uk: Математика, природничі науки

description: In this talk, we explain how two-stage worst-case regret minimization problems can be reformulated as two-stage robust optimization models. This allows us to employ both approximate and exact solution methods that are available in the recent literature to fficiently identify good solutions for these hard problems. In particular, our numerical experiments indicate that affine decision rules are particularly effective at identifying good conservative solutions for three different types of decision problems: a multi-item newsvendor problem, a lot-sizing problem, and a production-transportation problem.

uk: вхід без авторизації

name: Worst-case regret minimization in a two-stage linear program


Phebe Vayanos

type: Person

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: Robust optimization is a popular paradigm for modeling and solving two-stage decision-making problems affected by uncertainty. Most approaches assume that the uncertain parameters can be observed for free and that the sequence in which they are revealed is independent of the decision-maker's actions. Yet, these assumptions fail to hold in many real-world applications where the time of information discovery is decision-dependent and the uncertain parameters only become observable after an often costly investment. This is the case for example in clinical trial planning, in offshore oilfield exploration, in active preference elicitation, and in R&D project portfolio optimization. To fill this gap in the literature, we consider two-stage robust optimization problems in which (part of) the first stage variables decide on the uncertain parameters that will be observed between the first and the second decision stages. The information available in the second stage is thus decision-dependent and can be discovered (at least in part) by making strategic exploratory investments in the first stage. We propose a novel min-max-min-max formulation of the problem. We prove correctness of this formulation and leverage this new model to provide a solution method inspired from the K-adaptability approximation approach, whereby K candidate strategies are chosen here-and-now and the best of these strategies is selected after the portion of the uncertain parameters that was chosen to be observed is revealed. We reformulate the problem as an MILP solvable with off-the-shelf solvers and demonstrate its effectiveness on several stylized problems.

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: Two-Stage Robust Optimization with Decision-Dependent Information Discovery

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

type: Organization

cs: Video

de: Video

fi: Video

uk: Відео

en: Video

fr: Vidéo

da: Video

nl: Video

es: Video


uk: Математика, природничі науки

description: We consider the problem of multi-objective maximization of monotone submodular functions subject to cardinality constraint, often formulated as max|A|=kmini∈{1,…,m}fi(A). While it is widely known that greedy methods work well for a single objective, the problem becomes much harder with multiple objectives. In fact, Krause et al.\ (2008) showed that when the number of objectives m grows as the cardinality k i.e., m=Ω(k), the problem is inapproximable (unless P=NP). We focus on the case where the number of objectives is super-constant yet much smaller than the cardinality of the chosen set. We propose the first constant factor algorithms for this regime, including one with the best achievable asymptotic guarantee and also a more practical nearly linear time algorithm. Experiments on synthetic data show that a heuristic based on our more practical and fast algorithm outperforms existing heuristics.

uk: вхід без авторизації

name: Multi-objective Maximization of Monotone Submodular Functions with Cardinality Constraint


uk: Математика, природничі науки

description: This work presents a systematic study of the preservation of supermodularity under parametric optimization, that allows us to derive complementarity among parameters and monotone structural properties of optimal policies in many operations models. We introduce new concepts of mostly-lattice and additive mostly-lattice, which significantly generalize the commonly imposed lattice condition, and use them to establish the necessary and sufficient conditions on the feasible set so that supermodularity can be preserved under various assumptions on the objective functions. We further identify some classes of polyhedral sets which satisfy these concepts. Finally, we illustrate how our results can be used on a two-stage optimization problem.

uk: вхід без авторизації

name: Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures


uk: Математика, природничі науки

description: Markov decision processes (MDPs) are a common approach to model dynamic optimization problems in many applications. However, in most real world problems, the model parameters that are estimated from noisy observations are uncertain, and the optimal policy for the nominal parameter values might be highly sensitive to even small perturbations in the parameters leading to significantly suboptimal outcomes. We consider a robust approach where the uncertainty in probability transitions is modeled as an adversarial selection from an uncertainty set. Most prior work considers the case where uncertainty on parameters related to different states is unrelated and the adversary is allowed to select worst possible realization for each state unrelated to others, potentially leading to highly conservative solutions. On the other hand, the case of general uncertainty sets is known to be intractable. We consider a factor model for probability transitions where the transition probability is a linear function of a factor matrix that is uncertain and belongs to a factor matrix uncertainty set. This a significantly less conservative approach to modeling uncertainty in probability transitions while allowing to model dependence between probability transitions across different states. We show that under a certain rectangularity assumption, we can efficiently compute the optimal robust policy under the factor matrix uncertainty model. We also present a computational study to demonstrate the usefulness of our approach.

uk: вхід без авторизації

name: Robust Markov Decision Processes: Beyond (and back to) Rectangularity


Harmonia

keywords:
Climate change
AI
Earth Observations
Open Data
decision-making
Horizon-2020

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: HARMONIA will provide a resilience assessment platform to help urban stakeholders understand and quantify Climate Change effects. Based on satellite and auxiliary data, the HARMONIA platform will offer a user-friendly knowledge base, dispensing detailed information on a local neighbourhood and street level. This will support local decision-making and foster a wide range of applications dedicated to climate adaptation and mitigation, such as Carbon Capture and Storage technologies. At the workshop hosted by the Open-Earth-Monitor project during the EuroGEO 2022, Anastasios Temenos from the National Technical University of Athens, presented this H2020-funded project.

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Бібліотекознавство, документознавство

en: Information and Library Sciences

de: Geisteswissenschaften

uk: Гуманітарні науки

en: Humanities

@language: uk

uk: вхід без авторизації

name: Open access, open science, open data: how it was and where we are going (to the 20th anniversary of the Budapest open access declaration)

name: State Scientific and Technical Library of Ukraine

addressCountry: UA

addressLocality: Kyiv

addressRegion: Kyiv City


uk: Комп'ютерні науки

uk: Бібліотекознавство, документознавство

uk: Гуманітарні науки

uk: вхід без авторизації

name: National Repository of Academic Texts in the System of Open Science: Current State and Future Development


uk: Комп'ютерні науки

uk: Бібліотекознавство, документознавство

uk: Гуманітарні науки

uk: вхід без авторизації

name: Developing the open science infrastructure: a supercomputing platform for large matrix computing


de: Physik, Astronomie

fi: fysiikka, tähtitiede

uk: Фізика, Астрономія

en: Physics, Astronomy

fr: Physique, Astronomie

da: Fysik, Astronomi

es: Física, Astronomía

nl: Natuurkunde, Astronomie

uk: Бібліотекознавство, документознавство

uk: Математика, природничі науки

uk: Гуманітарні науки

uk: вхід без авторизації

name: Open Science in universities: European experience and prospects for Ukraine


uk: Комп'ютерні науки

uk: Бібліотекознавство, документознавство

uk: Гуманітарні науки

uk: вхід без авторизації

name: Key trends in Research Institutions Evaluation


de: Wirtschaftswissenschaften

uk: Бізнес та економіка

en: Business and Economics

uk: Бібліотекознавство, документознавство

de: Rechts-, Wirtschafts- und Sozialwissenschaften

uk: Право, економіка та суспільні науки

en: Law, Economics and Social Sciences

uk: Гуманітарні науки

uk: вхід без авторизації

name: Funding Open Science with new crowdfunding methodologies: new perspectives and challenges in an uncertain era


Meet up DeepTechAccelerator

uk: Фізика, Астрономія

uk: Комп'ютерні науки

uk: Бібліотекознавство, документознавство

uk: Математика, природничі науки

uk: Гуманітарні науки

uk: вхід без авторизації


uk: Фізика, Астрономія

uk: Комп'ютерні науки

uk: Бібліотекознавство, документознавство

uk: Математика, природничі науки

uk: Гуманітарні науки

uk: вхід без авторизації

name: Transdisciplinary clusters of narratives of scientific and scientific and technical production


uk: Комп'ютерні науки

uk: Фізика, Астрономія

uk: Бібліотекознавство, документознавство

uk: Математика, природничі науки

uk: Гуманітарні науки

uk: вхід без авторизації

name: Open Science in Europe: two specific examples


de: Architektur, Innenarchitektur

uk: Архітектура, дизайн інтер'єру

en: Architecture, Interior Architecture

uk: Бібліотекознавство, документознавство

uk: Гуманітарні науки

uk: вхід без авторизації

name: Empovering cultural heritage and research assets value


Delta PCC over 3 years - UP component

de: Geowissenschaften (ohne Geographie)

uk: Науки про Землю(крім географії)

en: Geosciences (excl. Geography)

uk: Математика, природничі науки

uk: вхід без авторизації

Leibniz Universität Hannover (LUH)

addressCountry: DE

addressLocality: Hanover

addressRegion: Lower Saxony


uk: Математика, природничі науки

description: We will talk about convergence rates for the empirical spectral measure of a unitary Brownian motion. We give explicit bounds on the 1-Wasserstein distance of this measure to both the ensemble-averaged spectral measure and to the large-N limiting measure identified by Biane. We are then able to use these bounds to control the rate of convergence of paths of the measures on compact time intervals. The proofs use tools developed by the first author to study convergence rates of the classical random matrix ensembles, as well as recent estimates for the convergence of the moments of the ensemble-average spectral distribution.

uk: вхід без авторизації

name: Convergence rates for paths of the empirical spectral distribution of unitary Brownian motion


uk: Математика, природничі науки

uk: вхід без авторизації

name: Brownian Motion and Hamilton´s Gradient Estimate


Heat content on the Heisenberg group

uk: Математика, природничі науки

description: In this talk we study small time asymptotic of the heat content for a smoothly bounded domain with non-characteristic boundary in the Heisenberg group, which captures geometric information of the of the boundary including perimeter and the total horizontal mean curvature of the boundary of the domain. We use probabilistic method by studying the escaping probability of the horizon- tal Brownian motion process that is canonically associated to the sub-Riemannian structure of the Heisenberg group. This is a joint work with J. Tyson.

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Geometric and Stochastic Analysis on Totally Geodesic Foliations under Ricci Flow


Global Existence of RDEs on Manifolds

uk: Математика, природничі науки

description: In this talk we will discuss a theorem guaranteeing the existence of global (in time) solutions to rough path differential equations on a smooth manifold.

uk: вхід без авторизації

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


uk: Математика, природничі науки

description: A general framework on Dirichlet spaces is developed to prove a weak form of the Bakry-Emery estimate and study its consequences. This estimate may be satisfied in situations, like metric graphs, where generalized notions of Ricci curvature lower bounds are not available. We also talk about current research directions by taking limits.

uk: вхід без авторизації

name: Differential one-forms on Dirichlet spaces and Bakry-Emery estimates on metric graphs


uk: Математика, природничі науки

description: I will talk about the dimension-free Lp boundedness of operators on manifolds obtained as conditional expectations of martingale transforms à la Gundy-Varopoulos. Applications on Lie groups of compact type and the Heisenberg group will be introduced.

uk: вхід без авторизації

name: Gundy-Varopoulos martingale transforms and their projection operators


uk: Математика, природничі науки

description: Generalized diamond fractals constitute a parametric family of spaces that arise as scaling limits of so-called diamond hierarchical lattices. The latter appear in the physics literature in the study of random polymers, Ising and Potts models among others. In the case of constant parameters, diamond fractals are self-similar sets. This property was exploited in earlier investigations by Hambly and Kumagai to study the corresponding diffusion process and its heat kernel. These questions are of interest in this setting in particular because the usual assumption of volume doubling is not satisfied. For general parameters, also the self-similarity is lost. Still, a diamond fractal can be regarded as an inverse limit of metric measure graphs and a canonical diffusion process obtained through a general procedure proposed by Barlow and Evans. This approach will allow us to provide a rather explicit expression of the associated heat kernel and deduce several of its properties. As an application, we will discuss some functional inequalities of interest.

uk: вхід без авторизації

name: Heat kernels and functional inequalities on generalized diamond fractals


uk: Математика, природничі науки

description: We study a "div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub- Riemannian manifold. We prove a short time asymptotic expansion of the heat trace up to any order. Our main result holds true for any smooth measure on the manifold, but it has a spectral geometric meaning when Popp's measure is considered. Our proof is probabilistic. In particular, we use S. Watanabe's distributional Malliavin calculus.

uk: вхід без авторизації

name: Heat trace asymptotics for equiregular sub-Riemannian manifolds


uk: Математика, природничі науки

uk: вхід без авторизації

name: Path Development and the Length Conjecture


uk: Математика, природничі науки

description: In this talk, we will consider high-dimensional Wishart matrices associated with a rectangular random matrix X_{n,d) whose entries are jointly Gaussian and correlated. Our main focus will be on the case where the rows of X_{n,d) are independent copies of a n-dimensional stationary centered Gaussian vector of correlation function s. When s is 4/3-integrable, we will show that a proper normalization of the corresponding Wishart matrix is close in Wasserstein distance to the corresponding Gaussian ensemble as long as d is much larger than n3, thus recovering the main finding of Bubeck et al. and extending it to a larger class of matrices.

uk: вхід без авторизації

name: Asymptotic Behavior of Large Gaussian Correlated Wishart Matrices


uk: Математика, природничі науки

description: In this talk, we use the techniques of fractional calculus and the fix-point theorem to show that a semilinear fractional differential equation driven by a gamma-Holder continuous noise, gamma>2/3, has a unique solution. The initial condition could be not defined at zero and the involve integral is in the Young sense.

uk: вхід без авторизації

name: Semilinear fractional differential equations driven by a fractional Brownian motion with H>2/3


uk: Математика, природничі науки

description: Hitting questions play a central role in the theory of Markov processes. For example, it is well known that Brownian motion hits points in one dimension, but not in higher dimensions. For a general Markov process, we can determine whether the process hits a given set in terms of potential theory. There has also been a huge amount of work on the related question of when a process has multiple points. For stochastic partial differential equations (SPDE), much less is known, but there has been a growing number of papers on the topic in recent years. Potential theory provides an answer in principle. But unfortunately, solutions to SPDE are infinite dimensional processes, and the potential theory is intractible. As usual, the critical case is the most difficult. We will give a brief survey of known results, followed by a discussion of an ongoing project with R. Dalang, Y. Xiao, and S. Tindel which promises to answer questions about hitting points and the existence of multiple points in the critical case.

uk: вхід без авторизації

name: Hitting questions and multiple points for stochastic PDE in the critical case


uk: Математика, природничі науки

description: In this talk, we examine the connection between the hyperbolic and parabolic Anderson models in arbitrary space dimension d, with constant initial condition, driven by a Gaussian noise which is white in time. We consider two spatial covariance structures: (i) the Fourier transform of the spectral measure of the noise is a non-negative locally-integrable function; (ii) d = 1 and the noise is a fractional Brownian motion in space with index 1/4 < H < 1/2. In both cases, we show that there is striking similarity between the Laplace transforms of the second moment of the solutions to these two models. Building on this connection and the recent powerful results of Huang, Le and Nualart (2017) for the parabolic model, we compute the second order (upper) Lyapunov exponent for the hyperbolic model. In case (i), when the spatial covariance of the noise is given by the Riesz kernel, we present a unified method for calculating the second order Lyapunov exponents for the two models.

uk: вхід без авторизації

name: Second order Lyapunov exponent for hyperbolic Anderson model


uk: Математика, природничі науки

uk: вхід без авторизації

name: Stochastic lattice models driven by fractional Brownian motion


uk: Математика, природничі науки

description: This talk is concerned with sample path regularities of isotropic Gaussian fields and the solution of the stochastic heat equation on the unit sphere S. In the first part, we establish the property of strong local nondeterminism of an isotropic spherical Gaussian field based on the high-frequency behavior of its angular power spectrum; we then apply this result to establish an exact uniform modulus of continuity for its sample paths. We also discuss the range of values of the spectral index for which the sample functions exhibit fractal or smooth behavior. In the second part, we consider the stochastic heat equation driven by an additive infinite dimensional fractional Brownian noise on S2 and establish the exact uniform moduli of continuity of the solution in the time and spatial variable, respectively. This talk is based on joint works with Xiaohong Lan and Domenico Marinucci.

uk: вхід без авторизації

name: Regularity Properties of Gaussian Random Fields and Stochastic Heat Equation on the Sphere


uk: Математика, природничі науки

description: In this talk, we study the stochastic heat equation on R^d driven by a multiplicative Gaussian noise which is white in time and colored in space. The diffusion coefficient rho can be degenerate, which includes the parabolic Anderson model rho(u)= u as a special case. The initial data is rough in the sense that it can be any measure, including the Dirac delta measure, that satisfies some mild integrability conditions. Under these degenerate conditions, for any given t>0 and distinct m points x_1, ... x_m in R^d, we establish the existence, regularity, and strict positivity of the joint density of the random vector (u(t,x_1), ...u(t,x_m)). The talk is based on a recent jointwork with Yaozhong Hu and David Nualart for the spatial dimension case, and an ongoing research project with Jingyu Huang for the higher spatial dimension case.

uk: вхід без авторизації

name: Density properties of the stochastic heat equations with degenerate conditions


keywords:
Glasbauteilprüfung
Bauteilprüfung
Friedrich-von-Siemens-Laboratorium
Glasbau
DIN 356

@language: de

uk: вхід без авторизації

name: Team des Friedrich-von-Siemens-Laboratorium (TU Dresden)

name: Kugelfallversuch (DIN 356): VSG mit unterschiedlichen PVB-Schichten

name: Institut für Baukonstruktion der TU Dresden


uk: Математика, природничі науки

description: Quadrature-based moment methods (QBMM) are employed to solve generalized population balance equations (GPBE) and are especially useful for poly-disperse multiphase flows. Starting from a closed GPBE, the unclosed moment equations are formulated and closed using QBMM. The accuracy of the closure is controlled by the order of the moments used in QBMM. For example, poly-disperse gas–particle flows can be described by a GPBE for the particle-phase mass-velocity number distribution function (NDF). In practice, the choice of the moments used in the closure is crucial. For particles with a continuous distribution of masses (e.g., same material with different diameters), the mean velocity and granular temperature of each size can be different. Thus, in addition to size moments, the velocity moments conditioned on size are needed to approximate the NDF. Here, the particle-phase model found from the GPBE with the Boltzmann–Enskog collision operator will be used to explain the methodology. Once the moment equations have been formulated, the numerical algorithms used to solve them must be consistent with the underlying GBPE. For example, the numerical methods employed to solve the spatial advection terms and the source terms must guarantee that the transported moments remain realizable (i.e., they must correspond to a NDF). This can be accomplished with kinetic-based, finite-volume methods. With QBMM, the NDF is represented by a finite set of weighted delta functions, corresponding to discrete velocities and sizes, that agree with the transported moments. Thus, it is often convenient to develop algorithms in terms of the quadrature variables in place of the moments. Employing applications from poly-disperse gas–particle flows, several examples of the numerical issues arising with QBMM will be discussed, along with some open issues related to the numerical algorithms.

uk: вхід без авторизації

name: Modeling polydisperse multiphase flows using quadrature-based moment methods


uk: Математика, природничі науки

description: Heavy inertial particles in spatially and temporally flows can form clusters if their relaxation time is in the order of the dissipation time scale of the flow. This regime, identified by St = O(1), is investigated in this study using analytical tools. We show that the nonlinear variation of segregation versus St can be explained by considering a one-dimensional canonical setting where particles are subjected to an oscillatory velocity gradient that is constant in space. Our analysis shows that the Lyapunov exponent, as a measure of particle segregation, reaches a minimum at St = O(1) and becomes positive at St >> 1 and approaches zero as St goes to 0 or infinity. These predictions, which are corroborated by the numerical results, are directly linked and compared against measurements of the dispersion and segregation in three-dimensional turbulence. Our analysis reveals a strongly nonlinear behavior of the Lyapunov exponents in the straining regimes of strong oscillations. This work was supported by the United States Department of Energy under the Predictive Science Academic Alliance Program 2 (PSAAP2) at Stanford University.

uk: вхід без авторизації

name: Particle clustering in multidimensional isotropic flows revisited from a new perspective

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


uk: Математика, природничі науки

description: Triboelectrification or tribocharging is a process by which two materials exchange electric charge upon mechanical contact and it has been observed in many industrial applications such as fluidised beds, pneumatic conveying systems and silo flows. In this study, we seek to shed light on dynamics of tribo-electrically charged particles in gas-solid flows through a combination of computational modelling and experiments. To study how tribocharging affects hydrodynamics of gas-solid flows, we have developed Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) augmented by a finite-volume based Poisson solver for electric field and a charge transfer model. In the charge model, the charging tendency of particles is captured by effective work function difference between the contacting surfaces and the electrical field at contact. In recent studies, we performed vibrated and fluidized bed experiments and measured average charge on polyethylene particles at different humidity conditions. We also performed CFD-DEM simulations of the same flow configurations and showed that the predicted charge values were in a good agreement with experimental data. As CFD-DEM simulations are limited to flow systems with a relatively small number of particles and there is a need to examine the interplay of flow and tribocharging in large-scale systems, we have also formulated a kinetic-theory based Euler-Euler model for monodisperse particles with tribocharging. To this end, we derived the mean charge transport equation from the Boltzmann equation allowing for conduction of mean charge through collisions in the presence of electric field, and boundary condition capturing tribocharging at the wall. These models were implemented in an open-source continuum physics software, OpenFOAM. Model predictions were then assessed through comparisons with hard-sphere Euler-Lagrange simulations and experimental studies.

uk: вхід без авторизації

name: Modelling of Gas-Solid Flows with Tribocharging


uk: Математика, природничі науки

description: Novel efficient numerical algorithms and large-scale super computers are enabling interface-resolved simulations of turbulent multiphase flows, giving access to details that improve our fundamental understanding and provide input for modelling efforts. In particular, we will first consider heat and mass transfer in particulate suspensions and perform direct numerical simulations to study the heat transfer within a suspension of neutrally buoyant, finite-size spherical particles in laminar and turbulent pipe flows, using the immersed boundary method (IBM) to account for the solid fluid interactions and a volume of fluid (VoF) method to resolve the temperature equation both inside and outside the particles. We examine particle volume fractions up to 40% for different pipe to particle diameter ratios. We report a considerable heat transfer enhancement (up to 330%) in the laminar regime by adding spherical particles, where larger particles are found to have a greater impact on the heat transfer enhancement than on the wall-drag increase. In the turbulent regime, however, only a transient increase in the heat transfer is observed and the heat flux decreases below the values in single-phase flows as high volume fractions of particles laminarize the core region of the pipe. A heat transfer enhancement, measured with respect to the single phase flow, is only achieved at volume fractions as low as 5% in a turbulent flow. Finally, we will consider emulsions in laminar and shear flows and examine the role of surfactants and short-range interaction forces on the rheology. As concerns the turbulent regime, we study homogeneous shear turbulence and report attenuation in the presence of a dispersed second phase. WE show how droplets break up and coalesce to reach a steady state number, with large size following the Hinze prediction.

uk: вхід без авторизації

name: Numerical simulations of rigid particles and droplets in turbulent shear flows


uk: Математика, природничі науки

description: Euler-Lagrange simulations of pointwise particles in turbulence have been widely employed for understanding the fundamental physics of dispersed flows. Most of the times, particles are modelled as isotropic and rigid. In this paper, we investigate the dynamics of elongated flexible particles in turbulent channel flow. We consider particles that are longer than the Kolmogorov length scale of the carrier flow, and their velocity relative to the surrounding fluid is non negligible. Such particles are modelled as chains of sub-Kolmogorov rigid rods connected through ball-and-socket joints that enable bending and twisting under the action of the local fluid velocity gradients. We examine the effect of local shear and turbulence anisotropy on the translational and rotational behaviour of the fibers, considering different elongation (parameterized by the aspect ratio) and inertia (parameterized by the Stokes number). Velocity, orientation and concentration statistics, extracted from one-way and two-way coupled direct numerical simulations, will be presented to give insights into the complex fiber-turbulence interactions that arise when non-sphericity and deformability add to inertial bias. The physical problem considered here provides a useful foundation for exploring the capability of the point-particle approach to capture the macroscopic features of multiphase flows of elongated deformable particles.

uk: вхід без авторизації

name: Point-particle Euler-Lagrange simulations of flexible fibers in turbulence


uk: Математика, природничі науки

description: Dispersed multiphase flows with deformable interfaces are frequently encountered in industrial processes involving large scale synthesis of base chemicals and energy carriers. In these flows complex processes, such as formation, coalescence and break-up of the dispersed elements (bubbles or drops), take place with accompanying physical and/or chemical transformations. These processes significantly influence the specific interfacial area, mixing of chemical species, mass and heat transfer rates as well as the large scale circulation patterns and ultimately the performance of multiphase chemical reactors. Due to the inherent complexity of these multiphase flows a multi-scale modeling approach is adopted in which the interactions between the phases can be properly accounted for. The idea is essentially that detailed models are used to generate closures for the interphase transfer coefficients to feed coarse-grained (such as stochastic Euler-Lagrange) models which can be used to compute the system behavior on a much larger (industrial) scale. In this contribution recent advances in the area of multi-scale simulation of dispersed multi-phase flows with deformable interfaces will be highlighted with emphasis on coupled mass, momentum and heat transfer. In addition, areas which need substantial further attention will be discussed.

uk: вхід без авторизації

name: Multi-scale simulation of mass, momentum and heat transfer in dispersed multiphase flows with deformable interfaces


uk: Математика, природничі науки

description: Over the last two decades, the focus of research in multiphase CFD has been on the development of advanced numerical methods, which leveraged the rapid increase in computing power. Even with the advent of exascale computing in the foreseeable future, detailed simulations of industrial-scale multiphase flows will remain out of reach for decades to come. Within many engineering processes, such as fluidized bed reactors, two-phase flow instabilities often lead to ‘demixing’ resulting in spatially non-uniform suspensions that obstruct chemical/thermal efficiencies, which current turbulence models fail to capture at large scales. As highly-resolved multiphase flow data continues to come online, new techniques are needed to integrate this information across scales. In addition, to aid in decision making, multiphase flow simulations have to be augmented to estimate underlying uncertainties in simulation components. In this talk, we will present a data-driven framework for model closure of the multiphase Reynolds Average Navier—Stokes (RANS) equations. Data generated from high-fidelity simulations are used in combination with state-of-the-art inverse modeling and machine learning techniques to (i) quantify model form uncertainty in existing models and (ii) infer the functional form of new turbulence models across a broad range of two-phase flow regimes.

uk: вхід без авторизації

name: Data-driven methods for multiphase turbulence modeling


uk: Математика, природничі науки

description: During the past two decades, the steady increase in the power of parallel super-computers participated heavily in developing 3D unsteady CFD modeling approaches. In these approaches, where the flow fluctuations are time and space resolved on a computational mesh, the cost of a simulation is directly linked to the size ratio between the largest and smallest resolved scales. Turbulent combustion and primary atomization modeling have both strongly benefited from this evolution as it enabled to increase the gas/liquid or burnt/unburnt gas interface resolution, the problem size and to include more physics. However, Direct Numerical Simulation (DNS) is still out-of-reach for most of practical configurations. Adaptive mesh refinement (AMR) is an appealing technique to reach DNS at a lower CPU cost. AMR has been originally designed for Cartesian grids and the major challenge for its use on distributed memory machines is its parallelization. The local mesh refinement indeed creates load imbalance that needs frequent repartitioning and balancing. The presentation will detail recent numerical developments on dynamic adaptation of tetrahedron-based unstructured grids. The use of tetrahedra has two advantages for practical configurations: complex geometries are easily meshed and the mesh is locally more isotropic than Cartesian grids. The proposed methodology relies on frequent sequential calls to a remeshing library (www.mmgtools.org), which adapt the mesh inside each MPI rank without modifying the interface shared with the other ranks. Then, repartitioning and transfer of cell groups is performed to ensure an optimal load balance and to modify the cells at the interface. All the underlying algorithms have been optimized to reach good performances with grids of several billion cells on more than 10'000 cores. This dynamic mesh adaptation strategy has been implemented in the YALES2 code (www.coria-cfd.fr) and applied to the modeling of premixed flames and primary atomization. In these applications, the local adaptation enabled to reduce drastically the CPU cost compared to the fixed grid approach and to reach unprecedented mesh resolutions at the interface.

uk: вхід без авторизації

name: Parallel dynamic mesh adaptation of unstructured grids: application to premixed flame and primary atomization modeling


PDE solvers on Octree grids

uk: Математика, природничі науки

description: Many problems in science and engineering demand that numerical methods be developed on adaptive grids in order to capture small scale details while minimizing computational resources. I will present recent (and less recent) results on the development and application of numerical methods on Octree Cartesian grids with an emphasis on free boundary problems.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In this talk we will present our current work on particles made cohesive through the existence of liquid bridges. We will present some rheological studies and some numerical simulations all aimed at elucidating the role that liquid bridges play on the “flowability” of particles. We also discuss the modelling efforts and how they could help bridge the gap between the particle and the equipment scale. Whilst we recognise that quasi-static and rapid flows rely on well established theories, the intermediate regime between those two limits is still not well understood. The models presented are aimed to elucidate the physics responsible for the bulk properties of powders flowing at the intermediate regime; the bulk properties strongly affect the performance of powders at the equipment scale. As an example, in slightly wet particles, the liquid bridges between particles reduce the inter-particle friction (lubrication) by switching the frictional contacts to fluid shear resistance. We use a shear cell apparatus to characterise powder stresses. The experimental results are compared with discrete element modelling simulation results. Finally, we use these results to propose coarse-grained models for large-scale applications.

uk: вхід без авторизації

name: Wet Particles Systems: from fundamentals to applications


uk: Математика, природничі науки

description: We study dilute gas-solid flows of cohesive grains in unbounded fluidization via CFD-DEM simulations, focusing on two types of heterogeneities: particle clusters of hydrodynamic origin and agglomerates of cohesive origin. Clusters refer to the regions of higher solid concentrations than surroundings, while agglomerates are particles held together by cohesive forces. Both heterogeneities have significant impacts on reaction rates, heat and mass transfer in multiphase flows. By tracking enduring contacts, we isolate agglomerates from the overall system heterogeneities quantified by local particle number density fluctuations. We found that with increasing system volume, the degree of clustering increases, while agglomeration decreases, contrary to the behavior of granular (no fluid) systems, where clustering enhances agglomeration due to the reduced relative velocities of particles in clusters. Based on statistical and theoretical analyses of particle velocities, higher levels of clustering in larger systems are shown to result in increased relative velocities between the gas and solid phases. This increased relative velocity between the phases serves as an added source of granular temperature, thereby enhancing deagglomeration. We coin this newly-identified mechanism as “cluster-induced deagglomeration” and demonstrate its robustness in systems with increasing cohesion, where saturating agglomeration level with increasing cohesion is observed, as opposed to the monotonic behavior in granular systems.

uk: вхід без авторизації

name: Cluster-induced deagglomeration in dilute gravity-driven gas-solid flows of cohesive particles with increasing domain size


uk: Математика, природничі науки

description: Numerical modeling of the phenomena in multiphase flows is today a necessary stage when developing or improving materials, technology as well as processes. Model development is based on the understanding of the basic physical phenomena. For this purpose, it is essential to simultaneously carry out numerical and experimental studies on some basic configurations to understand all the underlying phenomena. Direct Numerical Simulations is a powerful tool to understand basic physics and to interpret some experimental observations. Particularly with the advance of supercomputers nowadays, the limits of DNS are constantly extending. This presentation gives some examples of research projects that simultaneously include DNS and experimental study on e.g., gas-fluidization, bubbly flows and wet granulation. Potential of DNS to describe the physical phenomena in gas-liquid-nanoparticle three phase flows is briefly discussed as well.

uk: вхід без авторизації

name: Potential of DNS for the understanding of multiphase flows


uk: Математика, природничі науки

description: In this work, the fluid-solid heat transfer is studied by means of particle-resolved direct numerical simulations performed by using a Lagrangian VOF approach based on fictitious domain and penalty methods. The first non-isothermal test case studied in detail consists in a cold fluid flow across an array of hot particles at a given temperature. Particles are fixed and randomly arranged, and their volume fraction spans from 0.1 to 0.4 in order to cover the typical values encountered in fluid-particle dense flows. Three Reynolds numbers, with unity Prandtl number, are investigated. From the fully resolved fluid velocity and temperature fields, macroscopic quantities are obtained by means of spatial averages over the entire domain or over planes normal to the streamwise direction. These quantities are then used to investigate the gas-solid heat transfer at macroscopic scale with the goal to support two-fluid model development. At such macroscopic scale, the fluid energy equation makes appear a velocity-temperature correlation term which accounts for the microscopic heterogeneous distributions of both the fluid velocity and temperature due to the momentum and heat transfer with the solid particles. In this study, such a contribution is written in terms of a bulk-temperature tensor. In the presence of a unidirectional mean flow, this tensor reduces to the unique component representing the well-known bulk temperature, as classically defined. A connection between this contribution and the ratio of two Nusselt numbers based, respectively, on the fluid temperature and on the bulk temperature, is pointed out. These Nusselt numbers are computed and compared to the correlations available from the literature. Their ratio is also computed and compared to the literature. On the basis of such a ratio, a model for the fluctuating velocity-temperature contribution is proposed. In a second stage, particle-resolved numerical simulations were carried out for several configurations of non-isothermal liquid-solid fluidized beds with a limited number of particles (280, 520 and 1280) at a given temperature with the fluid flow injected at a uniform and constant cold temperature. Then, in this work, simulations results are mainly analyzed in terms of macroscopic variables. In particular, the measured fluid-particle heat transfer coefficient and fluid velocity- temperature spatial correlations are compared with the mathematical modeling approach derived for the fixed bed.

uk: вхід без авторизації

name: Particle-resolved numerical simulations of fluid-particle dense flows and macroscopic modeling of interphase heat transfer and fluid velocity-temperature spatial correlations


uk: Математика, природничі науки

description: Multiphase flows are central to many manufacturing and processing technologies, with applications spanning energy generation, material science and biomedical settings. Despite advancing computational resources, the complex dynamics of production processes are challenging to simulate, and the use of empirical correlations remains the norm. This talk will summarise recent efforts to develop predictive numerical tools that can be used as a basis for engineering design. In a multi-fidelity approach, we apply highly resolved hybrid front-tracking techniques to clarify fundamental flow features, and utilise low-cost simulation variants to address engineering design questions. We will share simulation results inspired by industrially relevant problems related to liquid–liquid displacements in pipe flows, mixing of miscible and immiscible fluids, two-phase flows with and without surfactants, and two- and three-phase microfluidics, amongst others. The simulation techniques presented can be coupled to novel surrogate models for exploiting advances in optimisation and machine learning, being the new frontier in multiphase fluid dynamics.

uk: вхід без авторизації

name: Tracking complexity in multiphase flow simulations


uk: Математика, природничі науки

description: I will present a new numerical scheme to model surface tension for an interface represented by a level-set function. In contrast with previous schemes, the method conserves fluid momentum and recovers Laplace’s equilibrium exactly. It is formally consistent and does not require the introduction of an arbitrary interface thickness, as is classically done when approximating surface-to-volume operators using Dirac functions. Variable surface tension is naturally taken into account by the scheme and accurate solutions are obtained for thermocapillary Marangoni flows.

uk: вхід без авторизації

name: A conservative and well-balanced surface tension model


uk: Математика, природничі науки

description: It has been a misconception that CFD of commercial fluidized and circulating fluidized beds is only in its infancy. Indeed, codes and computers are fast enough to now simulate large-scale unit operations in a reasonable amount of time (i.e., weeks). However, CFD has been used for over 20 years in the application with significant impact. Today, CFD is being used for a wide range of industrial applications and targeting complex problems in the industry such as NOx emissions, particle attrition, erosion, maldistribution of feed gases, debottlenecking, etc. Yet, a successful model stems from how well the modeler and stakeholders understand the fundamentals and the constitutive equations used for closing those fundamentals. A lack of this understanding has never changed in the last 20 years, and has resulted in the tarnishing of a valuable tool (CFD, DEM, DNS). In other words, the promise of higher order modeling is confounded by a myriad of mistakes including not understanding the underlining assumptions and the limitations they come with, oversimplifying boundary conditions, ignoring transient versus steady-state behavior, and not realizing the benefits of a poor fit. All of these issues have been the result of failed opportunities that should have been identified at the very least in retrospect. This presentation will focus on the some of the gaps that a modeler often misses or opportunities that were never capitalized.

uk: вхід без авторизації

name: CFD Modeling in the Petrochemical and Chemical Industry


uk: Математика, природничі науки

description: Between the late 1990s and the early 2000s a plethora of methods for the coupling between population balance models (PBM) and computational fluid dynamics (CFD) in the context of the Euler-Euler framework have been developed. Among them quadrature-based moment methods (QMOM, DQMOM, CQMOM, EQMOM) have been very successful. In the last years, due also to the availability of computational power, these methods have been extensively applied to the simulation of real industrial multiphase flows. This has shown the potentiality of the methods but also their limitations, mainly related to the lack of reliable physical and chemical models to describe the relevant phenomena involved under industrial conditions. Industrial conditions, in this context, mean dense systems (i.e. high concentration of the disperse phase) and complex chemical compositions. In this talk we will show what are the progresses made in the last five years to address these issues with a specific focus on coalescence and breakage kernels and interfacial force models. Examples taken from our recent work with commercial and open-source CFD codes will be discussed and critically analyzed with particular attention to energy applications: gas-liquid bioreactors under the heterogeneous regime, boiling flows, turbulent liquid-liquid emulsions, complex fluids in porous media and precipitation of materials of lithium batteries.

uk: вхід без авторизації

name: Simulation of polydisperse multiphase flows with CFD-PBM for energy applications: the challenge of industrial applications


uk: Математика, природничі науки

description: This talk aims at introducing our current understanding of the rheology of suspensions of non-Brownian particles in non-Newtonian fluids. These complex suspensions can be found in natural settings such as landslides, mudslides, and submarine avalanches as well as industrial applications such as in mining operations, chemical mechanical, conversion of biomass into fuel, the petroleum industry, etc. The main scientific challenge is to establish a continuum framework and refine it through microstructure investigations. Suspensions may vary on the particle scale from Stokesian behavior to inertial behavior depending on the flow configuration, the type of suspending fluids, etc. We present a tensorial continuum framework based on our recent computational and experimental works and discuss how this framework can be used to study the dispersion of solids in industrial processes and geophysical flows.

uk: вхід без авторизації

name: Suspensions of non-Brownian Particles in Complex Fluids


uk: Математика, природничі науки

description: Granular material subjected to agitation is encountered in many practical applications of material processing (e.g., cooling, heating, granulation, and clinkering). Furthermore, many of these applications also involve heat transfer whereby solids face cooling or heating surfaces, and heat is exchanged not only between individual particles, but also between the particles and external surfaces throughout the duration of the particle–particle or particle–surface contact. This work focuses on understanding the heat transfer mechanisms in a granular bed inside a rotary drum, which is one of the most commonly used process equipment. All modes of heat transfer are quantified under varying operating conditions to establish a strong understanding of the heat transport. For this, CFD-DEM (using MFIX-DEM, an open source multi-solver suite) simulation techniques are used to analyze the thermal behavior. The heat transfer coefficient of the particles is derived to validate the conduction heat transfer model implemented in MFIX-DEM, and the effects of various parameters are studied.

uk: вхід без авторизації

name: Modeling Granular Heat Transfer in a Rotary Drum


uk: Математика, природничі науки

description: This talk will present recent work investigating the use of elasto-plastic continuum models for predicting the flow behavior of particulate materials. Several constitutive relations have been implemented in a commercial finite element method (FEM) software package to predict flow and stress fields in hoppers and tumbling blenders. The stress and velocity fields and mass flow rates match well with other widely accepted models and correlations. Particle mixing and segregation are incorporated by coupling the FEM-predicted continuum flow field with an advection-diffusion-segregation equation, which includes correlations derived from experiments and discrete element method simulations. The blending and segregation results match experimental results well. These models hold the promise of modeling particulate flows at industrial scales.

uk: вхід без авторизації

name: Continuum Modeling of Powder Flow, Blending, and Segregation

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


uk: Математика, природничі науки

description: Gasoline direct injection (GDI), because it improves fuel economy, has seen rapid adoption, despite large emissions of harmful nanoparticles. To overcome this shortcoming, Selective Catalytic Reduction Filters (SCRF), a combination of a Selective Catalytic Reduction system (SCR) and a Particulate Filter (PF) meant to reduce both NOx gas and Particulate Matters (PM), have also attracted OEMs’ interest due to lower cost and volume than existing engine exhaust after-treatment systems. Practically speaking, integrating the two technologies consists in depositing a layer of a catalytic washcoat into the PF, but this usually affects negatively the PM capture and back-pressure in the filter. Seeking a possible synergistic effect such that an optimum balance between catalyst effectiveness, PM capture, back-pressure and cost is found is of prime interest. To predict how the washcoat deposition profile can affect the SCRF performance, a four-step numerical model was developed. It consists of: (1) the numerical reconstruction of a representative volume of the porous wall with various washcoat distributions and coat weights based on X-ray computed tomography (CT) data, the computation of both (2) the pressure drop and (3) the NOx catalytic reduction effectiveness through the coated porous wall by solving, using the Lattice Boltzmann Method (LBM), a coupled problem involving the Navier-Stokes equations and an advection-diffusion-reaction equation, and (4) the prediction of the PF filtering performance by means of the solution of a Langevin problem.

uk: вхід без авторизації

name: Optimizing the Performance of Engine Exhaust After-treatment System using Numerical Simulation


uk: Математика, природничі науки

description: The Eulerian-Lagrangian point-particle method has become a leading paradigm in the study of dispersed particle-laden flows. This strategy simultaneously represents the non-continuum physics of the dispersed phase coupled to the continuum physics of the carrier fluid. However, while verifiable strategies for one-way coupled particles have been available for decades, it has not been until recently that verifiable strategies have been developed for two-way coupled flows. The purpose of this talk is to present some of the current state of understanding with regard to verifiable simulation of two-way coupled particle-laden flows. One key idea centers around the notion of undisturbed fluid properties evaluated at the location of each particle. In dilute regimes, we will show that removal of the self-disturbance portion of the flow computed in point-particle simulations is necessary for accurate comparison with particle-resolved simulation. In denser regimes, theory and simulations reveal that particle-particle screening cannot be ignored. We may also draw upon the Squires jet as a means for forming reasonable expectations about point- particle simulations. Time permitting, we will also discuss two-way coupled heat transfer in the context of point-particle simulations.

uk: вхід без авторизації

name: New developments in point-particle simulation: insights from particle-resolved simulations and theory


uk: Математика, природничі науки

description: Fluidized-bed reactors (FBR) are found in a large variety of industrial processes ranging from coal gasification to water treatment. In reactive FBR processes, gas-solid mixing and interactions can be enhanced as well as the chemical reaction rate. These properties are particularly interesting to achieve low-temperature combustion with high conversion efficiency and low pollutant emissions such as nitrogen oxides. The objective of this study is to achieve simulations of a FBR at mesoscopic scale using a coupled CFD/DEM (Discrete Element Method) approach in order to gain insight into the physics of such processes and to extract information to be used in the modeling at macroscopic scale. The chosen configuration is a semi-industrial FBR fed with a mixture of natural gas and air containing 200M sand beads. Experimental data show a shift in the combustion regime above a critical temperature of 800°C. Large-Eddy Simulations (LES) are performed using the finite-volume code YALES2, a low-Mach number solver based on unstructured meshes. Its DEM solver has been designed to perform simulations in arbitrarily complex geometries and optimized for massively parallel computing: it features a dynamic collision detection grid for unstructured meshes, packing/unpacking of the halo data for non-blocking MPI exchanges and a dynamic load balancing algorithm.

uk: вхід без авторизації

name: Simulation of a reactive fluidized bed reactor using coupled CFD/DEM


uk: Математика, природничі науки

description: Using a direct-forcing immersed boundary method (IBM) at fully resolved grid resolutions, we study the interaction between the fluid in the lid-driven cavity and ensuing response of a collection of identical cylindrical particles immersed in the cavity. The particles are fixed in lattice location but are free to rotate, and reach steady-state angular velocities under low to moderate Reynolds numbers. The goal is to find the effect of different lattice configurations on the dynamical response of the cylinders – particularly the angular velocities that develop spontaneously and the forces exerted on each of them by the fluid motion. Two lattices, one triangular and one rectangular, are considered. The two configurations exhibit quite different responses. The rectangular lattice contains two kinds of flow paths, an axis-aligned primary path, and a secondary path in the diagonal direction. This gives it a rich response to the fluid forcing as Reynolds number is increased. The triangular lattice only has one kind of flow path and behaves in a more consistent manner. By increasing the cylinder radius, the secondary path in the rectangular lattice can be eliminated. This qualitatively alters its nature and response to the fluid forcing, and could be considered as a phase transition.

uk: вхід без авторизації

name: Understanding fluid-particle interaction in structured environments by Direct Numerical Simulation


Geographies of Globalization

keywords:
Institut für Geographie
Universität Osnabrück
Globalization
Economic Geography
Germany
Turkey

uk: Науки про Землю(крім географії)

uk: Право, економіка та суспільні науки

uk: Математика, природничі науки

description: In this video, an introduction to geographical globalization research is given. Globalization processes are illustrated using Germany and Turkey as examples.

uk: вхід без авторизації


From one to two parameters

uk: Математика, природничі науки

description: It is widely known that persistent homology in more than one parameter is significantly more "complicated" than in the single-parameter setting. In this talk I will discuss in what sense it is more complicated from the point of view of representation theory, and from the point of view of algorithms. I will also give examples of how multi-parameter persistence modules naturally appear in applications.

uk: вхід без авторизації


uk: Математика, природничі науки

description: I will discuss how topological summaries can be used to model various shapes as well as other high-dimensional data. I will talk about geometric and statistical properties of the space of summaries and how these summaries are the result of various filtrations. I will then discuss why multi-parameter persistence would be a very nice tool for these problems. The first half of the talk will be a review and I will focus on some of my research in the second half.

uk: вхід без авторизації

name: Topological Summaries and Sufficient Statistics


uk: Математика, природничі науки

description: The usual definition of minimal primary decomposition in commutative algebra grants a little too much leeway. Making minimality work for real multiparameter persistence modules -- that is, multigraded modules over rings of polynomials with real exponents -- requires tighter control over what algebraists call socles and computational topologists call deaths. Functorial definitions yield finiteness statements for primary decompositions of reasonable persistence modules. In contrast, for irreducible decompositions finiteness is impossible with continuous parameters; but nonetheless minimality can be characterized by density with respect to certain topologies arising in the context of partially ordered vector spaces.

uk: вхід без авторизації

name: What makes primary decomposition minimal?


uk: Математика, природничі науки

description: Theoretical methods in persistent homology have traditionally considered one of two viewpoints: R-indexed/sub-level set persistence, or zig-zag/level-set persistence. Even in the case of a single variable real-valued function, there is still much to be understood by combining these two forms of persistence together. This version of multiparameter persistence naturally lends itself to analysis of families of functions on smooth manifolds, as well as generalized versions of Reeb graphs and Merge trees. In this talk, I will show what we hope to learn by mixing these two together through a variety of examples, ranging from manifolds to Arnold's Calculus of Snakes.

uk: вхід без авторизації

name: Combining sub-level and level-set persistence


Perspectives on Categorical Persistence

uk: Математика, природничі науки

description: Peter Bubenik and Jonathan Scott, in 2012, made the perspicuous suggestion that any functor, from a suitable source category into any target category, could be regarded as a "generalised persistence module" (GPM), and that categories of GPM carried natural distance functions called interleaving metrics. I will discuss several examples and constructions on GPM. These include Reeb graphs, merge trees, dynamical systems, Morse functions. I will also discuss a recently joint project, led by Anastasios Stefanou and Liz Munch, which extends the interleaving distance from GPM categories to, more generally, categories with a flow.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Discovering a new drug costs more than a billion dollars and takes ten years or more. So researchers are always looking for new ways to use computers to find more promising candidate drugs. We present a promising new system that applies the two-parameter persistent homology to the complex task of finding good drug candidates, by finding similarities in the 3D shapes of the molecules.

uk: вхід без авторизації

name: The shape of medicines to come: Two-parameter persistence for virtual ligand screening


uk: Математика, природничі науки

description: Computation of the interleaving distance between persistence modules is a central task in topological data analysis. For 1-D persistence modules, thanks to the isometry theorem, this can be done by computing the bottleneck distance with known efficient algorithms. The question is open for most n-D persistence modules, n>1, because of the well recognized complications of the indecomposables. Here, we consider a reasonably complicated class called {\em 2-D interval decomposable} modules whose indecomposables may have a description of non-constant complexity. We present a polynomial time algorithm to compute the interleaving distance between two such indecomposables. This leads to a polynomial time algorithm for computing the bottleneck distance between two 2-D interval decomposable modules, which bounds their interleaving distance from above. We give another algorithm to compute a new distance called {\em dimension distance} that bounds it from below.

uk: вхід без авторизації

name: Computing Interleaving and Bottleneck Distance for 2-D Interval Decomposable Modules


Clustering from (co)torsion pairs

uk: Математика, природничі науки

description: In joint work with Ulrich Bauer, Magnus Botnan and Steffen Oppermann, we construct equivalences relating certain subcategories of abelian categories. (These arise as components in so-called torsion and cotorsion pairs.) I will explain how this construction works, and with this as a fairly general starting point, we will see how this can be specialized to 2-parameter clustering. For the last part, I will give examples to show that the finiteness of representation type is sensitive to the orientation of the underlying quivers.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In persistence theory and practice, measuring distances between modules is central. The Wasserstein distances are the standard family of Lp distances (with 1≤p≤∞) for persistence modules. We give an algebraic formulation of these distances. For p=1 it generalizes to abelian categories and for arbitrary p it generalizes to Krull-Schmidt categories. These distances may be useful for the computation of distance between generalized persistence modules.

uk: вхід без авторизації

name: Wasserstein distance for generalized persistence modules and abelian categories


uk: Математика, природничі науки

description: I will discuss the efficient computation of the Vietoris–Rips persistence barcode for a finite metric space. The implementation in the C++ code „Ripser“ focuses on memory and time efficiency, outperforming previous software on typical benchmark examples both in terms of time and memory. The improved computational efficiency is based on a close connection between persistent homology and discrete Morse theory, together with novel algorithmic design principles, avoiding the explicit construction of the filtration boundary matrix.

uk: вхід без авторизації

name: Multi starts at one: Efficient computation of Vietoris–Rips persistence barcodes


uk: Математика, природничі науки

description: Topological Data Analysis is a relatively new paradigm in data-science that models datasets as point-clouds sampled from a shape embedded in an Euclidean space. The inference problem is to estimate the essential topological features of the underlying shape from a point-cloud sampled from it. This is done through a technique called persistent homology which is a mathematical formalism based on algebraic topology. A necessary step in the persistent homology pipeline is the reduction a so-called boundary matrix, which is a process reminiscent to Gaussian elimination. In this talk, I present a number of structural dependencies in boundary matrices and use them to design a novel parallel algorithm for their reduction, which is especially fit for GPUs. Simulations on synthetic examples show that the computational burden can be conducted in a small fraction of the number of iterations needed by traditional methods. For example, numerical experiments show that for a boundary matrix with 10^4 columns, the reduction completed to within 1% in about ten iterations as opposed to nearly approximately eight thousand iterations for traditional methods.

uk: вхід без авторизації

name: Parallel reduction of boundary matrices in Persistent Homology


The Utility of Sheaves in Persistence

uk: Математика, природничі науки

description: In this talk I'll review some of the basic concepts of sheaf theory as it is relevant to persistence in one or more parameters. One of the themes that will be emphasized is how the same formalism can be used and simply by changing the underlying topology many different constructs in TDA can be obtained: multi-filtered homology (Alexandrov/gamma topology), level set persistence and Reeb spaces (Euclidean topology), the persistent homology transform and vineyards (mixture of Alexandrov and Euclidean topologies). Additionally, I'll describe how sheaves can be used to organize various counting problems associated to persistence.

uk: вхід без авторизації


Kunneth formuale in persistent homology

uk: Математика, природничі науки

description: The classical Kunneth formula in homological algebra provides a link between the homology of a product space and that of its factors. We will show in this talk a collection of similar results for persistent homology. That is, we show how the persistent homology of a filtered product space --- different product filtrations lead to different formulae --- can be recovered from that of its filtered factors.

uk: вхід без авторизації


uk: Математика, природничі науки

description: A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter family of spaces obtained from the data. In applications data often depend on several parameters, and in this case one is interested in studying the persistent homology of a multiparameter family of spaces associated to the data. While the theory of persistent homology for one-parameter families is well-understood, the situation for multiparameter families is more delicate. Following Carlsson and Zomorodian we recast the problem in the setting of multigraded algebra, and we propose multigraded Hilbert series, multigraded associated primes and local cohomology as invariants for studying multiparameter persistent homology. Multigraded associated primes provide a stratification of the region where a multigraded module does not vanish, while multigraded Hilbert series and local cohomology give a measure of the size of components of the module supported on different strata. These invariants generalize in a suitable sense the invariant for the one-parameter case.

uk: вхід без авторизації

name: Stratifying Multiparameter persistent homology


uk: Математика, природничі науки

description: Our primary motivation for persistent homology is in its applications to shape similarity measures. Multidimensional or multiparameter persistence comes into play in that context when two objects are to be simultaneously compared according to several features. The ideas go back to early 1900s when Pareto’s optimal points of multiple functions were studied with applications to economy on mind. In our previous work, we developed an algorithm that produces an acyclic partial matching (A, B, C) on the cells of a given simplicial complex, in the way that it is compatible with a vector-valued function given on its vertices. This implies the construction can be used to build a reduced filtered complex with the same multidimensional persistent homology as of the original one filtered by the sublevel sets of the function. Until now, any simplex added to C by our algorithm has been defined as critical. It was legitimate to do so, because an application- driven extension of Forman’s discrete Morse theory to multi-parameter functions has not been carried out yet. In particular, no definition of a general combinatorial critical cell has been given in this context. We now propose new definitions of a multidimensional discrete Morse function (for short, mdm function), of its gradient field, its regular and critical cells. We next show that the function f used as input for our algorithm gives rise to an mdm function g with the same order of sublevel sets and the same partial matching as the one produced by our algorithm.

uk: вхід без авторизації

name: Multidimensional Discrete Morse Function for Persistent Homology Computation


A Kernel for Multiparameter Persistence

uk: Математика, природничі науки

description: Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques, We contribute a kernel construction for multiparameter persistence by integrating a one-parameter kernel along straight lines. We prove a stability result for our construction and show that our kernel can be approximated in polynomial time to any absolute precision.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The interleaving distance for persistence modules, originally defined by Chazal et al., is arguably the most powerful, generalizable mathematical idea to come out of TDA in the last decade. The categorification of persistence modules and the related interleaving distance provided a plug-and-play system to create new metrics for functors with a poset category domain. In this talk, we will generalize this work even further to give a definition of the interleaving distance for a category with a flow; that is, a category C with a functor S:R≥0→End(C) which satisfies certain compatibility conditions. From this framework, we can see that many commonly used metrics, such as the Hausdorff distance on sets and the ℓ∞ distance on \Rn are all examples of interleaving distances. The categorical viewpoint gives an immediate construction for a host of stability theorems. Further, a new construction on elements of a category with a flow called a hom-tree provides a lower bound for the interleaving distance.

uk: вхід без авторизації

name: Interleavings for categories with a flow and the hom-tree lower bound


uk: Математика, природничі науки

description: The Gromov-Haudorff distance is a common way to measure the distortion between two metric spaces. Given two tree metric spaces (metric trees), it provides a natural distance for them. The merge tree is a simple yet meaningful (topological) summary of a scalar function defined on a domain. There are various ways to define the distance between merge trees, including the so-called interleaving distance between trees. In this talk, I will present an interesting relationship between the Gromov-Hausdorff distance and the interleaving distance. I will then show that these distances are NP-hard to approximate within a certain constant factor. But I will also present a fix-parameter-tractable (FPT) algorithm to compute the interleaving distance. Due to the relation between Gromov-Hausdorff distance and interleaving distances, this also lead to a FPT approximate algorithm for the Gromov-Hausdorff distance between general metric trees.

uk: вхід без авторизації

name: Gromov-Hausdorff and Interleaving distance for trees


uk: Математика, природничі науки

description: Completeness, separability, and characterization of the precompact subsets are important for doing probability and statistics on a metric space, using tools like Prokhorov's Theorem. Recently in applied topology, a common type of (pseudo/quasi)metric space is an interleaving distance on a category. We relate the metric limit of a Cauchy sequence in such a space to the categorical limit of a corresponding diagram. Using this, we show that many familiar examples in the applied topology literature are metrically complete. We also study separability and precompactness for some familiar examples. Finally, we show how this new understanding can be used to prove results about probability and statistics on these spaces.

uk: вхід без авторизації

name: Classical Metric Properties for Categories with the Interleaving Distance

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


uk: Математика, природничі науки

description: We propose a new link between quantum invariants of 3-manifolds and the geometry of wild Hitchin moduli spaces. The construction goes through a class of four-dimensional quantum field theories known as Argyres-Douglas theories. Every such theory realizes a wild Hitchin space as its Coulomb branch and defines a VOA on the Higgs branch. The latter can be used to construct a non-unitary modular tensor category, which leads to 3d TQFTs that are generically semisimple but non-unitary. This is based on joint work with Mykola Dedushenko, Sergei Gukov, Hiraku Nakajima and Ke Ye.

uk: вхід без авторизації

name: Modular tensor categories from wild Higgs bundles


4d/2d duality and class S theory

uk: Математика, природничі науки

description: Rastelli et. al have constructed a map from 4d N=2 SCFTs to VOAs in such a way that the Schur index of a 4d N=2 SCFT coincides with the character of the corresponding VOA. Later, Rastelli and Beem have further conjectured that the Higgs branch of a 4d N=2 SCFT should coincide with the associated variety of the corresponding VOA. In my talk we confirm the conjecture of Rastelli and Beem for the theory of class S.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Many properties of an algebraic variety X can be expressed in terms of the derived category of coherent sheaves on X (or its differential-graded enhancement). Kontsevich proposed to view arbitrary smooth and proper dg-categories as non-commutative analogs of smooth projective varieties. I will show how holomorphic functions with isolated singularities fit into this picture. In the first part of the lecture we will talk about Chern characters and the Hirzebruch-Riemann-Roch theorem for dg-categories and will see how classical invariants of singularities appear via dg-categories of matrix factorizations. Then we will turn to quantum invariants and cohomological field theories - an algebraic structure underpinning formal properties of the Gromov-Witten invariants. For a quasi-homogeneous singularity W and a finite group G of its symmetries we will describe a CohFT whose state space is the equivariant local algebra (Milnor ring) of W and whose correlators can be viewed as analogs of Gromov-Witten invariants for the non-commutative space associated with the pair (W,G). The role of the virtual fundamental class from the Gromov-Witten theory is played here by a "fundamental matrix factorization" over a certain moduli space.

uk: вхід без авторизації

name: Cohomological field theories, Chern characters and matrix factorizations (introductory lecture)


uk: Математика, природничі науки

description: In this talk, we will review a proposal by B. Eynard and my self to solve W-symmetric Ward identities on the sphere at generic values of the background charge. It will consist in the introduction of a hierarchy of so-called generalized Ward identities, their solution in topological regimes by topological recursion for quantum spectral curves and eventually obtaining the conformal blocks by integrating special geometry relations. This can also be interpreted as a computation in refined topological string theory where the refinement parameter is identified with the background charge.

uk: вхід без авторизації

name: Generalized Ward identities and refined topological expansion of Toda conformal blocks


uk: Математика, природничі науки

description: To any vertex algebra, one can attach in a canonical way a certain Poisson variety, called the associated variety. When the associated variety has only finitely many symplectic leaves, the vertex algebra is called quasi-lisse. In this talk, I will give various examples of quasi-lisse vertex algebras. Using the notion of chiral symplectic leaves, one can show that any quasi-lisse vertex algebras is a quantization of the arc space of its associated variety. If time allows, I will also give an application to the arc space of Slodowy slices and W-algebras.

uk: вхід без авторизації

name: Chiral symplectic leaves and quasi-lisse vertex algebras


uk: Математика, природничі науки

description: Among the invariants that have a double life in geometry and in conformal field theory, there are the Euler characteristic and its refinements to complex elliptic genera. We argue that superconformal field theory motivates further refinements, resulting in a choice of several new invariants, the so-called Hodge-elliptic genera. At least for K3 surfaces and K3 theories, higher algebra and conformal field theory select the same refinement as the most natural one, allowing insights into generic features of K3 theories.

uk: вхід без авторизації

name: Hodge elliptic genera in geometry and in CFT


uk: Математика, природничі науки

description: By definition, the endomorphism spaces of tensor powers of objects of a braided tensor category carries a representation of the braid group. For Lie types A and C, this can be used to classify all braided tensor categories whose fusion ring is the one of the representation category of the related Lie algebra. We also discuss the situation for other classical Lie types and some exceptional types. There are several different ways how to construct TQFTs and modular functors. One of the motivations for these categorical questions was to decide when these constructions yield the same results.

uk: вхід без авторизації

name: Classification of certain braided tensor categories


uk: Математика, природничі науки

description: In the past ten years, an inductive procedure called topological recursion proved to provide a very efficient way of solving many problems of enumerative geometry through the computation of intersection of tautological classes over the Deligne-Mumford compactification of the moduli space of Riemann surfaces. In order to understand the mysterious geometric origin of this procedure, we developed a new inductive procedure called geometric recursion together with Andersen and Borot. This geometric recursion is a machinery defining all sorts of mapping class group invariant objects attached to surfaces. In this lecture, I will first review the original topological recursion formalism together with its application to the study of Cohomological Field Theories before presenting the formalism of geometric recursion. I will finally present some examples of application including some generalisation of Mirzakhani-McShane identities and the computation of some closed forms on Teichmuller space.

uk: вхід без авторизації

name: Geometric recursion (introductory lecture)


uk: Математика, природничі науки

description: In this talk I will survey some results on and techniques to study actions of (finite-dimensional) Hopf algebras on noncommutative algebras. Many examples will be provided and the categorical context for such results will be emphasized.

uk: вхід без авторизації

name: Quantum Symmetry in the context of Hopf algebra actions on noncommutative algebras


uk: Математика, природничі науки

description: In this introductory lecture I would like to discuss vertex operator algebras which allow for non-semisimple representations. There will be two parts, which will roughly relate to genus 0 and genus 1 properties. In the first part I will try to motivate why one might want to look at such VOAs and give the basic example, symplectic fermions. We will briefly look at VOA modules and intertwiners to get an idea of how the category of VOA modules can become a braided monoidal category. For the second part we look at certain traces over VOA modules and modular properties of conformal blocks on the torus. These have an intriguing relation to tensor product multiplicities, known as the Verlinde formula, which is a theorem for finitely semisimple theories and a conjecture without the semisimplicity assumption.

uk: вхід без авторизації

name: Logarithmic vertex operator algebras (introductory lecture)


uk: Математика, природничі науки

description: Unitary vertex operator algebras and conformal nets are mathematical axiomatizations of roughly the same physical idea: a two-dimensional unitary chiral conformal field theory. From a mathematical perspective, the axiomatizations are quite different in nature, and physical ideas which have been rigorously proven in one framework sometimes remain quite difficult in the other. In this talk I will explain a positivity conjecture for unitary VOAs which arose in the course of ongoing work to compare the theory of tensor products (i.e. fusion of sectors) as it appears in both settings. The conjecture is not limited to rational VOAs, and it suggests a general construction of unitary tensor products of modules. As time allows, I will present ongoing work to relate the representation theory of conformal nets and VOAs, as well as work in progress to establish the positivity conjecture in a broad class of examples.

uk: вхід без авторизації

name: A positivity conjecture for unitary VOAs


uk: Математика, природничі науки

uk: вхід без авторизації

name: Modified trace and logarithmic invariants


Fantastic beasts and where to find them

uk: Математика, природничі науки

description: In recent years, subfactor methods have constructed hundreds of new fusion categories, with strong evidence these live in infinite families. Taking their doubles, we obtain hundreds (and probably infinite families) of new modular tensor categories. These modular tensor categories have a distinctive appearance. Abstracting this appearance, it is natural to guess that there is a new construction, which we call the smashed-sum, combining old modular tensor categories into new ones. It is tempting to guess the smashed-sum construction also lives in the VOA world, in fact this may be its natural home. An example of such a VOA would be the mythical Haagerup VOA.

uk: вхід без авторизації


uk: Комп'ютерні науки

uk: Бібліотекознавство, документознавство

uk: Гуманітарні науки

description: In dieser Folge werfen wir zunächst einen Blick auf die interessante Geschichte von ActivityPub, dem Protokoll hinter Mastodon und ähnlichen Diensten. Danach schauen wir darauf, wie verschiedene Forschenden-Communitys Mastodon mit ganz unterschiedlichen Ansätzen aufgreifen.

uk: вхід без авторизації

name: Folge 2: ActivityPub – ein Blick in den Technikraum von Mastodon und Co.


Normed motivic spectra

uk: Математика, природничі науки

description: Normed motivic spectra are motivic spectra equipped with a coherent system of multiplicative norms along finite etale maps. Many motivic spectra of interest admit canonical normed structures, e.g. the motivic cohomology spectrum, the algebraic K-theory spectrum, and the algebraic cobordism spectrum. For example, the normed structure on HZ underlies Fulton and MacPherson’s norm maps on Chow groups as well as Voevodsky’s power operations in motivic cohomology. Among other things, the formalism of normed spectra allows us to extend the Fulton-MacPherson norms to Chow groups in mixed characteristic and to Chow-Witt groups. This is joint work with Tom Bachmann.

uk: вхід без авторизації


Thom ring spectra and orientation

uk: Математика, природничі науки

description: I'll describe the multiplicative structure of Thom spectra, and the theory of multiplicative orientations of stable fibrations from the ∞-categorical perspective pioneered by Ando, Blumberg, Gepner, Hopkins and Rezk. This is joint work with Tobias Barthel.

uk: вхід без авторизації


The geometry of the cyclotomic trace

uk: Математика, природничі науки

description: Algebraic K-theory -- the analog of topological K-theory for varieties and schemes -- is a deep and far-reaching invariant, but it is notoriously difficult to compute. To date, the primary means of understanding K-theory is through its "cyclotomic trace" map K→TC to topological cyclic homology. This map is usually advertised as an analog of the Chern character, but this is something of a misnomer: TC is a further refinement of any flavor of de Rham cohomology (even "topological", i.e. built from THH), though this discrepancy disappears rationally. However, despite the enormous success of so-called "trace methods" in K-theory computations, the algebro-geometric nature of TC has remained mysterious. In this talk, I will describe a new construction of TC that affords a precise interpretation of the cyclotomic trace at the level of derived algebraic geometry, which is based on nothing but universal properties (coming from Goodwillie calculus) and the geometry of 1-manifolds (via factorization homology).

uk: вхід без авторизації


The genuine stabilization of a G-topos

uk: Математика, природничі науки

description: Let G be a finite group and X a topos with homotopy coherent G-action. From this, we construct a stable homotopy theory SpG(X) which recovers and extends the theory of genuine G-spectra. We explain what our construction yields when: (i) X is the topos of sheaves on a topological space with G-action (ii) X is the etale C2-topos of a scheme S adjoined a square root of -1.

uk: вхід без авторизації


Galois Equivariant Étale Realization

uk: Математика, природничі науки

description: Étale homotopy theory, as originally introduced by Artin and Mazur in the late 60s, is a way of associating to a suitably nice scheme a pro-object in spaces. We will explain how, when working over a base field k, a modern reformulation in terms of the theory of infinity-topoi leads to a more refined invariant, which takes into account the action of the absolute Galois group. We will then explain joint work of ours with Elden Elmanto that extends the étale realization functor of Isaksen, which provides a bridge between unstable motivic homotopy theory and étale homotopy theory, to a functor taking into account the Galois group action. Time permitting, we will explain work in progress extending this to the stable setting.

uk: вхід без авторизації


uk: Математика, природничі науки

description: This talk is themed around the idea that stratifications are a powerful source of correspondences between categorical and geometric structure. I'll discuss connections between stratifications and the categorical property of orbitality, which is central to parametrized higher algebra. I'll also introduce stratified higher topos theory, giving a new computation of an étale homotopy type as an application. There will be a couple of open questions.

uk: вхід без авторизації

name: Some topics in stratified higher category theory


Adjoints and orthogonal groups

uk: Математика, природничі науки

description: In this talk I will articulate and contextualize the following sequence of results. - The Bruhat decomposition of the general linear group defines a stratification of the orthogonal group. - Matrix multiplication defines an algebra structure on its exit-path category in a certain Morita category of categories. - In this Morita category, this algebra acts on the category of n-categories -- this action is given by adjoining adjoints to n-categories. This result is extracted from a larger program -- entirely joint with John Francis, some parts joint with Nick Rozenblyum -- which proves the cobordism hypothesis.

uk: вхід без авторизації


Additivity theorem for Poisson algebras

uk: Математика, природничі науки

description: The Dunn--Lurie additivity theorem states that an algebra with n compatible multiplications is the same as an algebra over the operad of little n-disks, i.e. an En-algebra. I will describe a similar statement for shifted Poisson algebras. Namely, an En-algebra in the category of m-shifted Poisson algebras is the same as an (n+m)-shifted Poisson algebra. I will explain motivitations for such a result coming from mathematical physics and derived Poisson geometry.

uk: вхід без авторизації


uk: Математика, природничі науки

description: We construct a t-structure on the stable infinity-category of cyclotomic spectra and show that the homotopy objects with respect to this t-structure on naturally Dieudonné modules, i.e., abelian groups equipped with operations V and F such that FV=p. For smooth schemes over perfect fields of characteristic p>0, these cyclotomic homotopy objects are the terms in the de Rham—Witt complex. As an application, I will explain how certain formal moduli problems associated to Calabi-Yau varieties admit cyclotomic interpretations, which can be used to strengthen past results about the behavior of these invariants under Fourier—Mukai equivalence.

uk: вхід без авторизації

name: Dieudonné modules and cyclotomic spectra


uk: Математика, природничі науки

description: In this talk I will explain how one can use geometric arguments to obtain results on dualizablity in a "factorization version" of the Morita category. We will relate our results to previous dualizability results (by Douglas-Schommer-Pries-Snyder and Brochier-Jordan-Snyder on Turaev-Viro and Reshetikin-Turaev theories). We will discuss applications of these dualiability results: one is to construct examples of low-dimensional field theories "relative" to their observables. An example will be given by Azumaya algebras, for example polynomial differential operators (Weyl algebra) in positive characteristic and its center. (This is joint work with Owen Gwilliam.)

uk: вхід без авторизації

name: Dualizability in the factorization higher Morita category


Enriched ∞-operads

uk: Математика, природничі науки

description: We introduce enriched ∞-operads as certain presheaves which generalize Barwick's complete Segal operads. The simple structure of the indexing categories allows us to define algebras between enriched ∞-operads. By comparing this presheaf model with an enriched version of Moerdijk-Cisinski's dendroidal Segal spaces, we then prove a rectification theorem which states that the homotopy theory of ∞-operads enriched in a nice symmetric monoidal model category is equivalent to that of strictly enriched operads. From this we can easily infer that all established models for ∞-operads are equivalent to simplicially enriched operads.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In joint work with Dominic Verity we prove that four models of (∞,1)-categories — quasi-categories, complete Segal spaces, Segal categories, and 1-complicial sets — are equivalent for the purpose of developing ∞-category theory. To prove this we first introduce the notion of an ∞-cosmos, a category in which ∞-categories live as objects, an example of which is given by each of the four models mentioned above. We then explain how the category theory of ∞-categories can be developed inside any ∞-cosmos; eg, we define right adjoints and limits and prove that the former preserve the latter. We conclude by arguing that the four above mentioned ∞-cosmoi all biequivalent, the upshot being that ∞-categorical structures are preserved, reflected, and created by a number of “change-of-model” functors. More precisely, we show that each of these ∞-cosmoi have a biequivalent “calculus of modules,” modules between ∞-categories being a vehicle to express ∞-categorical universal properties.

uk: вхід без авторизації

name: A proof of the model-independence of ∞-category theory


Lie algebras and vn-periodic spaces

uk: Математика, природничі науки

description: I will discuss an infinity-category obtained from that of pointed spaces by inverting the maps inducing isomorphisms in vn-periodic homotopy groups. The case n=0 corresponds to rational homotopy theory. In analogy with Quillen’s results in the rational case, I will outline how this vn-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in T(n)-local spectra (or a variant for K(n)-local spectra). One can also compare it to the homotopy theory of cocommutative coalgebras in T(n)-local spectra, where there is only an equivalence up to a certain "Goodwillie convergence" issue. I will describe the relevant operadic and cooperadic structures and a form of Koszul duality relevant to this setting.

uk: вхід без авторизації

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


keywords: OER ORCA.nrw OER-Fachtag Ingenieurwissenschaften

description: Im Rahmen des OER-Fachtags Ingenieurwissenschaften 2022 stellt Geschäftsführer Dr. Markus Deimann das Landesportal ORCA.nrw vor. Dieses bietet seit September 2021 ein umfangreiches Service-Angebot für die öffentlich-rechtlichen Hochschulen in Nordrhein-Westfalen. Im Zentrum stehen frei zugängliche Bildungsmaterialien / Open Educational Resources aus allen Fachgebieten, die kostenfrei genutzt und weiterverwendet werden können. Dazu bietet ORCA eine Suche, die auch andere Bundesländer beinhaltet sowie die Möglichkeit zum Hochladen selbst-erstellter OER. Die Basis-Infrastruktur von ORCA dient dazu, die vielfältigen Herausforderungen der Digitalisierung von Hochschulen kooperativ und nachhaltig bewältigen zu können.

uk: вхід без авторизації

name: Das Landesportal ORCA.nrw als Quelle für ingenieurwissenschaftliche OER


uk: Математика, природничі науки

description: I will describe an extension to the boundary of the cosphere bundle and geodesic flow of an asymptotically hyperbolic manifold. I will then discuss injectivity results for X-ray transforms on tensors and the boundary rigidity problem of determining an asymptotically hyperbolic metric from the renormalized lengths of geodesics joining boundary points. One part is work with Colin Guillarmou, Plamen Stefanov and Gunther Uhlmann and another part is work with Nikolas Eptaminitakis.

uk: вхід без авторизації

name: Geodesic flow, X-ray transform, and boundary rigidity on asymptotically hyperbolic manifolds


The sound of a singularity?

uk: Математика, природничі науки

description: Analytically computing the spectrum of the Laplacian is impossible for all but a handful of classical examples. Consequently, it can be tricky business to determine which geometric features are spectrally determined; such features are known as geometric spectral invariants. Weyl demonstrated in 1912 that the area of a planar domain is a geometric spectral invariant. In the 1950s, Pleijel proved that the n-1 dimensional volume of a smoothly bounded n-dimensional Riemannian manifold is a geometric spectral invariant. Kac, and McKean & Singer independently proved in the 1960s that the Euler characteristic is a geometric spectral invariant for smoothly bounded domains and surfaces. At the same time, Kac popularized the isospectral problem for planar domains in his article, ``Can one hear the shape of a drum?'' Colloquially, one says that one can ``hear'' spectral invariants. In this talk I will not only discuss my work with many collaborators (Rafe Mazzeo, Zhiqin Lu, Clara Aldana, Klaus Kirsten, David Sher, Medet Nursultanov) but also highlight the works of many other colleagues, who share a similar interest in ``hearing singularities.''

uk: вхід без авторизації


uk: Математика, природничі науки

description: The concentration properties of eigenfunctions of the Laplace-Beltrami operator are closely linked the the underlying geometry (and dynamics) on manifolds. It this talk I will discuss the known concentration results and the models we use to test sharpness. Such problems are effectively forward problems, I will also discuss what an inverse problem would look like in this setting.

uk: вхід без авторизації

name: Eigenfunction concentration and its connection to geometry