron. We solve mathematically a problem by R. Feynman from 1965, which was to prove that the model reproduces the usual quantum-mechanical free-particle kernel for large time, small average velocity, and small lattice step. We compute the small-lattice-step and the large-time limits, justifying heuristic derivations by J. Narlikar from 1972 and by A.Ambainis et al. from 2001. The main tools are the Fourier transform and the stationary phase method.

uk: вхід без авторизації

name: Feynman Checkers: Number theory methods in quantum theory

name: Centre International de Rencontres Mathématiques (CIRM)


keywords:
discrepancy theory
jittered sampling
stratified sampling
energy minimization

uk: Математика, природничі науки

description: In this talk I will report on recent progress on two different problems in discrepancy theory.In the first part I will present a recent extension of the notion of jittered sampling to arbitrary partitions of the unit cube. In this joint work with Markus Kiderlen from Aarhus, we introduce the notion of a uniformly distributed triangular array. Moreover, we show that the expected Lp-discrepancy of a point sample generated from an arbitrary equi volume partition of the unit cube is always strictly smaller than the expected Lp-discrepancy of a set of N uniform random samples for p > 1. The second part of the talk is dedicated to greedy energy minimization. I will give a new characterisation of the classical van der Corput sequence in terms of a minimization problem and will discuss various related open questions.

uk: вхід без авторизації

name: On two different topics in discrepancy theory: From the discrepancy of stratified samples to greedy energy minimization (part 1)


uk: Математика, природничі науки

uk: вхід без авторизації

name: Discrepancy of stratified samples from partitions of the unit cube (part 2)


uk: Математика, природничі науки

uk: вхід без авторизації

name: Greedy energy minimization and the van der Corput sequence (part 3)


Metric discrepancy theory

keywords:
discrepancy
limit laws
lacunary sequences
Diophantine equations

uk: Математика, природничі науки

description: This is a survey on progress in metric discrepancy theory and probabilistic aspects in harmonic analysis. We start with classical limit theorems of Salem and Zygmund as well as with the work of Erdoes and Gaal and of Walter Philipp. A focus lies on laws of the iterated logarithm for discrepancy functions of lacunary sequences. We show the connection to certain diophantine properties of the underlying lacunary sequences obtaining precise asymptotic formulas. Different phenomena for subexponentially growing, for exponentially growing and for superexponentially growing sequences are established. Furthermore, relations to arithmetic dynamical systems and to Donald Knuth`s concept of pseudorandomness are discussed. Recent results are contained in joint work with Christoph Aistleitner and Istvan Berkes and it is planed to publish parts of it in a Jean Morlet Springer lecture Notes volume.

uk: вхід без авторизації


keywords:
uniform distribution
pair correlation

uk: Математика, природничі науки

description: We recall some classical results for uniform distribution modulo one, and relate them with their counterparts in the "localized" setting of correlation functions and gap statistics. We discuss the difficulties arising from the localized setting, with a particular emphasis on questions concerning the almost everywhere behavior of parametric sequences. It turns out that in this metric setting one is naturally led to a Diophantine counting problem, which has interesting connections to additive combinatorics and to moment bounds for the Riemann zeta function.

uk: вхід без авторизації

name: Local and global statistics for point sequences


keywords:
integer points
Pick's theorem
Euler-Maclaurin summation formula

uk: Математика, природничі науки

description: We show a connection between Fourier series and a celebrated theorem of G. Pick on the number of integer points in an integer polygon. Then we discuss an Euler-Maclaurin formula over polygons.

uk: вхід без авторизації

name: Pick's theorem and Riemann sums: a Fourier analytic tale


Normal and non-normal numbers

keywords:
normal numbers
radix representation
symbolic dynamics

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

description: We are primarily concerned with the distribution of billiard orbits and geodesics in nonintegrable flat dynamical systems, those that exhibit split singularities. This is an area which has been studied over a number of decades by different authors, and many deep results have been obtained.We are particularly interested in results concerning density and uniformity. However, until very recently, the major known results are time-qualitative and do not seem to say anything definite about the necessary time range. Their proofs all use Birkhoff's ergodic theorem, which is quantitative in the sense that it can tell us precisely how often some relevant event is going to take place, but time-qualitative in the sense that it requires unlimited time range.This leads to a very natural question as to what can happen in a realistic finite time scale.In these two talks, we describe a new non-ergodic method which is a combination of combinatorics, number theory and linear algebra, and which leads to time-quantitative results concerning density and uniformity of some billiard orbits and geodesics in many nonintegrable flat dynamical systems. We discuss two versions of the technique, an eigenvaluebased version as well as an eigenvalue-free version which relies on size magnification.This is work with Jozsef Beck, Michael Donders and Yuxuan Yang.

uk: вхід без авторизації

name: Billiard orbits and geodesics in non-integrable flat dynamical systems (part 1)


keywords: geodesics billiards equidistribution density

uk: Математика, природничі науки

uk: вхід без авторизації

name: Billiard orbits and geodesics in non-integrable flat dynamical systems (part 2)


keywords:
Strategieprozesse
Hochschulmanagement
Wissenschaftsmanagement
Fusionierte Universität
Fallstudie
Strategieentwicklung
Strategisches Management

de: Rechts-, Wirtschafts- und Sozialwissenschaften

uk: Право, економіка та суспільні науки

en: Law, Economics and Social Sciences

de: Wirtschaftswissenschaften

uk: Бізнес та економіка

en: Business and Economics

description: Dies ist die Lösung zur Aufgabe "Fallstudie fusionierte Universität". In diesem Screencast beschreibt Professor Ziegele, welche Maßnahmen im Prozess zu ergreifen sind und macht Vorschläge für Wege aus der Problemsituation. Zudem stellt er einen Optimalen Prozess vor und fürht schritt für schritt durch einen möglichen Prozessablauf.

@language: de

uk: вхід без авторизації

name: Lösung Fallstudie fusionierte Universität

Hochschule Osnabrück

addressCountry: DE

addressLocality: Osnabrück

addressRegion: Lower Saxony


keywords:
structured matrices
eigenvalue computation
functions of matrices

uk: Математика, природничі науки

description: Structure is a fundamental concept in linear algebra: matrices arising from applications often inherit a special form from the original problem, and this special form can be analysed and exploited to design efficient algorithms. In this short course we will present some examples of matrix structure and related applications. Here we are interested in data-sparse structure, that is, structure that allows us to represent an n × n matrix using only O(n) parameters. One notable example is provided by quasi separable matrices, a class of (generally dense) rank-structured matrices where off-diagonal blocks have low rank. We will give an overview of the properties of these structured classes and present a few examples of how algorithms that perform basic tasks - e.g., solving linear systems, computing eigenvalues, approximating matrix functions - can be tailored to specific structures.

uk: вхід без авторизації

name: Topics in structured linear algebra - lecture 1


uk: Математика, природничі науки

uk: вхід без авторизації

name: Topics in structured linear algebra - lecture 2


keywords:
Gröbner bases
Castelnuovo-Mumford regularity
solving degree
lest fall degree

uk: Математика, природничі науки

description: I will start from reviewing Gröbner bases and their connection to polynomial system solving. The problem of solving a polynomial system of equations over a finite field has relevant applications to cryptography and coding theory. For many of these applications, being able to estimate the complexity of computing a Gröbner basis is crucial. With these applications in mind, I will review linear-algebra based algorithms, which are currently the most efficient algorithms available to compute Gröbner bases. I will define and compare several invariants, that were introduced with the goal of providing an estimate on the complexity of computing a Gröbner basis, including the solving degree, the degree of regularity, and the last fall degree. Concrete examples will complement the theoretical discussion.

uk: вхід без авторизації

name: Complexity of Gröbner bases computations and applications to cryptography - lecture 1


keywords:
poset
incidence algebra
Coxeter polynomial
pre-Lie algebra
shuffle algebras

uk: Математика, природничі науки

description: Algebraic combinatorics studies combinatorial objects with an algebraic point of view, and conversely. As such, it is also a very fertile ground for experimental mathematics, involving both classical and new algorithms. I will discuss two topics: finite partially ordered sets and their invariants, and tree-indexed polynomials and power series. Finite partially ordered sets are discrete objects, that can be seen as directed graphs, but also possess an interesting representation theory. This leads to many difficult questions about a subtle equivalence relation, namely posets having equivalent derived categories. The theme of tree-indexed series, which can be traced back to Cayley, plays a role in the study of vector fields and ordinary differential equations. It is nowadays better understood in the framework of operads and can be considered as a nonassociative version of the study of alphabets, words and languages. Surprisingly maybe, rooted trees also appear in the study of iterated integrals, stemming out of the usual "integration-by-part" rule. I will describe the corresponding notions of algebras, without diving too much into the theory of operads. On the way, I will discuss some of the involved algorithms and their implementations.

uk: вхід без авторизації

name: Combinatorics and algebra of partially ordered sets - lecture 1


uk: Математика, природничі науки

uk: вхід без авторизації

name: Tree-indexed polynomials and power series - lecture 2


uk: Математика, природничі науки

uk: вхід без авторизації

name: Complexity of Gröbner bases computations and applications to cryptography - lecture 2


Strategieprozesse an Hochschulen

keywords:
Strategieprozesse
Top-down
Bottom-up
Gegenstromverfahren
Gegenstrom
Hochschulmanagement
Wissenschaftsmanagement
Strategisches Management

uk: Право, економіка та суспільні науки

uk: Бізнес та економіка

description: In diesem Screencast geht Professor Ziegele auf die Grundlagen von Strategieprozessen an Hochschulen ein. Dabei wird ein idealtypischer Prozess des strategischen Managements aufgezeigt und verdeutlicht, wie dies auf eine Hochschule übertragbar ist. Dabei geht Herr Ziegele auch auf die Unterscheidung ziwschen Bottom-up und Top-down Prozesse ein und wie diese jeweils sinnvoll eingesetzt werden können.

uk: вхід без авторизації


uk: Математика, природничі науки

description: We study the expectation of the matrix of overlaps of left and right eigenvectors in the complex Ginibre ensemble, conditioned on a fixed number of k complex eigenvalues. The diagonal (k=1) and off-diagonal overlap (k=2) were introduced by Chalker and Mehlig. They provided exact expressions for finite matrix size N, in terms of a large determinant of size proportional to N. In the large-N limit these overlaps were determined on the global scale and heuristic arguments for the local scaling at the origin were given. The topic has seen a rapid development in the recent past. Our contribution is to derive exact determinantal expressions of size k x k in terms of a kernel, valid for finite N and arbitrary k. It can be expressed as an operator acting on the complex eigenvalue correlation functions and allows us to determine all local correlations in the bulk close to the origin, and at the spectral edge. The methods we use are bi-orthogonal polynomials in the complex plane and the analyticity of the diagonal overlap for general k. This is joint work with Roger Tribe, Athanasios Tsareas, and Oleg Zaboronski.

uk: вхід без авторизації

name: Determinantal structure of eigenvector correlations in the complex Ginibre ensemble


uk: Математика, природничі науки

description: A fundamental question in random matrix theory is to understand how much the eigenvalues of a random matrix fluctuate. I will address this question in the context of unitary invariant ensembles, by studying the global rigidity of the eigenvalues, or in other words the maximal deviation of an eigenvalue from its classical location. Our approach to this question combines extreme value theory of log-correlated stochastic processes, and in particular the theory of multiplicative chaos, with asymptotic analysis of large Hankel determinants with Fisher-Hartwig symbols of various types. In addition to optimal rigidity estimates, our approach sheds light on the extreme values and on the fractal geometry of the eigenvalue counting function. The talk will be based on joint work in progress with Benjamin Fahs, Gaultier Lambert, and Christian Webb.

uk: вхід без авторизації

name: Optimal global rigidity estimates in unitary invariant ensembles


uk: Математика, природничі науки

description: For the commonly studied Hermitian random matrix models there exist tridiagonal matrix models with the same eigenvalue distribution and the same spectral measure vn at the vector e1. These tridiagonal matrices give recurrence coefficients that can be used to build the family of random polynomials that are orthogonal with respect to νn. A similar bijection between spectral data and recurrence coefficients also holds for the Unitary ensembles. This time in stead of obtaining a tridiagonal matrix you obtain a sequence {αk}n−1k=0 Szegö coefficients. The random orthogonal polynomials that are generated by this process may then be used to study properties of the original eigenvalue process. These techniques may be used not just in the classical cases, but also in the more general case of β-ensembles. I will discuss various ways that orthogonal polynomials techniques may be applied including to show convergence of the Circular β-ensemble to Sineβ. I will finish by discussing a result on the maximum deviation of the counting function of Sineβ from it expected value. This is related to studying the phases of associated random orthogonal polynomials.

uk: вхід без авторизації

name: Random orthogonal polynomials: from matrices to point processes

name: Centre International de Rencontres Mathématiques (CIRM)


uk: Математика, природничі науки

description: In many interesting cases, distribution functions of random matrix theory and correlation functions of integrable models of statistical mechanics and quantum field theory are given by tau functions of Painlevé equations. I will discuss an extension of the Jimbo-Miwa-Ueno differential to the space of monodromy data and explain how this construction can be used to compute constant terms in the tau function asymptotics.

uk: вхід без авторизації

name: Monodromy dependence of Painlevé tau functions


Zeros, moments and determinants

uk: Математика, природничі науки

description: For 20 years we have known that average values of characteristic polynomials of random unitary matrices provide a good model for moments of the Riemann zeta function. Now we consider mixed moments of characteristic polynomials and their derivatives, calculations which are motivated by questions on the distribution of zeros of the derivative of the Riemann zeta function.

uk: вхід без авторизації


Integrable systems and spectral curves

uk: Математика, природничі науки

description: Usually one defines a Tau function Tau(t_1,t_2,...) as a function of a family of times having to obey some equations, like Miwa-Jimbo equations, or Hirota equations. Here we shall view times as local coordinates in the moduli-space of spectral curves, and define the Tau-function of a spectral curve Tau(S), in an intrinsic way, independent of a choice of coordinates. Deformations are tangent vectors, and the tangent space is isomorphic to the space of cycles (cf Goldman bracket), so that Hamiltonians can be represented by cycles. All the integrable system formalism can then be represented geometrically in the space of cycles: the Poisson bracket is the intersection, the conserved quantities are periods, Miwa-Jimbo equations and Seiberg-Witten equations are a mere consequence of the definition, Hirota equation is a vanishing monodromy condition, and Virasoro-W constraint are automatically satisfied by our definition, showing that our Tau-function is also a conformal block. Our definition contains KdV, KP multicomponent KP, Hitchin systems, and probably all known classical integrable systems.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The determinantal point processes arise naturally from different areas such as random matrices, representation theory, random graphs and zeros of holomorphic functions etc. In this talk, we will briefly talk about determinantal point processes related to spaces of holomorphic functions, in particular, we will discuss some results concerning the conditional measures, rigidity property and the Olshanskis problem on this area. The talk will be based on several works joint with Alexander Bufetov, Alexander Shamov and Shilei Fan.

uk: вхід без авторизації

name: Determinantal point processes and spaces of holomorphic functions


uk: Математика, природничі науки

description: Random band matrices (RBM) are natural intermediate models to study eigenvalue statistics and quantum propagation in disordered systems, since they interpolate between mean-field type Wigner matrices and random Schrodinger operators. In particular, RBM can be used to model the Anderson metal-insulator phase transition (crossover) even in 1d. In this talk we will discuss some recent progress in application of the supersymmetric method (SUSY) and transfer matrix approach to the analysis of local spectral characteristics of some specific types of 1d RBM. Joint project with Maria Shcherbina.

uk: вхід без авторизації

name: Transfer matrix approach to 1d random band matrices


Hodge-GUE Correspondence

uk: Математика, природничі науки

description: An explicit relationship between certain cubic Hodge integrals on the Deligne–Mumford moduli space of stable algebraic curves and connected GUE correlators of even valencies, called the Hodge–GUE correspondence, was recently discovered. In this talk, we prove this correspondence by using the Virasoro constraints and by deriving the Dubrovin–Zhang loop equation. The talk is based on a series of joint work with Boris Dubrovin, Si-Qi Liu and Youjin Zhang.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The Spherical Sherrington-Kirkpatrick (SSK) model is defined by the Gibbs measure on a highdimensional sphere with a random Hamiltonian given by a symmetric quadratic function. The free energy at the zero temperature is the same as the largest eigenvalue of the random matrix associated with the quadratic function. Even for the finite temperature, there is a simple relationship between the free energy and the eigenvalues. We will discuss how one can study the fluctuations of the free energy using this relationship and results from random matrix theory. We will also discuss the distribution of the spin sampled from the Gibbs measure.

uk: вхід без авторизації

name: Spherical Sherrington-Kirkpatrick model and random matrix


keywords:
free convolution
tensor product
lozenge tilings
normalised Shur function
infinite-dimensional unitary group
Perelomov-Popov measures
law of large numbers
enveloping algebra

uk: Математика, природничі науки

description: Asymptotic representation theory deals with representations of groups of growing size. For classical Lie groups there are two distinguished regimes of growth. One of them is related to representations of infinite-dimensional groups, and the other appears in combinatorial and probabilistic questions. In the talk I will discuss differences and similarities between these two settings.

uk: вхід без авторизації

name: Representations of classical Lie groups: two regimes of growth


uk: Математика, природничі науки

description: We establish a new connection between moments of n×n random matrices Xn and hypergeometric orthogonal polynomials. Specifically, we consider moments ETrX−sn as a function of the complex variable s∈C, whose analytic structure we describe completely. We discover several remarkable features, including a reflection symmetry (or functional equation), zeros on a critical line in the complex plane, and orthogonality relations. In each of the classical ensembles of random matrix theory (Gaussian, Laguerre, Jacobi) we characterise the moments in terms of the Askey scheme of hypergeometric orthogonal polynomials. We also calculate the leading order n→∞ asymptotics of the moments and discuss their symmetries and zeroes. We discuss aspects of these phenomena beyond the random matrix setting, including the Mellin transform of products and Wronskians of pairs of classical orthogonal polynomials. When the random matrix model has orthogonal or symplectic symmetry, we obtain a new duality formula relating their moments to hypergeometric orthogonal polynomials.

uk: вхід без авторизації

name: Moments of random matrices and hypergeometric orthogonal polynomials


When J. Ginibre met E. Schrödinger

uk: Математика, природничі науки

description: The real Ginibre ensemble consists of square real matrices whose entries are i.i.d. standard normal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble, real eigenvalues in the real Ginibre ensemble attain positive likelihood. In turn, the spectral radius of a real Ginibe matrix follows a different limiting law for purely real eigenvalues than for non-real ones. Building on previous work by Rider, Sinclair and Poplavskyi, Tribe, Zaboronski, we will show that the limiting distribution of the largest real eigenvalue admits a closed form expression in terms of a distinguished solution to an inverse scattering problem for the Zakharov-Shabat system. This system is directly related to several of the most interesting nonlinear evolution equations in 1+1 dimensions which are solvable by the inverse scattering method, for instance the nonlinear Schrödinger equation.

uk: вхід без авторизації


keywords:
log-gases
loop equation

uk: Математика, природничі науки

description: We study a general class of log-gas ensembles on a quadratic lattice. Using a variational principle we prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance. We apply our general results to analyze the asymptotic behavior of a q-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field. Our approach is based on a q-analogue of the Schwinger-Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to a quadratic lattice.

uk: вхід без авторизації

name: Log-gases on a quadratic lattice via discrete loop equations


uk: Математика, природничі науки

description: I will discuss polynomials PN of degree N that satisfy non-Hermitian orthogonality conditions with respect to the weight (z+1)N(z+a)Nz2N on a contour in the complex plane going around 0. These polynomials reduce to Jacobi polynomials in case a = 1 and then their zeros cluster along an open arc on the unit circle as the degree tends to infinity. For general a, the polynomials are analyzed by a Riemann-Hilbert problem. It follows that the zeros exhibit an interesting transition for the value of a = 1/9, when the open arc closes to form a closed curve with a density that vanishes quadratically. The transition is described by a Painlevé II transcendent. The polynomials arise in a lozenge tiling problem of a hexagon with a periodic weighting. The transition in the behavior of zeros corresponds to a tacnode in the tiling problem. This is joint work in progress with Christophe Charlier, Maurice Duits and Jonatan Lenells and we use ideas that were developed in [2] for matrix valued orthogonal polynomials in connection with a domino tiling problem for the Aztec diamond.

uk: вхід без авторизації

name: Tilings of a hexagon and non-hermitian orthogonality on a contour


uk: Математика, природничі науки

description: The universality properties of the Sine process (corresponding to inverse temperature beta equal to 2) are now well known. More generally, a family of point processes have been introduced by Valko and Virag and shown to be the bulk limit of Gaussian beta ensembles, for any positive beta. They are defined through a one-parameter family of SDEs coupled by a two-dimensional Brownian motion (or more recently as the spectrum of a random operator). Through these descriptions, some properties have been derived by Holcomb, Paquette, Valko, Virag and others but there is still much to understand. In a work with David Dereudre, Adrien Hardy (Université de Lille) and Thomas Leblé (Courant Institute, New York), we use tools from classical statistical mechanics based on DLR equations to give a completely different description of the Sine beta process and derive some properties, such as rigidity and tolerance.

uk: вхід без авторизації

name: A statistical physics approach to the sine beta process


uk: Математика, природничі науки

description: In this talk, we discuss the application of the Yang-Baxter equation for the quantum affine lie algebra Uq(sln+1ˆ) to interacting particle systems. The asymmetric simple exclusion process (ASEP) is a continuous-time Markov process of interacting particles on the integer lattice. We distinguish particles to be either a first class or a second class particle. In particular, the second class particles are blocked in their movement by all other particles, while the first class particles are only blocked by other first class particles. We consider the step initial conditions so that all non-negative integer positions are occupied and all other positions are vacant at time zero. Moreover, we take exactly L second class particles to be located at the very front of the configuration at time zero. Then, using recent results of Tracy-Widom (2017) and Borodin-Wheeler (2018), we compute the asymptotic speed of the leftmost second class particle. This is joint work with Promit Ghosal (Columbia University) and Ethan Zell (University of Virginia) in arXiv:1903.09615.

uk: вхід без авторизації

name: The speed of a second class particle in the ASEP


keywords:
asymmetric simple exclusion process
Kardar-Parisi-Zhang scaling
cluster probabilities
step initial condition

uk: Математика, природничі науки

description: In earlier work (arXiv:1707.04927) the authors obtained formulas for the probability in the asymmetric simple exclusion process that at time t a particle is at site x and is the beginning of a block of L consecutive particles. Here we consider asymptotics. Specifically, for the KPZ regime with step initial condition, we determine the conditional probability (asymptotically as t→∞) that a particle is the beginning of an L-block, given that it is at site x at time t. Using duality between occupied and unoccupied sites we obtain the analogous result for a gap of G unoccupied sites between the particle at x and the next one.

uk: вхід без авторизації

name: Blocks & gaps in the asymmetric simple exclusion process


uk: Математика, природничі науки

description: We identify the persistence probability for the zero-temperature non-equilibrium Glauber dynamics of the half-space Ising chain as a particular Painlevé VI transcendent, with monodromy exponents (1/2,1/2,0,0). Among other things, this characterization a la Tracy-Widom permits to relate our specific Bonnet-Painlevé VI to the one found by Jimbo & Miwa and characterizing the diagonal correlation functions for the planar static Ising model. In particular, in terms of the standard critical exponents eta=1/4 and beta=1/8 for the latter, this implies that the probability that the limiting Gaussian real Kac's polynomial has no real root decays with an exponent 4(eta+beta)=3/4.

uk: вхід без авторизації

name: A tale of Pfaffian persistence tails told by a Bonnet-Painlevé VI transcendent


Non linear random matrix models.

uk: Математика, природничі науки

description: The talk concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider M=1mYY∗ with Y=f(WX) where W and X are random rectangular matrices with i.i.d. centered entries. The function f is applied pointwise and can be seen as an activation function in (random) neural networks. We compute the asymptotic empirical distribution of this ensemble in the case where W and X have subGaussian tails and f is smooth. This extends a result of [PW17] where the case of Gaussian matrices W and X is considered. We also investigate the same questions in the multi-layer case, regarding neural network applications.

uk: вхід без авторизації


The supercooled Stefan problem

uk: Математика, природничі науки

description: We will consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to define global solutions, even in the presence of blow-ups of the freezing rate. We will provide a complete description of such solutions, by relating the temperature distribution in the liquid to the regularity of the ice growth process. The latter is shown to transition between (i) continuous differentiability, (ii) Holder continuity, and (iii) discontinuity. In particular, in the second regime we rediscover the square root behavior of the growth process pointed out by Stefan in his seminal paper [Ste89] from 1889 for the ordinary Stefan problem. In our second main theorem, we will establish the uniqueness of the global solutions, a first result of this kind in the context of growth processes with singular self-excitation when blow-ups are present. Based on joint work with Francois Delarue and Sergey Nadtochiy.

uk: вхід без авторизації


uk: Математика, природничі науки

description: We consider the domino tilings of a large class of Aztec rectangles. For an appropriate scaling limit, we show that, the disordered region consists of roughly two arctic circles connected with a finite number of paths. The statistics of these paths is governed by a kernel, also found in other models (universality). The kernel thus obtained is believed to be a master kernel, from which the kernels, associated with critical points, can all be derived.

uk: вхід без авторизації

name: Universality in tiling models: a Master kernel


TIB AV-Portal - Tutorial (2022/ukr)

uk: Комп'ютерні науки

uk: Бібліотекознавство, документознавство

en: Information and Library Sciences

de: Geisteswissenschaften

uk: Гуманітарні науки

en: Humanities

description: Наукові відео, записи лекцій та конференцій чи комп’ютерна анімація – частина Вашої щоденної роботи? Тоді чому б Вам не скористатись AV-порталом Німецької національної науково-технічної бібліотеки (TIB AV-portal).

@language: uk

uk: вхід без авторизації

Technische Informationsbibliothek (TIB)

addressLocality: Hanover


Advent City

keywords:
Virtual Reallity
3D Modell
Spitzbergen
Archäologie

de: Geschichte

uk: Історія

en: History

uk: Гуманітарні науки

description: Located just a few kilometers north of Longyearbyen on the other side of Adventfjord, Advent City was the first coal mine on Spitsbergen to operate year-round. It was abandoned just five years after work began due to unprofitable operations. While parts of the settlement have been left to decay for over a hundred years, many of the buildings were rebuilt elsewhere shortly after mining operations were abandoned and largely still stand in their new positions today. In addition to the remains of buildings and technical installations on site, as well as the wooden huts that are still standing, a whole series of historical photographs have survived that show us a very accurate picture of the settlement. From the various sources, a comprehensive 3D model of Advent City was developed, showing the British mine at the time of its operation in the early 20th century. This model was then transferred into a virtual reality application that allows the user to experience the settlement immersively. In our paper we will discuss in detail the genesis of the 3D model as well as the VR environment and afterwards discuss the benefit of such a digital world for disseminating the results of polar archaeological research to a broad audience.

uk: вхід без авторизації


keywords:
Event-based surveillance
infectious diseases
zoonosis
epidemiology
text mining
spatial information
health

uk: Комп'ютерні науки

description: Syed Mehtab Alam is doing his PhD on topic “Generic methods for epidemiological monitoring based on the integration of heterogeneous textual data” funded by H2020 MOOD project. His PhD work focuses on the development of generic methods in order to extract new and relevant event in heterogeneous data textual in a One Health context. Previously, he was Research Associate in University of Bozen-Bolzano, Italy in which he mainly contributed in European funded project “COCkPiT” from 2018-2020. Since 2010, he was a part of different software organizations in which he was involved in different software development project across different domains i.e. Healthcare, European Taxi Systems, Mobile TV systems etc. The presentation is about the importance of relative spatial information (RSI) in EBS. Mehtab described the approach to extract RSI from different unofficial media sources and how to accurately geographically map this information for different events in EBS.

uk: вхід без авторизації

name: Importance of Relative Spatial Information (RSI) in EBS


uk: Математика, природничі науки

description: When we construct mathematical models to represent a given real-world system, there is always a degree of uncertainty with regards to the model specification - whether with respect to the choice of parameters or to the choice of formulation of model functions. This can become a real problem in some cases, where choosing two different functions with close shapes in a model can result in substantially different model predictions. This phenomenon is known as structural sensitivity, and is a significant obstacle to improving the predictive power of models - particularly in fields where it is not possible to derive the functions suitable for representing system processes from theory or physical laws, such as the biological sciences. In this talk, I shall revisit the notion of structural sensitivity and propose a general approach to reveal structural sensitivity which is a far more powerful technique than the conventional approach consisting of fixing a particular functional form and varying its parameters. I will demonstrate that conventional methods based on variation of parameters alone will often miss structural sensitivity. I shall discuss the consequences that structural sensitivity and the resulting model uncertainty may have for the modelling of biological systems. In particular, it will be shown the concept of a 'concrete' bifurcation structure may no longer be relevant in the case of structural sensitivity, thus we can only describe bifurcations of completely deterministic systems with a certain probability. Finally, I will show that structural sensitivity can be a possible explanation of the observed irregularity of oscillations of population densities in nature. At the end, we will discuss the current challenges related to structural sensitivity in models and data.

uk: вхід без авторизації

name: Structural sensitivity of ecological models: state of the art and challenges

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


Introduction and Perspectives

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

description: Many systems from the natural world have to adapt to continuously changing external conditions. Some systems have dangerous levels of external conditions, defined by catastrophic bifurcations, above which they undergo a critical transition (B-tipping) to a different state; e.g. forest-desert transitions. Other systems can be very sensitive to how fast the external conditions change and have dangerous rates - they undergo an unexpected critical transition (R-tipping) if the external conditions change slowly but faster than some critical rate; e.g. critical rates of climatic changes. R-tipping is a genuine non-autonomous instability which captures ``failure to adapt to changing environments" [1,2]. However, it cannot be described by classical bifurcations and requires an alternative mathematical framework. In the first part of the talk, we demonstrate the nonlinear phenomenon of R-tipping in a simple ecosystem model where environmental changes are represented by time-varying parameters [Scheffer et al. Ecosystems 11 2008]. We define R-tipping as a critical transition from the herbivore-dominating equilibrium to the plant-only equilibrium, triggered by a smooth parameter shift [1]. We then show how to complement classical bifurcation diagrams with information on nonautonomous R-tipping that cannot be captured by the classical bifurcation analysis. We produce tipping diagrams in the plane of the magnitude and `rate’ of a parameter shift to uncover nontrivial R-tipping phenomena. In the second part of the talk, we develop a general framework for R-tipping based on thresholds, edge states and a suitable compactification of the nonautonomous system. This allows us to define R-tipping in terms of connecting heteroclinic orbits in the compactified system, which greatly simplifies the analysis. We explain the key concept of threshold instability and give rigorous testable criteria for R-tipping in arbitrary dimensions. References: [1] PE O'Keeffe and S Wieczorek,'Tipping phenomena and points of no return in ecosystems: beyond classical bifurcations', arXiv preprint arXiv:1902.01796 [2] A Vanselow, S Wieczorek, U Feudel, 'When very slow is too fast: Collapse of a predator-prey system' Journal of Theoretical Biology (2019).

uk: вхід без авторизації

name: Rate-Induced Tipping: Beyond Classical Bifurcations in Ecology


uk: Математика, природничі науки

description: Classical ecological theory relies heavily on the principles of deterministic dynamical systems, and methods from mathematics and physics that are more appropriate for stochastic systems are unfamiliar to many ecologists. As a result, when stochasticity plays an important role in shaping ecological dynamics — as it often does — our ability to fully address certain questions can be limited. In this talk, I will give an overview of some new (or at least newly extended for ecological applications) mathematical methods that bring important new classes of questions into reach.

uk: вхід без авторизації

name: Open ecological questions that we can answer when we think carefully about stochasticity


uk: Математика, природничі науки

description: The dynamics of species’ densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. The interplay between these variables and species densities can determine whether a particular population persists or goes extinct. I will present recent theorems for stochastic persistence and exclusion for stochastic ecological difference equations accounting for internal and external variables, and will illustrate their utility with applications to models of eco-evolutionary dynamics.

uk: вхід без авторизації

name: Population persistence and species coexistence in the face of environmental uncertainty


uk: Математика, природничі науки

description: Understanding stability of ecosystems and communities has always been major challenge for ecologists. Definitions and measures of stability abound and at times are confusing. Nowadays it is in general accepted that stability is multidimensional and it needs to be measured in different ways. Some of the metrics are used to highlight resistance of ecological systems to a specific type of perturbations (like an invasion of an alien). Others have been developed to highlight the approach to tipping points (that is catastrophic transitions between different dynamical states). As long-term data become increasingly available and experimental approaches are improving, the challenge is how to apply our theoretical metrics on these ecological dynamics to understand stability. In the talk, I will present a possible way for identifying best suitable metrics for measuring stability in ecological communities. More in depth, I will also focus on how changes in dynamical properties of ecological dynamics can be used as early warnings to abrupt ecological changes using examples from ecology and the climate.

uk: вхід без авторизації

name: Understanding ecological dynamics: Stability metrics and Early warnings


uk: Математика, природничі науки

description: Some basic ideas behind optimal control of ODEs and PDEs will be introduced. Control of a flow rate in a PDE model for a population in a river will be illustrated. Harvesting in a system of ODEs representing an anchovy ecosystem in the Black Sea will be discussed. Issues and new features of control approaches will be presented at the end and could lead to discussions later at this workshop.

uk: вхід без авторизації

name: Optimal control of two ecological models


uk: Математика, природничі науки

description: Ecosystem-based approaches to management are desirable for many reasons. However quantitative approaches to ecosystem management are hampered by incomplete knowledge of the system state and uncertainty in the underlying dynamics. In principal, we can circumvent these difficulties using nonparametric approaches to model the uncertain dynamics and using time-delay embedding to implicit account for missing state variables. However, these methods are incredibly data-hungry and tend to be sensitive to observation noise. Here I propose to mitigate these practical obstacles a) by adopting a state-space perspective that allows us to partition observation and process uncertainty and b) by combining data from multiple locations using hierarchical and spatial modeling approaches. We find that noise reduction substantially improves attractor reconstruction and reduces bias in the estimation of Lyapunov exponents from noisy time series. Spatial-delay embedding significantly increases the time horizon over which useful predictions can be made compared to more traditional local embedding.

uk: вхід без авторизації

name: Improved inference for nonparametric approaches to ecological dynamics


uk: Математика, природничі науки

description: One of the features that distinguishes biological systems is the wide range of scales in time and space on which processes and interactions occur. This is a form of complexity, but it is one that can sometimes be turned into an advantage. I will describe models for a couple of systems where my collaborators and I have found that to be the case. The first (from long ago) is a system with ladybugs preying on aphids. The ladybugs (which are highly mobile but reproduce slowly) experience the environment as a system of patches, while the aphids (which are much less mobile but reproduce quickly) experience each patch as spatial continuum. The second (more recent) is a system aimed at describing the evolution of dispersal. Dispersal starts with the movement of individuals, which can be observed by tracks or tracking and described in terms of random walks. That then produces spatial patterns, which then influence ecological interactions within and among populations. Those in turn exert selective pressure on traits that determine the spatial patterns, and finally the selective pressure together with the occasional the appearance of mutants results in the evolution of dispersal traits. All of these processes can, in some cases, operate on different scales in time and space. It turns out that this when this occurs it can be exploited to produce relatively simple models in some situations. The older research I will discuss was conducted in collaboration with Steve Cantrell; the newer was with Steve Cantrell, Mark Lewis, and Yuan Lou.

uk: вхід без авторизації

name: A convenient form of complexity in ecology: multiple timescales


uk: Математика, природничі науки

description: Human activities or natural events may perturb locally stable equilibrium communities. One can ask how long the community will take to return to its equilibrium and how "far" from the equilibrium it may get in the process. To answer those questions, we can measure the "resilience" and "reactivity" of a system. These concepts thus quantify one particular form of transient dynamics in ecological models. I will briefly review these measures and give some examples and known but still surprising insights. Then I will suggest extensions to periodically forced systems and periodic orbits in autonomous systems and examine some of their properties.

uk: вхід без авторизації

name: Transient dynamics in equilibrium and non-equilibrium communities


uk: Математика, природничі науки

description: We will discuss the recent progress in understanding the properties of transient dynamics in complex ecological systems. Predicting long-term trends as well as sudden changes and regime shifts in ecosystems dynamics is a major issue for ecology as such changes often result in population collapse and extinctions. Analysis of population dynamics has traditionally been focused on their long-term, asymptotic behavior whilst largely disregarding the effect of transients. However, there is a growing understanding that in ecosystems the asymptotic behavior is rarely seen. A big new challenge for theoretical and empirical ecology is to understand the implications of long transients. It is believed that the identification of the corresponding mechanisms should substantially improve the quality of long-term forecasting and crisis anticipation. Although transient dynamics have received considerable attention in physical literature, research into ecological transients is in its infancy and systematic studies are lacking. This work aims to partially bridge this gap and facilitate further progress in quantitative analysis of long transients in ecology. By revisiting and examining a variety of mathematical models used in ecological applications as well as some empirical facts, we reveal main mechanisms leading to the emergence of long transients both is spatial and nonspatial systems.

uk: вхід без авторизації

name: Long transients in ecology: theory and applications


uk: Математика, природничі науки

description: In many ecological problems spatial data are collected to satisfy the requirement that the population spatial distributions can be reconstructed with high accuracy. The situation, however, may be different when reconstruction of spatial distributions is required in the context of monitoring and control (M&C) protocol. In my talk I will argue that the M&C protocol can be thought of as a data filter as its application transforms the original dataset and it often results in a spatial distribution with essentially different properties. That transformation may, in turn, alleviate negative impact of uncertainty on the accuracy of results when spatial distributions are reconstructed from data with measurement errors. While original data are affected by the measurement errors, the filtered data may or may not be affected depending on the filter definition. In some cases, there is no need to ask for more accurate data collection as measurement errors will be `eliminated' by application of the M&C protocol. Meanwhile, it will also be shown in the talk that if inherent uncertainty presents in the model, the M&C data filter may become useless, no matter how accurate the data are. This is a joint work with John Ellis and Wenxin Zhang.

uk: вхід без авторизації

name: Handling uncertain spatial data in monitoring and control problems


Ecological Modelling with Data

uk: Математика, природничі науки

description: In order for models to make relevant predictions about real ecological systems, it is helpful to have data to guide the selection of, for example, parameter values, interaction functions, and dispersal kernels. For many ecological systems, however, data is sparse. Nonetheless, these data can still lead to the development of models that give rise to theoretical predictions with real relevance. Several examples will be presented and discussed in this talk.

uk: вхід без авторизації


Summary and Outlook

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Reverse mathematics and the ascending chain condition


uk: Математика, природничі науки

uk: вхід без авторизації

name: The open and clopen Ramsey theory in the Weihrauch lattice


Questions about Hindman’s theorem

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: The reverse mathematics of Büchi’s decidability theorem


Cohesive trees

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Open Problems in the Reverse Mathematics of Ramsey Theory on Trees and Graphs


uk: Математика, природничі науки

uk: вхід без авторизації

name: SRT22 does not imply COH in omega models


Lowness of the pigeonhole principle

uk: Математика, природничі науки

uk: вхід без авторизації


Reverse math of the dual Ramsey theorem

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Some propositions between WWKL0 and WKL0


uk: Математика, природничі науки

uk: вхід без авторизації

name: Recent struggling for the first-order part of Ramsey’s theorem for pairs

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

uk: вхід без авторизації

name: Weihrauch degrees of closed choice on finite spaces


uk: Математика, природничі науки

uk: вхід без авторизації

name: The reverse mathematics of an inside-outside Ramsey theorem


uk: Математика, природничі науки

uk: вхід без авторизації

name: Relationships between preservation properties of problems


uk: Математика, природничі науки

description: An n-knot is a locally flat PL n-sphere in Sn+2. We show that many decision problems about n-knot groups, n≥3, and groups of closed orientable surfaces in S4, are unsolvable. We will also discuss the case of 2-knots, where the corresponding questions are still open. This is joint work with Fico González-Acuña and Jonathan Simon.

uk: вхід без авторизації

name: Higher-dimensional knot groups and decision problems


uk: Математика, природничі науки

description: I will explain (older) joint work with Dror Bar-Natan on the relationship between 4-dimensional knot theory and Lie theory. On the knot theory side, this involves finite type invariants of welded knotted objects, in other words, a certain class of 4-dimensional tangles. On the Lie theory side stands the Kashiwara-Vergne problem, a famous problem that was first solved, after nearly 30 years, in 2006 by Alekseev and Meinrenken. I will also aim to describe more recent efforts to connect this work to related results of Alekseev-Kawazumi-Kuno-Naef, who provide a different topological interpretation of the Kashiwara-Vergne problem in terms of homotopy classes of loops on surfaces.

uk: вхід без авторизації

name: Four dimensional tangles, finite type invariants and Lie theory


Symplectic topology for 4-manifolds

uk: Математика, природничі науки

description: Symplectic topology has been behind many advances in the study of the smooth topology of 4-manifolds. 4-manifolds which admit a symplectic structure give a nice subclass of smooth 4-manifolds where additional tools are available, while still exhibiting many of the exotic and topological phenomena occurring in generic smooth 4-manifolds. We will discuss some of the tools and major theorems that symplectic topology brings to the table. Instead of going into full technical detail, we will focus on the topological applications of these tools to understanding 4-manifolds and the surfaces they contain. We hope to discuss: adjunction formula and standard neighborhoods, using pseudoholomorphic curves to prove existence of certain surfaces or foliations by surfaces, positivity of intersections for uniqueness of surfaces and controlling isotopies, and symplectic branched coverings.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In this talk we will define braided surfaces with caps, which generalizes the notion of braided surfaces to nonribbon surfaces in D4. We show that any surface in D4 can be isotoped to a braided surface with caps with only positive branch points, and that this isotopy can be taken rel boundary if the boundary is already a classical closed braid in S3. We will then discuss some applications of these surfaces to constructing Lefschetz fibrations with prescribed boundary open book decompositions and braiding closed surfaces in CP2.

uk: вхід без авторизації

name: Approaches to Computational Problems from Braided surfaces


Concordance of lightbulbs

uk: Математика, природничі науки

description: I use Dave Gabai's 4D light bulb theorem to prove an analogous statement in the setting of concordance: if two spheres R, R′ in a 4-manifold X are homotopic and R admits a dual sphere, then R and R′ are concordant (modulo a condition on 2-torsion in the fundamental group of X).

uk: вхід без авторизації


Knotted singular surfaces in S4

uk: Математика, природничі науки

description: All (closed oriented) smooth four-manifolds can be constructed as branched covers of the sphere. In this talk, I will consider a specific class of such covers: irregular 3-fold covers with non-smooth branching sets. This construction is particularly well-suited for explicitly constructing simply-connected manifolds. I'll give an overview of recent results in this area and discuss potential applications to understanding smooth structures and handle decompositions of simply-connected four-manifolds.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The disc embedding theorem for simply connected 4-manifolds was proved by Freedman in 1982 and forms the basis for his proofs of the h-cobordism theorem, the Poincare conjecture, the exactness of the surgery sequence, and the classification of simply connected manifolds, all in the topological category and dimension four. The disc embedding theorem for more general 4-manifolds is proved in the book of Freedman and Quinn. However, the geometrically transverse spheres claimed in the outcome of the theorem are not constructed. We close this gap by constructing the desired transverse spheres. We also outline where and why such transverse spheres are necessary. This is a joint project with Mark Powell and Peter Teichner.

uk: вхід без авторизації

name: Geometrically transverse spheres in 4-manifolds


Topologically trivial proper 2-knots

uk: Математика, природничі науки

description: We will discuss the knot theory of proper embeddings of the plane and half-open annulus in R4, focusing on what is arguably the simplest situation that is intrinsically noncompact. While it is still unknown if a smoothly knotted embedding S2→R4 can be topologically unknotted, there are various ways of realizing the analogous phenomenon for planes and annuli. We will show how to construct and distinguish various families of examples. These can exhibit remarkably different behavior, and can sometimes be explicitly drawn with level diagrams.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This represents joint work with Danny Ruberman. We will start with critical level embeddings of a pair of surfaces that are topologically isotopic but not smoothly isotopic. We will see how these surfaces may be used to construct exotic homotopy classes in the diffeomorphism group of some 4-manifolds and in spaces of embeddings. Invariants to detect exotic diffeomorphisms based on parameterized gauge theory will be defined along with a method to evaluate the invariants in some interesting cases. Given time, the talk would speculate on how these invariants could provide information about intersection patterns of surfaces in 4-manifolds tools.

uk: вхід без авторизації

name: From Exotic Surfaces to Exotic Homotopy Classes of Diffeomorphisms


Spines for spineless 4-manifolds

uk: Математика, природничі науки

description: A recent paper of Levine-Lidman gives examples of simply connected 4-manifolds X, homotopy equivalent to a 2-sphere, that do not admit PL spines. In other words, there is no PL (not necessarily locally flat) embedded sphere in X that is a strong deformation retract of X. I will show that a family of the Levine-Lidman examples admit a topological spine—a locally PL sphere that is a strong deformation retract of X. This is joint work with Hee Jung Kim.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Quandle cohomology and quandle extension theory is developed by modifying group cohomology and group extensions theory. In 1999, J. S. Carter, D. Jelsovsky, S. Kamada, L. Langford and M. Saito introduced an invariant by using quandle cocycles. It is helpful to study classical knots and knotted surfaces, and still many knot theorists have been studying quandle cocycle and quandle cocycle invariant. In this talk, we survey quandle cohomology and quandle extension theory, after then we study quandle 2-cocycles in a connection with group 2-cocycles. We also observe some properties of abelian extension of a quandle which is defined by a quandle 2-cocycle. This is a joint work with Y. Bae and J. S. Carter.

uk: вхід без авторизації

name: On quandle cocycles and abelian extensions associated with group extensions