de: Lehrperson

en: teacher

de: Lernende

en: student

uk: Соціальні комунікації/Журналістика

uk: Право, економіка та суспільні науки

description: This module serves as an introduction to communication in a professional context. In a world where change is constant and technology proliferates, the foundational skills developed here will enable students to balance the needs of their audience with their communication goals. Students will develop the skills for selecting the appropriate medium for their message and measuring their results; they will be prepared for high performance in today’s ever-changing workplace.

uk: вхід без авторизації

name: Professional Communications OER: Module 1: Foundations


cs: učitel

fi: Opettaja

uk: вчитель

fr: enseignant

da: lærer

es: profesor

nl: onderwijzer

cs: student

fi: Oppija

uk: студент

fr: étudiant

da: student/elev

es: estudiante

nl: student

Olds College OER Development Team

type: Organization

JR Dingwall

type: Person

de: Kommunikationswissenschaft/Publizistik

uk: Соціальні комунікації/Журналістика

en: Communication Science/Journalism

de: Rechts-, Wirtschafts- und Sozialwissenschaften

uk: Право, економіка та суспільні науки

en: Law, Economics and Social Sciences

description: This open educational resource (OER), developed by Olds College is collaboration with the Government of Alberta, is a series of modules intended for use in higher education courses or by independent learners. This resource is useful for instructors whose courses cover introductory communication skills, workplace communication, technical communication or business writing.It contains four modules, each with its own lesson plans, assessments, and supporting materials. This is module 3 of 4, in which students will learn the art and science of putting together an impressive presentation. Topics include presentation styles, developing a presentation strategy, presentation aids, and communicating with a live audience.

BC Campus

type: Service

type: WebContent

@language: en

cs: přihlášení není vyžadováno

de: keine Anmeldung erforderlich

uk: вхід без авторизації

en: no login required

nl: geen login vereist

name: Professional Communications OER: Module 3: Presentations

cs: Učebnice

de: Lehrbuch

fi: Oppikirja

uk: Підручник

en: Textbook

fr: Manuel Scolaire

da: Lærebog

nl: Studieboek

es: Libro de Texto


uk: Соціальні комунікації/Журналістика

uk: Право, економіка та суспільні науки

description: This open education resource (OER), developed by Olds College in collaboration with the Government of Alberta, is a series of modules intended for use in higher education courses or by independent learners. The resource is useful for instructors whose courses cover introductory communication skills, workplace communication, technical communication, or business writing. It contains four modules, each with its own lesson plans, assessments, and supporting materials. This is module 2 of 4, in which students learn to communicate in writing. Topics include grammar and punctuation, writing workplace documents, revising workplace documents, ethical guidelines for writing, and information literacy.

uk: вхід без авторизації

name: Professional Communications OER: Module 2: Writing


uk: Соціальні комунікації/Журналістика

uk: Право, економіка та суспільні науки

uk: Соціальні комунікації/Журналістика

description: In introduction to fundamentals of interpersonal relations including but not limited to sense of self, perception, role of emotions, components of verbals and nonverbal communication, effective listening, safe and brave spaces, and navigating conflict.

encodingFormat: application/pdf

type: MediaObject

uk: вхід без авторизації

name: An Introduction to Interpersonal Communication : A Primer on Communication Studies


description: Diese Literatur konnte freiwillig im Bereich des Projekts gelesen werden

@language: de

uk: вхід без авторизації

name: Einflussfaktoren bei der Social-Media-Nutzung in der Wissenschaftskommunikation

cs: Prezentace

de: Präsentation

fi: Esitys

uk: Презентація

en: Presentation

fr: Présentation

da: Præsentation

nl: Presentatie

es: Presentación


keywords: Fortbildung Mentoring Lehrfilm Schulpraktikum Unterrichtsberatung

de: Erziehungswissenschaften

uk: Педагогічні науки

en: Educational Sciences

de: Schulpädagogik

uk: Середня освіта

en: School Pedagogy

uk: Право, економіка та суспільні науки

description: Lehrkräfte in der Schule übernehmen eine verantwortliche Rolle als Lehrkräftebildner*innen, die aktiv gemeinsam mit Studierenden Unterricht planen, durchführen und reflektieren Vor dem Hintergrund der Diskussion um eine stärkere Theorie-Praxis-Vernetzung in der Lehrer*innenbildung sollten schulische Mentor*innen noch stärker darin unterstützt werden, den Studierenden während der Begleitung in ihrer Praxisphase bewusst Lerngelegenheiten bereitstellen zu können. Die Förderung der Professionalisierung von Studierenden in schulischen Praxisphasen stellt eine komplexe Aufgabe dar, auf die Mentor*innen vorbereitet werden müssen. Im Beitrag wird vorgeschlagen, hierzu in Fortbildungsveranstaltungen auch mit gescripteten Videovignetten zu arbeiten, anhand derer Mentor*innen fremdes Verhalten in Mentoringsituationen beobachten und analysieren können, bevor sie in einem weiteren Schritt an ihrer eigenen Unterstützungspraxis arbeiten. Im Folgenden wird eine vollständig videographierte „Unterstützungssequenz“, bestehend aus Videos einer Unterrichtsvorbesprechung, einer Unterrichtssituation im Teamteaching und einer Unterrichtsnachbesprechung, dargestellt. Ergänzend werden Beispielaufgaben für die Nutzung des Videomaterials vor allem in der Lehrkräftefortbildung veröffentlicht. Darüber hinaus werden erste Erfahrungen mit dem Material dokumentiert und weitere Einsatzmöglichkeiten skizziert.

uk: вхід без авторизації

name: Unterricht gemeinsam planen, durchführen und nachbesprechen. Coachen lernen anhand videographierter Situationen

Leuphana Universität Lüneburg

addressCountry: DE

addressLocality: Lüneburg

addressRegion: Lower Saxony

cs: Případová studie

de: Fallstudie

fi: Tapaustutkimus

uk: Приклад

en: Case Study

fr: Étude de Cas

da: Casestudie

nl: Case Study

es: Estudio de Caso

cs: Video

de: Video

fi: Video

uk: Відео

en: Video

fr: Vidéo

da: Video

nl: Video

es: Video


keywords:
Social values
Sustainability
Community
Projects
Initiatives

de: Geisteswissenschaften

uk: Гуманітарні науки

en: Humanities

description: Background: This paper presents a review of the literature and trends related to social values and sustainabledevelopment and describes a set of case studies from a variety of community‑based projects which illustrate theadvantages that social values bring about as part of efforts to promote sustainability. Three approaches were used todevelop this study: a bibliometric analysis of the topic "social values and sustainable development", an analysis of casestudies that concretely present community projects addressing social values and sustainability, and the developmentof a framework linking up bibliometric clusters and the cases studies. Results: While the bibliometric analysis revealed clusters where social values are strongly connected with sustain‑able development, the case studies indicated the lack of a common terminology and understanding of the relationbetween social values, sustainable development, and community‑based projects. Conclusions: The study concludes by suggesting a set of measures that could be deployed to better take socialvalues into account when planning policies or making decisions related to community projects.

uk: вхід без авторизації

name: Social values and sustainable development: community experiences

name: HFH · Hamburger Fern-Hochschule gemeinnützige

addressLocality: Hamburg

addressRegion: Hamburg

cs: Text

de: Textdokument

fi: Teksti

uk: Текстовий документ

en: Text

fr: Texte

da: Tekst

nl: Tekst

es: Texto


An introduction to the BV-BFV formalism

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: The BV-BFV formalism unifies the BV formalism (which deals with the problem of fixing the gauge of field theories on closed manifolds) with the BFV formalism (which yields a cohomological resolution of the reduced phase space of a classical field theory). I will explain how this formalism arises and how it can be quantized.

uk: вхід без авторизації

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


uk: Математика, природничі науки

description: There are various, quite different mathematical approaches to quantum field theories, among them functorial field theories in the sense of Atiyah and Segal and the factorization algebras of quantum observables of Costello and Gwilliam. In the talk I will describe a construction that produces a twisted functorial field theory from a factorization algebra, thus relating these two approaches. This is joint work with Bill Dwyer and Peter Teichner.

uk: вхід без авторизації

name: From factorization algebras to functorial field theories


uk: Математика, природничі науки

description: An algebraic quantum field theory (AQFT) presents a QFT on Lorentzian manifolds as an assignment of algebras to spacetimes, subject to physical axioms (e.g. Einstein causality). Such algebras are interpreted as quantizations of the function algebras on the moduli space of a classical field theory. In many cases, e.g. the stack of a gauge theory, moduli spaces encode "higher structures". As a consequence, functions on such spaces form "higher algebras", which can be analyzed by homotopical algebra (à la Quillen). Therefore, to investigate the quantization of such moduli spaces, one needs to infuse AQFT with homotopical algebra, resulting in "homotopical AQFT", i.e. the assignment of "higher algebras" to spacetimes. After motivating our approach with a concrete application of homotopical algebra to the Cauchy problem of the Yang-Mills stack, I will provide a "working definition" of homotopical AQFT, emphasize its role in relation to gauge theories and present two toy examples arising via homotopy Kan extensions. Based on [arXiv: 1503.08839, 1610.06071, 1704.01378].

uk: вхід без авторизації

name: Algebraic quantum field theory meets homotopical algebra


uk: Математика, природничі науки

description: Using local intersections, Goldman and Turaev defined a BV operator on the exterior algebra of homotopy classes of loops on a surface. On a genus zero surface with three boundary components the linearization problem of this structure is equivalent to the Kashiwara-Vergne problem in Lie theory. Motivated by this result a generalization of the Kashiwara-Vergne problem in higher genera is proposed and solutions are constructed in analogy with elliptic associators. This is joint work with A. Alekseev, N. Kawazumi and Y. Kuno.

uk: вхід без авторизації

name: Linearization of the Goldman-Turaev BV algebra using Kashiwara-Vergne theory


Cellular BV-BFV-BF theory

uk: Математика, природничі науки

description: We will present an example of a topological field theory living on cobordisms endowed with CW decomposition (this example corresponds to the so-called BF theory in its abelian and non-abelian variants), which satisfies the Batalin-Vilkovisky master equation, satisfies (a version of) Segal's gluing axiom w.r.t. concatenation of cobordisms and is compatible with cellularaggregations. In non-abelian case, the action functional of the theory is constructed out of local unimodular L-infinity algebras on cells; the partition function carries the information about the Reidemeister torsion, together with certain information pertaining to formal geometry of the moduli space of local systems. This theory provides an example of the BV-BFV programme for quantization of field theories on manifolds with boundary in cohomological formalism. This is a joint work with Alberto S. Cattaneo and Nicolai Reshetikhin.

uk: вхід без авторизації


Virasoro constraints and localization

uk: Математика, природничі науки

description: During last years numerous results were obtained for the exact partition functions and other supersymmetric observables for supersymmetric gauge theories in diverse dimensions. Typically the result can be expressed through the matrix model which satisfy the different versions of Virasoro constraints (or its deformations). I will review the subject and provide some examples for 3D and 4D gauge theories.

uk: вхід без авторизації


Axiomatic microlocal category.

uk: Математика, природничі науки

description: I am going to present a construction of an infinity stable category associated to a closed symplectic manifold whose symplectic form has integer periods. The category looks like the Fukaya category of M with coefficients in a certain local system. One first define an infinity category C_{rR} associated to the product of two symplectic balls B_r times B_R whose objects are (roughly) graphs of symplectomorphic embeddings B_r to B_R and homs are positive isotopies (it is defined via listing axioms which characterize it). We have a composition C_{r_1r_2} times C_{r_2r_3} to C_{r_1r_3} so that we have an infinity 2-category C whose 0- objects are balls and the category of morphisms between B_r and B_R is C_{rR} One has a functor F_M} from C to the infinity 2 category of infinity categories, where F_M(B_r) is the category of symplectic embeddings B_r—>M. One also has another functor P between the same infinity categories and one defines the micro local category on M as hom(P,F_M).

uk: вхід без авторизації


uk: Математика, природничі науки

description: Lie ∞-groupoids are simplicial manifolds which satisfy conditions similar to the horn filling conditions for Kan simplicial sets. Lie ∞-groupoids are to non–negatively graded dg manifolds, or L∞-algebroids, as Lie groups are to Lie algebras. In particular, there is an integration procedure based on a smooth analog of Sullivan’s realization functor from rational homotopy theory that pro- duces a Lie ∞-groupoid from dg– manifold. There is also a differentiation functor due to Sˇevera, which uses supergeometry to construct the 1-jet of a simplicial manifold. In this talk, I will present joint work (arXiv:1609.01394) in progress with Chenchang Zhu in which we study the relationship between these integration and differentiation procedures, in analogy with Lie’s Second Theorem. A crucial first step involves constructing a user–friendly homotopy theory for Lie ∞-groupoids. This is a subtle problem, due to the fact that the category of manifolds lacks limits. I will describe how results of Behrend and Getzler can be generalized to develop a homotopy theory for Lie ∞-groups/groupoids that is compatible with the well–known homotopy theory of L∞- algebras/algebroids. If time permits, I will mention some possible applications to AKSZ σ-models via Kotov–Strobl’s theory of characteristic classes for (non–trivial) Q-bundles.

uk: вхід без авторизації

name: Towards an adjunction between the homotopy theories of dg manifolds and Lie ∞-groupoids


Shifted geometric quantization

uk: Математика, природничі науки

description: Geometric quantization attaches vector spaces to symplectic manifolds equipped with extra data. In this talk I will discuss how higher, or categorified, geometric quantization looks like. The input this time will be a shifted symplectic space. As an example, in shift (-1) one discovers BV quantization.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Working towards the aim of axiomatizing realistic quantum field theories in a TQFT-type framework we focus on the simplest class of examples: linear field theories and their perturbation theory. In order to understand quantization it turns out to be useful to introduce an axiomatization of classical field theory also, on manifolds with boundary. We show how geometric quantization together with the Feynman path integral then leads to a quantization functor from (augmented) classical field theories to quantum field theories. We discuss scope, applications, limitations and future directions of this approach.

uk: вхід без авторизації

name: Functorial quantization of linear field theory


Vanishing of BV cohomology

uk: Математика, природничі науки

description: From the minute 14 of video does not have audio. Consider the BV cohomology associated to a solution of the BV master equation for field theory on a d-dimensional world sheet. When d=0, Felder and Kazhdan have suggested the additional axiom that the cohomology for a physically relevant theory vanish below dimension 0. The natural generalization of this to d>0 is that the cohomology vanish below dimension d. In earlier work, we have shown that this axiom is violated for the spinning particle, which is a toy model of a supersymmetric field coupled to supergravity in d=1. Sean Pohorence and I have shown that in contrast, the axiom holds for the superparticle, which is a toy model of the Green- Schwartz superstring in d=1. This theory exhibits some interesting features: there is an infinite tower of ghosts, so it is important to work with the correct completion of the space of local observables, and also one must work with Cech cochains at every stage of the calculation.

uk: вхід без авторизації


uk: Математика, природничі науки

description: I will report on progress of a joint project with Alan Weinstein in which we try to understand the initial value constraints of field theories with external symmetries as momenta of a Lie algebroid action on the presymplectic manifold of fields. Having shown earlier how a Lie algebroid symmetry naturally appears in General Relativity, we are currently studying a notion of hamiltonian momentum map for Lie algebroids. I will explain how hamiltonian Lie algebroids generally arise in lagrangian field theories with spacetime diffeomorphism symmetry.

uk: вхід без авторизації

name: The hamiltonian Lie algebroids of field theories


L1 full groups

uk: Математика, природничі науки

description: I will talk about L1 full groups of ergodic measure-preserving transformations, which are measurable analogues of topological full groups of minimal homeomorphisms of the Cantor space. After describing some of the basic properties of these groups, I will present a short proof that the index map takes values into Z which was found with Todor Tsankov. Finally, I will mention some results on the topological rank of L1 full groups.

uk: вхід без авторизації


Permutation representation theory

uk: Математика, природничі науки

description: I will survey a few papers concerning the following question: What can one learn about G from its representation theory into S. Where S=S∞ is the Polish group of all permutations of a countable set. Hom(G,S) is a Polish space in its own right. We focus on two aspects. How a (Baire) generic representation of G looks like. And the existence of representations with special transitivity properties such as faithful primitive actions, or faithful highly transitive actions of the group.

uk: вхід без авторизації


uk: Математика, природничі науки

description: We provide a direct proof of a recent theorem of Ben-Yaacov, Melleray, and Tsankov. If G is a Polish group and X is a minimal, metrizable G-flow with all orbits meager, we use X to produce a new G- ow SG(X) which is minimal and non-metrizable.

uk: вхід без авторизації

name: A direct solution to the Generic Point Problem


Finite element exterior calculus

uk: Математика, природничі науки

description: We will survey the key structures, examples, and applications of finite element exterior calculus (FEEC). FEEC is a canonical example of structure-preserving discretization which brings together geometry, topology, and analysis in order to unify, clarify, and refine many of the classical mixed finite element methods, and to enable the development of stable mixed finite elements for problems where they had previously not been available.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Many PDEs arise from a variational principle, and this leads to many of their qualitative properties. The discrete variational method (DVDM) is a technique for discretising such a PDE directly from this variational principle. It derivation ensures that it reproduces dissipation/energy preserving properties of the underlying PDE. The performance of these method is often very good. In this talk I will show that this is because the discrete solution satisfies a modified equation, which in turn satisfies a (form of a) variational principle which is a perturbation of the original. Properties of the solution of the DVDM can then be derived directly from this modified variational equation. This is Joint work with akaharu Yaguchi (Kobe) and Daisuke Furihata (Osaka).

uk: вхід без авторизації

name: Discrete variational derivative methods: Geometric Integration methods for PDEs


uk: Математика, природничі науки

description: Time dependent nonlinear partial differential equations, like for example reaction diffusion equations, are usually solved by classical time marching schemes, like Runge-Kutta methods, or linear multi-step methods. Such equations can however have solutions which blow up in finite time, and in the blowup regime, the behavior of the solution is dominated by the non-linearity. I will show two different approaches how one can construct specialized numerical time integrators which take into account the physics of the underlying non-linear problem. I will show both theoretically and numerically that their performance can be orders of magnitude better than the performance of classical time integrators for such problems.

uk: вхід без авторизації

name: B-Methods: Geometric Integrators for Blowup Problems


uk: Математика, природничі науки

description: Among the major applications of discrete exterior calculus (in the sense of Hirani et al) are discretization of the Hodge-Laplace operator and various related problems. However, convergence issues for those problems are not completely resolved; as far as we are aware, there is no proof of convergence except for the Poisson equation in two dimensions, which is immediate because the discrete problem is identical to the one that arises from affine finite elements. Moreover, even in two dimensions, there have been some puzzling numerical experiments reported in the literature, apparently suggesting that there is convergence without consistency.

uk: вхід без авторизації

name: On analysis of discrete exterior calculus


uk: Математика, природничі науки

description: This talk discusses the application of hybridizable discontinuous Galerkin (HDG) methods to canonical Hamiltonian PDEs. We present necessary and sufficient conditions for an HDG method to satisfy a multisymplectic conservation law, when applied to such a system, and show that these conditions are satisfied by "hybridized" versions of several of the most commonly-used finite element methods. These finite element methods may therefore be used for high-order, structure-preserving discretization of Hamiltonian PDEs on unstructured meshes. (Joint work with Robert McLachlan.)

uk: вхід без авторизації

name: Multisymplecticity of hybridizable discontinuous Galerkin methods


uk: Математика, природничі науки

description: Given a differential equation that admits a group of symmetries, it is frequently desirable to preserve those symmetries when constructing a numerical scheme. For solutions that exhibit sharp variations or singularities, symmetry-preserving numerical schemes have proven to give very good numerical results. In the last 25 years, most of the research in this field has focused on the construction of symmetry-preserving finite difference numerical schemes. Extending known results to other types of numerical methods (such as finite element, finite volume, or spectral methods) remains a challenge. In this talk, I will report on preliminary results related to the construction of symmetry-preserving finite element numerical schemes. This is a joint work with Professor Alexander Bihlo from Memorial University.

uk: вхід без авторизації

name: Symmetry-Preserving Finite Element Methods: Preliminary Results


uk: Математика, природничі науки

description: (Joint work with A. Le Boudec) We begin by giving a detailed overview of the tree almost automorphism groups and describing their relationship to Higman-Thompson groups and topological full groups. We then show each almost automorphism has one of two possible types, corresponding to the dynamics of the action on the boundary. We next consider the subgroups such that every element is contained in a compact subgroup; such groups are the topological analogue of torsion subgroups. We characterize these subgroups in terms of the dynamics of their action on the boundary and deduce that they are indeed locally elliptic - i.e. every finite set is contained in a compact subgroup. We finally consider the commensurated subgroups of almost automorphism groups; these subgroups generalize normal subgroups. We show every commensurated closed subgroup of an almost automorphism group is either finite, compact and open, or equal to the entire group.

uk: вхід без авторизації

name: Tree almost automorphism groups: elements and subgroups


uk: Математика, природничі науки

description: Let G be a locally compact group, let K be a closed subgroup of G, and let H be a group of automorphisms of G such that h(K)=K for all hinH. When is the action of H on G/K a small invariant neighbourhoods (SIN) action, i.e. when is there a basis of neighbourhoods of the trivial coset consisting of H-invariant sets? In general, the SIN property is a strong restriction, but when G is totally disconnected and H is compactly generated, it turns out to be equivalent to the seemingly weaker condition that the action of H on G/K is distal on some neighbourhood of the trivial coset. (The analogous statement is false in the connected case: compact nilmanifolds give rise to counterexamples.) This has some general consequences for the structure of t.d.l.c. groups: for example, given any compact subset X of a t.d.l.c. group G, there is an open subgroup containing X that is the unique smallest such up to finite index.

uk: вхід без авторизації

name: SIN actions on coset spaces in totally disconnected, locally compact (t.d.l.c.) groups


Computing the scale

uk: Математика, природничі науки

description: The scale of the endomorphism α of the totally disconnected, locally compact (t.d.l.c.) group G is a positive integer defined to be the minimum of the indices [α(U):α(U)∩U], where U ranges over the compact open subgroups of G. Existing methods for computing the scale draw on analogies with computing eigenvalues in linear algebra. These methods generally do not match the effectiveness of linear algebra however, the principal obstacle being the lack of a general description of t.d.l.c.~groups.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The Boris algorithm is the most popular time integrator for charged particle motion in electric and magnetic force fields. It is a symmetric one-step method, and it preserves the phase volume exactly. However, it is not symplectic. Nevertheless, numerical experiments confirm an excellent long-time near energy preservation of the system. In this talk we present a multistep extension of the Boris algorithm, which is explicit, symmetric, and has arbitrarily high order. Near preservation of energy and momentum for the underlying one-step method, and the boundedness of parasitic solution components are proved. A rigorous proof for the excellent near energy preservation of the Boris algorithm is still missing. (We thank Martin Gander for drawing our attention to this problem.)

uk: вхід без авторизації

name: Large Long-time behaviour of numerical integrators for charged particle dynamics


uk: Математика, природничі науки

description: We present a new class of conservative method, called the multiplier method, which enables systematic construction of conservative schemes for general dynamical systems. Specifically, the multiplier method can preserve arbitrary forms of conserved quantities and is applicable for systems without a symplectic or variational structure, such as dissipative problems. Moreover, we discuss a fundamental long-term stability property for general conservative methods. This is joint work with Alexander Bihlo and Jean-Christophe Nave.

uk: вхід без авторизації

name: Conservative methods and long-term stability for dynamical systems


uk: Математика, природничі науки

description: B-series are a special form of Taylor series, where the terms are indexed by rooted trees. The theory originated by the seminal work on numerical integration by John Butcher half a century ago. The theory has developed to become arguably the most important tool in the study of structure preservation of numerical integrators. Geometrically B-series are intimately connected to the geometry of Euclidean spaces. Lie-Butcher series is a generalisation which combines B-series with Lie series, aimed at the study of flows on manifolds. In this talk we will discuss the interplay between the algebraic and geometric structures underlying Lie-Butcher series. We will review various recent results and work in progress, both for ODEs and in the theory of Rough Paths (stochastic DEs).

uk: вхід без авторизації

name: Connections in Geometric Numerical Integration

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


Porous media modelling with Euler

uk: Математика, природничі науки

description: We solve the model of C.J. Budd, J.M. Stockie, Stud. Appl. Math. AA:1--29, 2015, treated numerically in the paper "Asymptotical computations for a model of flow in saturated porous media" by P. Amodio, C.J. Budd, O. Koch, G. Settanni and E. Weinmuller, Appl. Math. and Comput. 237 (2014), 155-167 by methods right out of Euler's "Institutiones Calculi Integralis" (1768/69/70). The obtained precision is only limited by that of the computer. A nice occasion to celebrate the 250th anniversary of this greatest classics for integration and differential equations.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In this talk we present a geometric variational discretization of equations describing compressible fluids. The numerical scheme is obtained by discretizing, in a structure-preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the associated variational principles. Our framework applies to irregular mesh discretizations in 2D and 3D. It systematically extends work previously made for incompressible fluids to the compressible case. We consider in details the numerical scheme on 2D irregular simplicial meshes and evaluate the scheme numerically for the rotating shallow water equations. In particular, we investigate whether the scheme conserves stationary solutions, represents well the nonlinear dynamics, and approximates well the frequency relations of the continuous equations, while preserving conservation laws such as mass and total energy.

uk: вхід без авторизації

name: Towards a geometric variational discretization of compressible fluids: the rotating shallow water equations


uk: Математика, природничі науки

description: The problem is to combine explicit time and mimetic spatial discretizations for wave equations so that the energy is conserved. It is easy to see that intuitive discretizations of the energy are not conserved. However it is possible to find conserved quantities that depend on the time step that are conserved and converge quadratically in the time step to the classical energy.

uk: вхід без авторизації

name: Combining Time and Mimetic Spatial Discretizations


Polish dendrites & Polish groups

uk: Математика, природничі науки

description: A dendrite is a continuum (i.e. a compact connected metrizable space) that is locally connected and such that any two points are joined by a unique arc. T. Wazewski introduced a universal dendrite in which any other dendrite can embedded. Its construction can be generalized to yield an uncountable family of non-homeomorphic dendrites. Their homeomorphism groups are closed subgroups of S∞ and thus are Polish groups. Moreover some of them are oligomorphic. In this talk, we will be interested in structural and topological properties of these groups like simplicity, Bergman property, property (T), existence of a dense or comeager conjugacy class, automatic continuity or small index property.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In this talk I will present joint work with Andreas Thom on bounded normal generation (BNG) for projective unitary groups of von Neumann algebras. We say that a group has (BNG) if the conjugacy class of every nontrivial element and of its inverse generate the whole group in finitely many steps. After explaining how one can prove (BNG) for the projective unitary group of a finite factor, I will present applications to automatic continuity of homomorphisms with SIN target groups. The talk will be closed with recent results on the Bergman property for unitary groups of II_1 factors and countable cofinality for compact connected Lie groups.

uk: вхід без авторизації

name: Bounded normal generation and the Bergman property for von Neumann algebras


uk: Математика, природничі науки

description: The first half of this talk presents a general overview of Geometric Numerical Integration of differential equations. The second half discusses geometric integrability properties of Kahan¹s method.

uk: вхід без авторизації

name: Geometric Numeriacal Integration of Differential Equations


uk: Математика, природничі науки

description: For locally compact groups amenability and Kazhdan's property (T) are mutually exclusive in the sense that a group having both properties is compact. This is no longer true for more general Polish groups. However, a weaker result still holds for SIN groups (topological groups admitting a basis of conjugation-invariant neighbourhoods of identity): if such a group admits sufficiently many unitary representations, then it is precompact as soon as it is amenable and has the strong property (T) (i.e. admits a finite Kazhdan set). If an amenable topological group with property (T) admits a faithful uniformly continuous representation, then it is maximally almost periodic. In particular, an extremely amenable SIN group never has strong property (T), and an extremely amenable subgroup of unitary operators in the uniform topology is never a Kazhdan group. This leads to first examples distinguishing between property (T) and property (FH) in the class of Polish groups. Disproving a 2003 conjecture by Bekka, we construct a complete, separable, minimally almost periodic topological group with property (T), having no finite Kazhdan set. Finally, as a curiosity, we observe that the class of topological groups with property (T) is closed under arbitrary infinite products with the usual product topology. A large number of questions about various particular topological groups remain open. The talk is based on the preprint [math.GR], to appear in Trans. Am. Math. Soc., never before presented at a conference.

uk: вхід без авторизації

name: Amenability versus property (T) for non locally compact topological groups.


Følner sets in topological groups

uk: Математика, природничі науки

description: Generalizing classical work of Day and Følner for discrete groups, I will present characterizations of amenability of (not necessarily locally compact) topological groups in terms of the existence of almost invariant vectors and almost invariant finite subsets, and discuss some applications of these results, e.g., concerning the coarse geometry of Polish groups. This is joint work with Andreas Thom. Furthermore, linked with concentration of measure, the mentioned amenability criteria provide sufficient conditions for (a strong form of) extreme amenability, which can be used to prove the extreme amenability of topological groups of measurable maps. This is joint work with Vladimir Pestov.

uk: вхід без авторизації


More on approximate Ramsey properties

uk: Математика, природничі науки

description: Using the metric version of the KPT correspondence, we prove that the automorphisms groups of several limits of finite dimensional operator spaces and systems are extremely amenable, including the Gurarij space and its non-commutative version NG. Dually, we prove that the universal minimal flow of the Poulsen simplex P is P itself, and again similarly for its non-commutative version NP. The approximate Ramsey properties (ARP) we find are consequence of the dual Ramsey Theorem (DRT) by Graham and Rothschild. In a similar way, we will see present an approximate Ramsey property for quasi-equipartitions and how to use it to deduce the ARP of the family {ℓnp}n, 1≤p≠2<∞. We will also discuss the reformulation of the (ARP) of {ℓnp}n∈\N as a weak version of a multidimensional Borsuk-Ulam theorem. Finally, we will see that - the DRT is a particular case of a factorization theorem for 0-1 valued matrices, - the Graham-Leeb-Rothschild Theorem on grassmannians over a finite field F is a particular case of a factorization theorem for matrices with values in F, and - the ARP of {ℓnp}n is a particular case of a factorization theorem for matrices with values in R or C. This is a joint work with D. Bartosova, M. Lupini and B. Mbombo, and with V. Ferenczi, B. Mbombo and S. Todorcevic.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Projection operators which commute with the governing differential operators are key tools for the stability analysis of finite element methods associated to a differential complex. In fact, such projections have been a central feature of the analysis of mixed finite element methods since the beginning of such analysis. However, a key difficulty is that, for most of the standard finite element spaces, the canonical projection operators based on the degrees of freedom require additional smoothness to be well--defined and thus are not bounded on the appropriate function spaces. More recently, bounded commuting projections have been constructed, but these lack a key property of the canonical projections; they are not locally defined. In this talk, we review the ideas behind the construction of bounded projections that commute with the exterior derivative and show how, using local operators defined on overlapping macroelements, it is possible to construct such operators that are also locally defined.

uk: вхід без авторизації

name: Construction of bounded cochain projections and their role in the FE exterior calculus


uk: Математика, природничі науки

description: When we want to use reference points located arbitrarily in two- or three-dimensional regions, it is essentially difficult to design some structure-preserving methods. The reason is that we should discretize some Gauss-Green formulae keeping some mathematical properties in that situations. Based on Voronoi-Delaunay triangulations, we can find some beautiful discrete Gauss-Green formulae and apply them to design some structure-preserving numerical methods. In the talk, we will indicate those formulae and their proofs in detail and the obtained discrete variational derivative methods based on Voronoi cells. Furthermore, if it is possible, we will show some relaxed structure-preserving methods to decrease computation cost.

uk: вхід без авторизації

name: Structure-preserving method on Voronoi cells


uk: Математика, природничі науки

description: In an effort to better understand what makes a numerical method mimetic we consider an exceptional case. The Keller-Box scheme is multi-symplectic (Reich 2000), it always propagates waves in the correct direction (Frank, 2006), and it discretizes the problem physics and calculus exactly (mimetic). However, the method is not easily described by algebraic topology or discrete differential forms. The properties of this unusual mimetic method are discussed and compared to the more classical mimetic finite element and finite volume methods.

uk: вхід без авторизації

name: A Mimetic Method that is a Bit Different


uk: Математика, природничі науки

description: Instead of the usual presentation given to the formulation of Initial Boundary Boundary Value Problems (IBVP), we do no take the partition of the continuous media directly to the limit of zero shrinking size concerning the spatial dimensions at any given time, which leads to some differential expression for the limiting net force upon the element. We consider each media element as a single particle evolving in “time” under a “force” represented by the discrete mimetic analog of the differential expression. We base our approach on a discrete extended Gauss’s divergence theorem, without using exterior calculus, to construct our mimetic operators combined with a symplectic integration scheme.

uk: вхід без авторизації

name: High-Order Mimetic Finite Differences and Geometric Integration


uk: Математика, природничі науки

description: Integral preserving schemes for ODEs can be derived by means of for instance discrete gradient methods. For PDEs, one may first discretize in space, using for instance finite difference methods or finite element methods, and then apply an integral preserving method for the corresponding ODEs. For PDEs discretized on moving grids, the situation is more complicated, it is not even clear exactly what should be meant by an integral preserving scheme in this setting. We shall propose a definition and then derive the resulting conservative schemes, both with finite difference schemes and with finite element schemes. We test the methods on problems with travelling wave solutions and demonstrate that they give remarkably good results, both compared to fixed grid and to non-conservative schemes. This is joint work with S. Eidnes and T. Ringholm.

uk: вхід без авторизації

name: Adaptive energy preserving methods for partial differential equations


uk: Математика, природничі науки

description: Let G be a locally compact group and let Sub(G) denote the compact space of closed subgroups of G. G acts naturally on Sub (G) by conjugation. A uniformly recurrent subgroup (URS) of G is a closed, minimal subset of Sub (G). To every minimal topological dynamical system of G one can naturally associate its stabilizer URS and Glasner and Weiss asked whether every URS can be obtained in this manner. We answer this question in the affirmative by constructing, for a fixed URS H, a G-flow with stabilizer URS equal to H and universal for all minimal flows whose stabilizer URS is subordinate to H. This is joint work with Nicolas Matte Bon.

uk: вхід без авторизації

name: Universal minimal flows relative to a URS


Shape analysis on homogeneous spaces

uk: Математика, природничі науки

description: Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. Shapes are in fact unparametrized curves, evolving on a vector space, on a Lie group or on a manifold. One popular approach to shape analysis is by the use of the Square Root Velocity Transform (SRVT). In this talk we propose a generalisation of the SRVT from vector spaces to Lie groups and to homogeneous manifolds. This is Joint work with S. Eidnes, A. Schmeding.

uk: вхід без авторизації


High order mimetic discretization

uk: Математика, природничі науки

description: In this work the High Order Mimetic Discretization Framework will be presented together with a discussion of two fundamental aspects for the construction of structure-preserving discretizations: (i) the definition of the discrete degrees of freedom of physical field quantities, and (ii) the formulation of the physical field laws. For the first, the geometric degrees of freedom (associated to point, lines, surfaces and volumes) will be introduced. For the second, the Navier Stokes equations will be used as an example.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The spectral instabilities of the stationary periodic solutions of the focusing NLS equation were completely characterized recently. The crux of this characterization was the analysis of the non-self adjoint Lax pair for the focusing NLS equation. Although all solutions are unstable in the class of bounded perturbations, different solutions were found to be spectrally stable with respect to certain classes of periodic perturbations, with period an integer multiple of the solution period. We prove that all solutions that are spectrally stable are also (nonlinearly) orbitally stable, using dierent Krein signature calculations. Similar, more recent results for the sine-Gordon equation will be shown as well.

uk: вхід без авторизації

name: Nonlinear stability of stationary periodic solutions of the focusing NLS equation


uk: Математика, природничі науки

description: In the 1960s, Benjamin and Feir, and Whitham, discovered that a Stokes wave would be unstable to long wavelength perturbations, provided that the product of the carrier wave number and the undisturbed water depth exceeds $\approx 1.363$. In the 1990s, Bridges and Mielke studied the corresponding spectral instability in a rigorous manner. But it leaves some important issues open, such as the spectrum away from the origin. The governing equations of the water wave problem are complicated. One may resort to simple approximate models to gain insights. I will begin by Whitham's shallow water equation and the modulational instability index for small amplitude and periodic traveling waves, the effects of surface tension and constant vorticity. I will then discuss higher order corrections, extension to bidirectional propagation and two-dimensional surfaces. This is partly based on joint works with Mat Johnson (Kansas) and Ashish Pandey (Illinois).

uk: вхід без авторизації

name: Full-dispersion shallow water models and modulational instability


uk: Математика, природничі науки

description: In this talk, we show some results on the existence and orbital stability of the peak-standing-wave solutions for the cubic-quintic nonlinear Schr\"odinger equation with a point interaction. Via a perturbation method and continuation argument, we obtain stability results in the case of attractive-attractive and attractive-repulsive nonlinearities. In the case of an attractive-attractive case and an focusing interaction we give an complete approach for stability based in the extension theory of symmetric operators.

uk: вхід без авторизації

name: On stability properties of the cubic-quintic Schrödinger equation with a Dirac potential


uk: Математика, природничі науки

description: In continuum models bilayers are homoclinic structures that are generically unstable within second-order systems as the associated translational mode has a single zero. Within the single-component, functionalized Cahn-Hillard (FCH) free energy the unstable mode balances against surface diffusion to generate pearling modes: spatially periodic high-frequency lateral variations in the bilayer width that can be weakly stable or weakly unstable. Almost all biologically relevant lipid bilayers are composed of multiple types of lipids. We present a two-component FCH system constructed from a Geirer-Meinhardt (GM) model that possesses one-parameter families of bilayers with adjustable composition. Tuning the composition induces a real-to-complex eigenvalue bifurcation in the underlying GM system yields robust pearling inhibition (stability) in the full system.

uk: вхід без авторизації

name: Robust pearling inhibition in multicomponent bilayers


uk: Математика, природничі науки

description: We consider the nonlinear Schrödinger equation in n space dimensions iut+Δu+|u|p−1u=0,x∈Rn,t>0 and study the existence and stability of standing wave solutions of the form {eiwtei∑kj=1mjθjϕw(r1,r2,…,rk),eiwtei∑kj=1mjθjϕw(r1,r2,…,rk,z),n=2kn=2k+1 for n=2k, (rj,θj) are polar coordinates in R2, j=1,2,…,k; for n=2k+1, (rj,θj) are polar coordinates in R2, (rk,θk,z) are cylindrical coordinates in R3, j=1,2,…,k−1. We show the existence of such solutions as minimizers of a constrained functional and conclude from there that such standing waves are stable if 1<p<1+4/n.

uk: вхід без авторизації

name: Stability of vortex solitons for n-dimensional focusing NLS


Overturned traveling interfacial waves

uk: Математика, природничі науки

description: Periodic traveling waves are computed on parameterized interfaces, which are not functions of the horizontal coordinate(s). These overturned traveling waves are computed on one and two-dimensional interfaces, on a classic interface between two fluids as well as on boundary formed by a hydroelastic ice sheet. Numerical continuation procedures are coupled with local and global bifurcation theorems. Extreme wave types and bifurcation surfaces are presented. The prospects for stability of overturned traveling waves are discussed.

uk: вхід без авторизації

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


uk: Математика, природничі науки

description: The Vortex Filament Equation (VFE) is part of an integrable hierarchy of filament equations. Several equations in this hierarchy have been derived to describe vortex filaments in various situations. Inspired by these results, we develop a general framework for studying the existence and the linear stability of closed solutions of the VFE hierarchy. The framework is based on the correspondence between the VFE and the nonlinear Schr\"odinger (NLS) hierarchies. Our results establish a connection between the AKNS Floquet spectrum and the stability properties of the solutions of the filament equations. We apply our machinery to solutions of the filament equation associated to the Hirota equation. We also discuss how our framework applies to soliton solutions.

uk: вхід без авторизації

name: Spectral stability of solutions to the vortex filament hierarchy


uk: Математика, природничі науки

description: In the stability and blowup for traveling or standing waves in nonlinear Hamiltonian dispersive equations, the non-degeneracy of the linearization about such a wave is of paramount importance. That is, one must verify the kernel of the second variation of the Hamiltonian is generated by the continuous symmetries of the PDE. The proof of this property can be far from trivial, especially in cases where the dispersion admits a nonlocal description where shooting arguments, Sturm-Liouville theories, and other ODE methods may not be applicable. In this talk, we discuss the non degeneracy and nonlinear orbital stability of antiperiodic traveling wave solutions to a class of defocusing NLS equations with fractional dispersion. Key to our analysis is the development of a ground state theory and oscillation theory for linear periodic, fractional Schrodinger operators with antiperiodic boundary conditions. This is joint work with Kyle Claassen (KU).

uk: вхід без авторизації

name: Nondegeneracy and stability of periodic traveling waves in a fractional NLS equation


uk: Математика, природничі науки

description: This talk examines a class of linear hyperbolic systems which generalizes the Goldstein-Kac model to an arbitrary finite number of speeds with transition rates. Under the basic assumptions that the transition matrix is symmetric and irreducible, and the speed differences generate all the space, the system exhibits a large-time behavior described by a parabolic advection-diffusion equation. The main contribution is to determine explicit formulas for the asymptotic drift speed and diffusion matrix in term of the kinetic parameters, establishing a complete connection between microscopic and macroscopic coefficients. It is shown that the drift speed is the arithmetic mean of the velocities. The diffusion matrix has a more complicated representation, based on the graph with vertices the velocities and arcs weighted by the transition rates. The approach is based on an exhaustive analysis of the dispersion relation and on the application of a variant of the Kirchoff's matrix tree theorem from graph theory.

uk: вхід без авторизації

name: Which drift/diffusion formulas for velocity-jump processes?


uk: Математика, природничі науки

description: We consider the problem of finding the spectrum of an operator taking the form of a low-rank (rank one or two) non-normal perturbation of a self-adjoint operator. We use a simple idea of classical differential geometry (the envelope of a family of curves) to analyze the spectrum. When the rank of the perturbation is two, this allows us to view the system in a geometric way through a ``phase plan'' in the perturbation strengths. We show how to apply this technique to two problems: a neural network model of the oculomotor integrator (Anastasio and Gad 2007), and a nonlocal model of phase separation (Rubinstein and Sternberg 1992). This is work with Tom Anastasio and Jared Bronski (UIUC).

uk: вхід без авторизації

name: A geometric method for analyzing operators with low-rank perturbations


uk: Математика, природничі науки

description: The Krein matrix is a matrix-valued function which can be used to study Hamiltonian spectral problems. Akin to the Evans matrix, it has the property that it is singular when evaluated at an eigenvalue. Unlike the Evans matrix, it is not analytic, but is instead meromorphic. I will briefly go over its construction, and then apply it to the study of spectral stability of small periodic waves for a couple of equations.

uk: вхід без авторизації

name: Analyzing Hamiltonian spectral problems via the Krein matrix


uk: Математика, природничі науки

description: This talk will consider the stability of time independent solutions to the incompressible, inviscid Euler equations on the torus whose stream functions have the form ψ=U(ξ)=U(p1x+p2y) for fixed integers p1 and p2. By an appropriate change of coordinates and separation of variables, the linearised spectral problem is reduced to the study of a Hill's equation with a complex potential. By using Hill determinants, an Evans function of the original linearised Euler equation can be constructed. For certain, well-known shear flows, the form of the Hill determinant makes such an Evans function numerically straightforward to compute.

uk: вхід без авторизації

name: An Evans function for 2-D shear flows of the Euler equations on the torus


uk: Математика, природничі науки

description: For Hamiltonian systems of PDEs the stability of periodic waves is encoded by the Hessian of an action integral, as shown in earlier work. This talk will deal with two asymptotic regimes, namely for waves of small amplitude and for waves of long wavelength. In both cases stability criteria can be investigated analytically, thanks to the asymptotic expansions of the Hessian of the action and their special structure. The stability results thus obtained apply to various models of mathematical physics for nonlinear dispersive waves.

uk: вхід без авторизації

name: Stability of periodic waves in Hamiltonian PDEs


uk: Математика, природничі науки

description: We consider the Whitham equation on the whole line. Due to the smoothing nature of the linear operator, the question for existence of traveling wave solutions has been open till recently. In 2012, Ehrnstroem-Groves-Wahlen (EGW) have constructed such waves, but only for values of c slightly bigger than one, even though the admissible range of wave speeds is c∈(1,2). The approach in EGW consists of a tour de force calculus of variations, supplemented by a bifurcation argument from the small KdV waves. Note that the EGW waves are of small amplitude. In this work (joint with M. Ehrnstroem), we construct a one parameter family of such waves, with wave speeds c∈(1,c0) for some limiting value c0, not necessarily close to 1. We conjecture that the wave with speed c0 is the maximal amplitude wave (i.e. the highest wave, with amplitude c/2) and there are no waves with wave speeds c∈(c0,2). However, we still find some interesting objects in the interval (c0,2). The argument uses calculus of variation construction, very different than the one employed by EGW. It is based on constraints on appropriately selected Orlicz spaces. Finally, all our traveling waves are shown to be bell-shaped, confirming the available numerical evidence. I will also speculate a bit about their stability as they are constructed as ground states of the appropriate constrained maximization problems.

uk: вхід без авторизації

name: Solitary waves for the Whitham equation on the whole line


uk: Математика, природничі науки

description: In this talk, we explore the simplest equation that exhibits high frequency instabilities, the fifth-order Korteweg-de Vries equation. We show how to derive the necessary condition for an instability of a perturbation of a small amplitude, periodic travelling wave solutions. We proceed by examining how these unstable perturbations change and grow in time as the underlying solution changes. We conclude by commenting on what happens with a different nonlinearity in the underlying equation.

uk: вхід без авторизації

name: Stability of periodic travelling wave solutions to Korteweg-de Vries and related equations


uk: Математика, природничі науки

description: In this talk, we will discuss the influence of inhibition on an activity-based neural field model consisting of an excitatory population with a linear adaptation term that directly regulates the activity of the excitatory population. Such a model has been used to replicate cortical traveling wave data as observed in clinical recordings. We will establish conditions for the existence of traveling wave solutions with properties observed in in vivo data. We will also discuss some results concerning the linear stability of traveling wave solutions of this model via the construction of an Evans function.

uk: вхід без авторизації

name: On the study of traveling wave solutions on a cortical wave propagation model including inhibition


uk: Математика, природничі науки

description: This is a joint work with M. Beck, G. Cox, C. Jones, R. Marangell, K. McQuighan, A. Sukhtayev, and S. Sukhtaiev. In this talk we discuss some recent results on connections between the Maslov and the Morse indices for differential operators. The Morse index is a spectral quantity defined as the number of negative eigenvalues counting multiplicities while the Maslov index is a geometric characteristic defined as the signed number of intersections of a path in the space of Lagrangian planes with the train of a given plane. The problem of relating these two quantities is rooted in Sturm's Theory and has a long history going back to the classical work by Arnold, Bott, Duistermaat, Smale, and has attracted recent attention of several groups of mathematicians. We will briefly mention how the relation between the two indices helps to prove the conjecture that a pulse in a gradient system of reaction diffusion equations is unstable. We will also discuss a fairly general theorem relating the indices for a broad class of multidimensional elliptic self-adjoint operators.

uk: вхід без авторизації

name: The Maslov index and the spectrum of differential operators


uk: Математика, природничі науки

description: Some PDEs and ODEs admit a Lax pair (a pair of linear operators) to be completely solve the equation. One of these operators defines a spectral problem. For some equations (as for the Korteweg-deVries, KdV, equation) this operator is self-adjoint and, consequently, its discrete spectrum is real. However, for some other equations, this operator is non-selfadjoint, such as for the nonlinear Schrödinger (NLS) equation or the Ablowitz-Ladik equation. In 2001, M. Klaus and J. K. Shaw found symmetries and conditions on the potentials for the Zakharov-Shabat system (spectral problem for the NLS equation) for the eigenvalues to lie on the imaginary axis. In this talk, I will show which would be an equivalent to the Klaus-Shaw theorem for the Ablowitz-Ladik lattice. This is a work in progress. This is a joint work with P. Shipman (Colorado State University) and S. Shipman (Louisiana State University).

uk: вхід без авторизації

name: Klaus-Shaw potentials for the Ablowitz-Ladik lattice


uk: Математика, природничі науки

description: Mesenchymal migration is a proteolytic and path generating strategy of individual cell motion inside the network of collagen fibres that compose the extracellular matrix of tissues. We analyze the spectral stability of the families of standing and traveling wave solutions of the one-dimensional version of the $M^5$-model, which was proposed by T. Hillen to describe mesenchymal cell movement. Regarding the standing waves, they are spectrally stable and the spectrum of the linearized operator around the waves consists solely of essential spectrum. To prove that in the standing case the point spectrum is empty we use energy estimates together with the integrated-variable technique of Goodman. The panorama is completely different in the traveling case; the wave profiles are spectrally unstable due to the fact that the essential spectrum reaches the closed right-half complex plane. In our pursuit of spectral stability, we have constructed a weighted Sobolev space where the essential spectrum lies inside the open left-half complex plane.

uk: вхід без авторизації

name: One-dimensional M5-model for mesenchymal migration


uk: Математика, природничі науки

description: In the present work, we intend to explore a variant of the ϕ6 model originally proposed in \textit{Phys. Rev. D} \textbf{12}, 1606 (1975) as a prototypical, so-called, ``bag'' model where domain walls play the role of quarks within hadrons. We examine the prototypical steady state of the model, namely an apparent bound state of two kink structures. We explore its linearization and find that as a function of a prototypical parameter controlling the curvature of the potential an effectively arbitrary number of internal modes may arise in the point spectrum of the linearized analysis. We \textit{intend to} use Evans function analysis to predict the bifurcation points of the relevant internal modes and confirm these theoretical predictions numerically. Finally, given the remarkable flexibility of the model in possessing different numbers of internal modes we \textit{once again intend to} explore the dynamics of multi-bound-state collisions to identify the role of the additional internal modes in enhancing the complexity of the observed scattering scenarios. I. Christov, P. G. Kevrekidis, A. Saxena, and R. Decker are my collaborators.

uk: вхід без авторизації

name: Kink dynamics in a parametric ϕ6 system: a model with controllably many internal modes


uk: Математика, природничі науки

description: The present talk deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Firstly, our main result does not depend on the parametrization of the periodic wave itself. Secondly, motivated by the well known orbital stability criterion for solitary waves, we show that the same criterion holds for periodic waves. In addition, we show that the positiveness of the principal entries of the Hessian matrix related to the ``energy surface function'' are also sufficient to obtain the stability. Consequently, we can establish the orbital stability of periodic waves for several nonlinear dispersive models. We believe our method can be applied in a wide class of evolution equations; in particular it can be extended to regularized dispersive wave equations. This is a joint work with A. Pastor (IMECC/UNICAMP-Brazil) and G. Alves (ULCO-France).

uk: вхід без авторизації

name: Sufficient conditions for orbital stability of periodic traveling waves


uk: Математика, природничі науки

description: Models describing waves in anisotropic media or media with imperfections usually have inhomogeneous terms. Examples of such models can be found in many applications, for example in nonlinear optical waveguides, water waves moving over a bottom with topology, currents in nonuniform Josephson junctions, DNA-RNAP interactions etc. Travelling waves in such models tend to interact with the inhomogeneity and get trapped, reflected, or slowed down. In this talk, wave equations with finite length inhomogeneities will be considered, assuming that the spatial domain can be written as the union of disjoint intervals, such that on each interval the wave equation is homogeneous. The underlying Hamiltonian structure allows for a rich family of stationary front solutions and the values of the energy (Hamiltonian) in each intermediate interval provide natural parameters for the family of orbits. It will be shown that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the energy density inside the inhomogeneity and we give a necessary and sufficient criterion for the change of stability. These results will be illustrated with some examples.

uk: вхід без авторизації

name: Existence and stability of fronts in inhomogeneous wave equations


uk: Математика, природничі науки

description: We consider a model of combustion in hydraulically resistant porous media. There are several reductions of this systems that can be used to understand the evolution of the combustion fronts. One reduction is based on the assumption that the ratio of pressure and molecular diffusivities is close to zero, a different reduction is obtained when the Lewis number chosen in a specific way. Fronts exists in both reduced systems. For the stability analysis of the fronts, we, first, consider initial conditions of a specific form, then show that the stability results extend to the fronts in the full system with the same Lewis number. The fronts are either absolutely unstable or convectively unstable.

uk: вхід без авторизації

name: Stability of traveling fronts in a model for porous media combustion

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


uk: Математика, природничі науки

description: Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier-Stokes shocks across the full range of shock amplitudes, including the infinite-amplitude limit, for monatomic or diatomic ideal gas equations of state and viscosity and heat conduction coefficients constant and in the physical ratios predicted by statistical mechanics, with Mach number $M>1.035$. Our results indicate unconditional stability within the parameter range considered, in agreement with the results of Erpenbeck and Majda in the corresponding inviscid case. Notably, this study includes the first successful numerical Evans computation for multi-dimensional stability of a viscous shock wave. This is joint work with J. Humpherys (BYU) and K. Zumbrun (Indiana).

uk: вхід без авторизації

name: Multidimensional stability of large-amplitude Navier-Stokes shocks


keywords: Calculus of variations and optimal control

uk: Математика, природничі науки

uk: вхід без авторизації

name: Some Dislocation Challenges For Mathematicians


uk: Математика, природничі науки

uk: вхід без авторизації

name: Evolutionary convergence of positive and negative dislocations in 2D


uk: Математика, природничі науки

uk: вхід без авторизації

name: Quantum Dots and Dislocations: Dynamics of Materials Defects


Dislocations in graphene

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Nearly Parallel Vortex Filaments in the 3D Ginzburg-Landau Equations.


uk: Математика, природничі науки

uk: вхід без авторизації

name: Discrete-to-continuum analysis for a generalized XY model: fractional vortices and string defects


uk: Математика, природничі науки

uk: вхід без авторизації

name: Discrete and continuum approaches to dislocation dynamics


uk: Математика, природничі науки

uk: вхід без авторизації

name: The relation between Willmore surfaces and the Cahn-Hilliard equation


uk: Математика, природничі науки

uk: вхід без авторизації

name: The ellipse law: from Kirchhoff elliptic vortices to dislocations


uk: Математика, природничі науки

uk: вхід без авторизації

name: Solving S-unit, Mordell, Thue, Thue–Mahler and generalized Ramanujan–Nagell equations via Shimura–Taniyama conjecture


uk: Математика, природничі науки

description: What makes an intersection likely or unlikely? A simple dimension count shows that two varieties of dimension r and s are non "likely" to intersect if r < codim s, unless there are some special geometrical relations among them. A series of conjectures due to Bombieri-Masser-Zannier, Zilber and Pink rely on this philosophy. After a small survey on these problems, I will speak about a joint work with F. Barroero (Basel) in this framework in the special case of curves in families of abelian varieties. This gives also applications to the study of the solvability of some polynomial Diophantine equations.

uk: вхід без авторизації

name: Unlikely intersections in families of abelian varieties and some polynomial Diophantine equations


uk: Математика, природничі науки

uk: вхід без авторизації

name: On k-free integers represented by binary forms


uk: Математика, природничі науки

uk: вхід без авторизації

name: A problematic excursion at the interface of number theory and analysis


uk: Математика, природничі науки

description: In 2002, Corvaja and Zannier obtained a new proof of Siegel's theorem (on integral points on curves) based on Schmidt's celebrated Subspace Theorem. Soon after that (and based on earlier work), Evertse and Ferretti applied Schmidt's theorem to give diophantine results for homogeneous polynomials of higher degree on a projective variety in Pn. This has led to further work of A. Levin, P. Autissier, M. Ru, G. Heier, and others. In particular, Ru has defined a number, \Nev(D), that concisely describes the best diophantine approximation obtained by this method, where D is an effective Cartier divisor on a projective variety X. In this talk, I will give an overview of variants of \Nev(D) as developed by Ru and myself, and indicate how an example of Faltings can be derived using these constants.

uk: вхід без авторизації

name: Birational Nevanlinna Constants and an Example of Faltings


uk: Математика, природничі науки

description: Many finiteness and enumerative problems in number theory rely on the finiteness/enumeration of the set of solutions to the equation x+y=1 over the group of S-units in a number field, where S is a finite set of primes. In 1995, Nigel Smart solved certain S-unit equations to enumerate all genus 2 curves defined over the rationals with good reduction away from p=2. Smart's work build on that of of Baker, de Weger, Evertse, Yu, and many others. In 2016, following Smart's methods, Malmskog and Rasmussen found all Picard curves over Q with good reduction away from p=3, and Angelos Koutsianas described methods for enumerating, and in some cases explicitly describes, all elliptic curves defined over a number field with good reduction outside S. Both projects required Sage implementation of special cases of Smart's general method. In January 2017, Alejandra Alvarado, Angelos Koutsianas, Beth Malmskog, Christopher Rasmussen, Christelle Vincent, and Mckenzie West combined these implementations and created new functions to solve the equation x+y=1 over the S-units of a general number field K for any finite set S of primes in K. The code is available on SageTrac and is under review for inclusion in future releases of Sage. This talk will give an overview of motivating problems and applications, the methods involved, and the current state of the implementation.

uk: вхід без авторизації

name: Solving S-unit equations in Sage and Applications to Algebraic Curves


uk: Математика, природничі науки

uk: вхід без авторизації

name: K-rational preperiodic hypersurfaces on Pn


Elliptic curves and isogenies

uk: Математика, природничі науки

uk: вхід без авторизації

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


uk: Математика, природничі науки

uk: вхід без авторизації

name: Uniformity of integral points in curves and surfaces


uk: Математика, природничі науки

uk: вхід без авторизації

name: New Pade approximation related to a series with periodic coefficients


uk: Математика, природничі науки

uk: вхід без авторизації

name: Finding well approximating lattices for a finite set of points


uk: Математика, природничі науки

uk: вхід без авторизації

name: S-parts of values of binary forms and decomposable forms


uk: Математика, природничі науки

uk: вхід без авторизації

name: On the digital representation of smooth numbers


uk: Математика, природничі науки

uk: вхід без авторизації

name: Eight Vertices, but only One Centre: Quadration


Numerical Range and Dilation

uk: Математика, природничі науки

description: We survey some results concerning the use of numerical ranges to study dilation theory of operators. Connections to problems arising in quantum information science will be mentioned.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Let $A$ be a matrix with spectrum $\sigma(A)$. The Kreiss Matrix Theorem (KMT), a well-known fact in applied matrix analysis, gives estimates of upper bounds for $\|A^n\|$ if $\sigma(A)$ is in the unit disc, or for $\|\text{e}^{tA}\|$ if $\sigma(A)$ is in the left-half plane based on the resolvent norm, or equivalently the pseudospectra. In this talk, we will discuss the extension of this celebrated theorem to an arbitrary holomorphic function. We will first briefly talk about the norm behavior of matrices that have identical or super-identical pseudospectra. Next we will focus on some generalizations of KMT for holomorphic functions on a general complex domain.

uk: вхід без авторизації

name: Pseudospectra and Kreiss Matrix Theorem on a General Domain


uk: Математика, природничі науки

description: A square matrix can be reduced to simpler form via similarity transformations. Here ``simpler form'' may refer to diagonal (when possible), triangular (Schur), or Hessenberg form. Similar reductions exist for matrix pencils if we consider general equivalence transformations instead of similarity transformations. For both matrices and matrix pencils, well-established algorithms are available for each reduction, which are useful in various applications. For matrix polynomials, unimodular transformations can be used to achieve the reduced forms but we do not have a practical way to compute them. In this work we introduce a practical means to reduce a matrix polynomial with nonsingular leading coefficient to a simpler (diagonal, triangular, Hessenberg) form while preserving the degree and the eigenstructure. The key to our approach is to work with structure preserving similarity transformations applied to a linearization of the matrix polynomial instead of unimodular transformations applied directly to the matrix polynomial. As an applications, we will illustrate how to use these reduced forms to solve parameterized linear systems.

uk: вхід без авторизації

name: Reducing Matrix Polynomials to Simpler Forms


uk: Математика, природничі науки

description: Finite, discrete, time-homogeneous Markov chains are frequently used as a simple mathematical model of real-world dynamical systems. In many such applications, an analysis of clustering behaviour is desirable, and it is well-known that the eigendecomposition of the transition matrix $T$ of the chain can provide such insight. In a recent paper (see [1]), a method is presented for determining clusters from a subdominant real eigenvalue $\lambda$ of $T$ which is close to the spectral radius 1. In this talk, we extend the method to include an analysis for complex eigenvalues of $T$ which are close to 1. Since a real spectrum is not guaranteed in most applications, this is a valuable result in the area of spectral clustering in Markov chains. This is joint work with Emanuele Crisostomi, Mahsa Faizrahnemoon, Steve Kirkland, and Robert Shorten. [1] Emanuele Crisostomi, Stephen Kirkland, and Robert Shorten. A Google-like model of road network dynamics and its application to regulation and control. $\textit{International Journal of Control}$, 84(3):633--651, 2011.

uk: вхід без авторизації

name: Clustering in Markov Chains with Subdominant Eigenvalues Close to One


uk: Математика, природничі науки

description: We consider upper Hessenberg unitary-plus-rank-one matrices, that is, matrices of the form $A = \tilde{U} + \tilde{x}\tilde{y}^{T}$, where $\tilde{U}$ is unitary, and $A$ is upper Hessenberg. This includes the class of Frobenius companion matrices, so methods for this type of matrix can be applied to the problem of finding the zeros of a polynomial. The unitary-plus-rank-one structure is preserved by any method that performs unitary similarity transformations, including Francis's implicitly-shifted $QR$ algorithm. We present a new implementation of Francis's algorithm that acts on a data structure that stores the matrix in $O(n)$ space and performs each iteration in $O(n)$ time. This is joint work with Jared Aurentz, Thomas Mach, and Raf Vandebril. Ours is not the first fast algorithm that has been proposed for this problem, but it is the first that has been shown to be backward stable, and it is faster than other fast algorithms that have been proposed previously.

uk: вхід без авторизації

name: Fast, Stable, Computation of the Eigenvalues of Unitary-plus-rank-one Matrices, including Companion Matrices


uk: Математика, природничі науки

description: In 2015, Armario conjectured that there exists a skew-symmetric EW matrix of order $4t+2$ if and only if there exists a tournament matrix $A$ with characteristic polynomial \[ \chi_A(x) = \left ( x^3 - (2t-1)x^2 - t(4t-1) \right ) \left ( x^2+x+t \right )^{2t-1}. \] In this talk, we prove Armario's conjecture . This is based on joint work with Gary Greaves.

uk: вхід без авторизації

name: Skew-symmetric EW Matrices and Tournaments


uk: Математика, природничі науки

description: According to a long standing conjecture (sometimes called the Perfect-Mirsky conjecture), the geometric location of eigenvalues of doubly stochastic matrices of order $n$ is exactly the union of all regular $k$-gons with $2 \leq k\leq n$ and anchored at 1 in the closed unit disc. It is easy to verify this fact for $n =2$ and $n=3$. But, for $n\geq  4$, it was an open question at least since 1965. Mashreghi-Rivard (2007) showed that the conjecture is wrong for $n = 5$. Then Levick-Pereira-Kribs (2014) added to the mystery by showing that the conjecture is true for $n=4$. For $n \geq 6$, the loci of eigenvalues is unknown. They also came up with a new formulation of the conjecture.

uk: вхід без авторизації

name: Eigenvalues of Doubly Stochastic Matrices, an Unfinished Story


uk: Математика, природничі науки

description: An $n$-by-$m$ Cauchon diagram $C$ is an $n$-by-$m$ grid consisting of $n∙m$ squares colored black and white, where each black square has the property that every square to its left (in the same row) or every square above it (in the same column) is black. Let $A=(a_{ij})$ be an $n$-by-$m$ matrix and $C$ an $n$-by-$m$ Cauchon diagram. Then we say that $A$ is a Cauchon matrix associated with the Cauchon diagram $C$ if for all $(i,j) \in \{1,…,n\} \times \{1,…,m\}$, we have $a_{ij}=0$ if and only if the corresponding square $(i,j)$ in $C$ is black. In this talk, we present a novel method for the determination of the rank of a matrix A and for checking a set of its consecutive row (or column) vectors for linear independence provided that the resulting matrix $\tilde{A}$ of the application of the condensed form of the Cauchon algorithm, see e.g., [2], is a Cauchon matrix. This method is also linked to the elementary bidiagonal factorization of a matrix under certain conditions [1]. This is joint work with Khawla Al Muhtaseb and Ayed Abdel Ghani (Palestine Polytechnic University, Hebron, Palestine), Shaun M. Fallat (University of Regina, Regina, Canada), and Juergen Garloff (University of Applied Sciences / HTWG Konstanz, and University of Konstanz, Konstanz, Germany). References: [1] M. Adm, K. Al Muhtaseb, A. Abedel Ghani, S. Fallat, and J. Garloff, A novel method for determining the rank of a matrix with application to bidiagonal factorization, submitted. [2] M. Adm and J. Garloff, Improved tests and characterizations of totally nonnegative matrices, Electron. J. Linear Algebra, 27, 588-610, 2014.

uk: вхід без авторизації

name: A Novel Method for Determining the Rank of a Matrix


uk: Математика, природничі науки

description: New and old results will be presented on the Envelope, $E(A)$, which is a bounded region in the complex plane that contains the eigenvalues of a complex matrix $A$. $E(A)$ is the intersection of an infinite number of regions defined by elliptic curves. As such, $E(A)$ resembles and is contained in the numerical range of $A$, which is the intersection of an infinite number of half-planes. The Envelope, however, can be much smaller than the numerical range, while not being much harder to compute.

uk: вхід без авторизації

name: Envelope: Localization of the Spectrum of a Matrix


uk: Математика, природничі науки

description: Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and such a network can be modelled mathematically by a graph. Here, we focus on the corresponding Laplacian matrix, and those graphs for which the Laplacian can be diagonalized by a Hadamard matrix. We characterize the graphs that are diagonalizable by the standard Hadamard matrix, showing a direct relationship to cubelike graphs. We give some example constructions illustrating our results. ${\bf Co-author(s):}$ N. Johnston (Mount Allison University), S. Kirkland (University of Manitoba), R. Storey (Brandon University), and X. Zhang (University of Manitoba).

uk: вхід без авторизації

name: Hadamard Diagonalizability and Cubelike Graphs


uk: Математика, природничі науки

description: It is well known that a complex zero-nonzero pattern cannot be spectrally arbitrary if its digraph doesn’t have at least two loops and at least one two cycle, or at least three loops. This talk focuses on several other combinatorial conditions on the digraph that preclude it from being spectrally arbitrary. In particular we are sometimes able to reduce the number of unknown entries to be below the threshold of $2n−1$. Furthermore there are several algebraic conditions on the coefficients of the characteristic polynomial that can be exploited to show that a pattern is not spectrally arbitrary over any field. Using Sage we were able to show that no zero-nonzero pattern with $2n−1$ nonzero entries will be spectrally arbitrary over $C$ where $n≤6$. When $n=7$ we find two zero-nonzero patterns that do not satisfy our algebraic conditions precluding them from being spectrally arbitrary.

uk: вхід без авторизації

name: Combinatorial and Algebraic Conditions that Preclude SAPpiness


uk: Математика, природничі науки

description: The notion of type of quadruples of rows is proven to be useful in the classification of Hadamard matrices. We investigate Hadamard matrices with few distinct types. Apparently, Hadamard matrices with few distinct types are very rare and have nice combinatorial properties. We show that there exists no Hadamard matrix of order larger than $12$ whose quadruples of rows are all of the same type. We then focus on Hadamard metrics with two distinct types. Among other results, the Sylvester Hadamard matrices are shown to be characterized by their spectrum of types. This is a joint work with A. Mohammadian.

uk: вхід без авторизації

name: Hadamard Matrices with Few Distinct Types

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


uk: Математика, природничі науки

description: This talk concerns the corona type Bezout equation $G(z)X(z)=I_p$, $z$ in $BD$. The function $G$ is the given function and $X$ is the unknown. Both functions are stable rational matrix functions, $G$ is of size $p\times q$ and $X$ of size $q\times p$, and $I_p$ stands for the $p\times p$ identity matrix. Here \emph{stable} means that the poles of the rational matrix functions involved are all outside the closed unit disc, and hence the entries of these matrix functions are $H^\infty$- functions. We shall use state space techniques from mathematical system theory to obtain necessary and sufficient conditions for existence of solutions. Furthermore, we derive an explicit formula for the least squares solution and an explicit description of all solutions, all in terms of a state space realization of the given function $G$. The state space formula for the least squares solution is easy to use in Matlab, and it shows that the McMillan degree of this solution is less than or equal to the McMillan degree of $G$. The talk is based on joint work with Art Frazho (Purdue University) and Andre Ran (VU Amsterdam).

uk: вхід без авторизації

name: Bezout Equations for Stable Rational Matrix Functions: The Least Squares Solution and Description of all Solutions


uk: Математика, природничі науки

uk: вхід без авторизації

name: On Working with Peter Lancaster for More than 50 Years


keywords:
Mathematics
Dynamical systems and ergodic theory
Global analysis, analysis on manifolds
Dynamical systems

uk: Математика, природничі науки

uk: вхід без авторизації

name: Introduction to sofic groups and entropy theory


Introduction to mean dimension

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Dynamical systems and C*-algebras: Up, up and away!


uk: Математика, природничі науки

description: I will show that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well-known factor theorem of Sinai.

uk: вхід без авторизації

name: Positive entropy actions of countable groups factor onto Bernoulli shifts


Blind multiband sampling algorithms

uk: Математика, природничі науки

description: For fixed A, N, L > 0, consider the set M of all L2 functions (signals) on the real line whose spectrum (i.e. support of the Fourier transform) is contained in the interval [-A, A] and simultanuosly in a sum of N intervals, each of length at most L (which can be positioned anywhere inside the interval [-A, A]). Blind multiband sampling deals with the problem of existence of a (stable) sampling set for M, i.e. a discrete subset of the real line, such that the signal from M is uniquely determined by its values on this set. During the talk I would present effective (yet, in general, not providing perfect reconstruction) algorithms for blind multiband sampling proposed by Y. Eldar and C. Mishali, which are based on the idea of compressed sensing.

uk: вхід без авторизації


uk: Математика, природничі науки

description: I would like to give a talk about a new Ornstein-Weiss type subadditive convergence theorem along hyperfinite exhaustions of pmp Borel equivalence relations. In collaboration with Amos Nevo (Techion), we used this result to define a new notion of entropy (cocycle entropy) for pmp actions of abritrary countable groups. It has turned out that for free actions, cocycle entropy coincides with Rokhlin entropy which is studied by Brandon Seward et al. However, using subadditive convergence techniques in order to assign entropy values to measured partitions, our definition is a priori quite different and more in line with the classical Kolmogorov-Sinai approach. Moreover, extending Elon Lindenstrauss' techniques to hyperfinite equivalence relations, we were able to settle the underlying Shannon-McMillan-Breiman theorem for a vast collection of pmp actions of general countable groups. Being of very general nature, we expect that our subadditive convergence theorem will have further important applications for non-amenable entropy theory and beyond. In the framework of future reserach activities, it is planned to define topological cocycle entropy and investigate the validity of a variational principle in terms of relation invariant measures. Further projects might concern (cocycle) mean dimension and determining the entropy for algebraic actions.

uk: вхід без авторизації

name: Subadditive convergence via hyperfinite equivalence relations


uk: Математика, природничі науки

description: In this talk I discuss higher dimensional versions of topological Rokhlin lemmas in a noncommutative context. I also describe the use of such lemmas in the structure and classification theory of simple amenable C*-algebras. Finally, I describe how to use Cartan MASAs to extract dynamical information from crossed product C*-algebras, both in the case of classical topological dynamical systems and coarse metric spaces.

uk: вхід без авторизації

name: Dimension type conditions in dynamics and C*-algebras


uk: Математика, природничі науки

description: Slow dimension growth condition is one of essentials in the classification of simple amenable C*-algebras, and it implies that the algebra is regular for the purpose of the classification, i.e., the algebra absorbs the Jiang-Su algebra Z tensorially. Consider a minimal homeomorphism with mean dimension zero, then the corresponding C*-algebra is shown to have slow dimension growth, and hence is covered by the recent progress of the classification program. In particular, this includes the C*-algebra of any uniquely ergodic system. The talk is based on a joint work with George A. Elliott.

uk: вхід без авторизації

name: Classification of C*-algebras and minimal homeomorphisms with mean dimension zero


uk: Математика, природничі науки

description: For free actions of amenable groups, we discuss an equivalent characterization of the small boundary property in terms of the existence of disjoint open towers with Folner shapes, small diameters, and the remainder having small orbit capacity. An ingredient behind this, which might be of independent interest, is a characterization of the small boundary property as having a special kind of extension on a totally disconnected space. We pose the question of whether this result can be strengthened for the remainder of the towers to be small in a stronger sense, and relate this to a desirable outcome for transformation group C*-algebras. If time permits, we may discuss actions of groups with the Tempelman condition, or possible applications for embeddings into cubical shifts. This is joint work in progress with David Kerr.

uk: вхід без авторизації

name: An Ornstein-Weiss-Rokhlin lemma for free actions with the small boundary property


uk: Математика, природничі науки

uk: вхід без авторизації

name: Predictability and entropy for actions of amenable and non-amenable groups


uk: Математика, природничі науки

uk: вхід без авторизації

name: Metric mean dimension is useful: the case of Brody curves


Brody curves and mean dimension

uk: Математика, природничі науки

uk: вхід без авторизації


Følner sets in topological groups

uk: Математика, природничі науки

description: Generalizing classical work of Day and Følner for discrete groups, I will present characterizations of amenability of (not necessarily locally compact) topological groups in terms of the existence of almost invariant vectors and almost invariant finite subsets, and discuss some applications of these results, e.g., concerning the coarse geometry of Polish groups. This is joint work with Andreas Thom. Furthermore, linked with concentration of measure, the mentioned amenability criteria provide sufficient conditions for (a strong form of) extreme amenability, which can be used to prove the extreme amenability of topological groups of measurable maps. This is joint work with Vladimir Pestov.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Given a module M of the integral group ring ZG of a discrete group G, one has the von Neumann-Lueck rank of M defined in the L2-invariants theory, closely related to the l2-Betti numbers. One also has the algebraic action of G on the Pontryagin dual of M defined, which makes the dynamical invariants available. I will discuss that the von Neumann-Lueck rank corresponds to the mean dimension in the case G is sofic. Two ingredients are needed. The first is that we have to introduce the mean dimension of one action relative to an extension, which is the same as the absolute mean dimension for amenable group actions but new for sofic group actions. The second is a way to define mean length for modules of the group ring for sofic group G so that an addition formula holds, which also has application to the direct finiteness problem for group rings of G. This is joint work with Bingbing Liang.

uk: вхід без авторизації

name: Mean dimension and von Neumann-Lueck rank


uk: Математика, природничі науки

description: We improve Ornstein-Weiss' quasitiling of a countable amenable group to a "perfect" tiling. The price is that the number of shapes increases drastically, nonetheless we manage to keep the entropy equal to zero. It remains a challenge to encode the system of tilings in a 0-1 subshift. So far we can do that only under the additional Tempelman's condition. Joint work with Dawid Huczek and Guohua Zhang. Last part with Maxence Phalempin.

uk: вхід без авторизації

name: Tilings of amenable groups and a problem of codeability


uk: Математика, природничі науки

description: In this talk we survey the known connections and evidence supporting the conjectured equivalence of the following three properties of a closed, connected, orientable, irreducible 3-manifold W: (i) W admits a co-oriented taut foliation; (ii) W has a left-orderable fundamental group; (iii) W is a Heegaard-Floer L-space. In particular, we discuss the relativisation of the conjectures which led to the confirmation of the conjecture for graph manifolds, and the subsequent open problems suggested by the work of Jonathan Hanselman, Jake Rasmussen, Sarah Rasmussen and Liam Watson.

uk: вхід без авторизації

name: Heegaard-Floer homology, foliations, and the left-orderability of fundamental groups


uk: Математика, природничі науки

description: Following up on a recent talk I gave at Skye, I'll discuss a topological invariant associated to a left order on the fundamental group of a prime, closed, oriented 3-manifold. I'll also describe some instances in which a left order with non-vanishing invariant can be deformed to an order giving rise to a taut foliation, and I'll characterize which foliations can be achieved by such constructions.

uk: вхід без авторизації

name: Left orders, transverse actions, and ordered foliations


TQFT structures in link Floer homology

uk: Математика, природничі науки

description: We will discuss a TQFT for the full link Floer complex, involving decorated link cobordisms. It is inspired by Juhasz's TQFT for sutured Floer homology. We will discuss how the TQFT recovers standard bounds on concordance invariants like Ozsvath and Szabo's tau invariant and Rasmussen's local h invariants (which are normally proven using surgery theory) and also gives a new bound on Upsilon. We will also see how well known maps in the link Floer complex can be encoded into decorations on surfaces, and as an example we will see how Sarkar's formula for a mapping class group action on link Floer homology is recovered by some simple pictorial relations. Time permitting, we will also discuss how these pictorial relations give a connected sum formula for Hendricks and Manolescu's involutive invariants for knot Floer homology.

uk: вхід без авторизації


On Alexander polynomials of graphs

uk: Математика, природничі науки

description: Using Alexander modules, one can define a polynomial invariant for a certain class of graphs with a balanced coloring. We will give different interpretations of this polynomial by Kauffman state formula and MOY relations. Moreover, there is a Heegaard Floer homology of graphs whose Euler characteristic is the Alexander polynomial. This is joint work with Yuanyuan Bao.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Let {Kn} be the family of knots obtained by twisting a knot K along an unknot c. When the winding number of K about c is non-zero, we show the limit of g(Kn)/g4(Kn) is 1 if and only if the winding and wrapping numbers of K about c are equal. When equal, this leads to a description of minimal genus Seifert surfaces of Kn for |n|≫0 and eventually to a characterization of when c is a braid axis for K. We then use this characterization to show that satellite L-space knots are braided satellites*. This is joint work with Kimihiko Motegi that builds upon joint work with Scott Taylor. (* Modulo a conjecture whose solution by Hanselman-Rasmussen-Watson has been announced.)

uk: вхід без авторизації

name: Satellite L-space knots are braided satellites*