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GrDyAp SIGNED

Groups, Dynamics, and Approximation

Total Cost €

0

EC-Contrib. €

0

Partnership

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 GrDyAp project word cloud

Explore the words cloud of the GrDyAp project. It provides you a very rough idea of what is the project "GrDyAp" about.

foundation    lattices    fruitful    homological    rings    approximation    local    disconnected    themes    homology    extend    combinatorial    totally    seek    pz    invariant    basic    dynamical    interaction    situations    generally    adic    theorems    sophisticated    of    theoretical    infinite    topology    ergodic    context    sequences       ring    thourough    kaplansky    pursue    variety    group    laudenbach    padic    introduce    subgroups    tries    eversince    conjecture    topological    groups    global    riemannian    homotopy    probability    clarify    tools    line    tool    found    betti    respect    locally    theory    interacting    extremely    functional    algebraic    kervaire    attack    compact    actions    finiteness    invariants    forms    content    fundamental    mathematical    physics    symmetry    random    sciences    geometry    asymptotic    generalizations    indispensible    relationship    torsion    longstanding    notions    lay    break    mathematics    direct    finite    analyis   

Project "GrDyAp" data sheet

The following table provides information about the project.

Coordinator
TECHNISCHE UNIVERSITAET DRESDEN 

Organization address
address: HELMHOLTZSTRASSE 10
city: DRESDEN
postcode: 1069
website: http://www.tu-dresden.de/

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Project website https://tu-dresden.de/mn/math/geometrie/thom/forschung/erc-projekte
 Total cost 2˙000˙000 €
 EC max contribution 2˙000˙000 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-CoG
 Funding Scheme ERC-COG
 Starting year 2016
 Duration (year-month-day) from 2016-10-01   to  2021-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    TECHNISCHE UNIVERSITAET DRESDEN DE (DRESDEN) coordinator 2˙000˙000.00

Map

 Project objective

Eversince, the study of symmetry in mathematics and mathematical physics has been fundamental to a thourough understanding of most of the fundamental notions. Group theory in all its forms is the theory of symmetry and thus an indispensible tool in many of the basic theoretical sciences. The study of infinite symmetry groups is especially challenging, since most of the tools from the sophisticated theory of finite groups break down and new global methods of study have to be found. In that respect, the interaction of group theory and the study of group rings with methods from ring theory, probability, Riemannian geometry, functional analyis, and the theory of dynamical systems has been extremely fruitful in a variety of situations. In this proposal, I want to extend this line of approach and introduce novel approaches to longstanding and fundamental problems. There are four main interacting themes that I want to pursue: (i) Groups and their study using ergodic theory of group actions (ii) Approximation theorems for totally disconnected groups (iii) Kaplansky’s Direct Finiteness Conjecture and p-adic analysis (iv) Kervaire-Laudenbach Conjecture and topological methods in combinatorial group theory The theory of `2-homology and `2-torsion of groups has provided a fruitful context to study global properties of infinite groups. The relationship of these homological invariants with ergodic theory of group actions will be part of the content of Part (i). In Part (ii) we seek for generalizations of `2-methods to a context of locally compact groups and study the asymptotic invariants of sequences of lattices (or more generally invariant random subgroups). Part (iii) tries to lay the foundation of a padic analogue of the `2-theory, where we study novel aspects of p-adic functional analysis which help to clarify the approximation properties of (Z/pZ)-Betti numbers. Finally, in Part (iv), we try to attack various longstanding combinatorial problems in group theory with tools from algebraic topology and p-local homotopy theory.

 Publications

year authors and title journal last update
List of publications.
2018 Henrik Densing Petersen, Roman Sauer, Andreas Thom
L2-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices
published pages: 257-282, ISSN: 1753-8416, DOI: 10.1112/topo.12056
Journal of Topology 11/1 2019-06-18
2018 Andreas Kübel, Andreas Thom
Equivariant differential cohomology
published pages: 8237-8283, ISSN: 0002-9947, DOI: 10.1090/tran/7315
Transactions of the American Mathematical Society 370/11 2019-05-29
2018 Andreas Thom, John Wilson
Some geometric properties of metric ultraproducts of finite simple groups
published pages: 113-129, ISSN: 0021-2172, DOI: 10.1007/s11856-018-1721-1
Israel Journal of Mathematics 227/1 2019-05-29
2019 Philip A. Dowerk, Andreas Thom
Bounded normal generation and invariant automatic continuity
published pages: 124-169, ISSN: 0001-8708, DOI: 10.1016/j.aim.2019.01.047
Advances in Mathematics 346 2019-06-06
2019 Henry Bradford, Andreas Thom
Short laws for finite groups and residual finiteness growth
published pages: 6447-6462, ISSN: 0002-9947, DOI: 10.1090/tran/7518
Transactions of the American Mathematical Society 371/9 2019-06-06
2018 Nikolay Nikolov, Jakob Schneider, Andreas Thom
Some remarks on finitarily approximable groups
published pages: 239-258, ISSN: 2270-518X, DOI: 10.5802/jep.69
Journal de l’École polytechnique — Mathématiques 5 2019-05-29
2018 Nikolay Nikolov, Jakob Schneider, Andreas Thom
Some remarks on finitarily approximable groups
published pages: 239-258, ISSN: 2270-518X, DOI: 10.5802/jep.69
Journal de l’École polytechnique — Mathématiques 5 2019-06-06
2019 Marcus De Chiffre, Narutaka Ozawa, Andreas Thom
OPERATOR ALGEBRAIC APPROACH TO INVERSE AND STABILITY THEOREMS FOR AMENABLE GROUPS
published pages: 98-118, ISSN: 0025-5793, DOI: 10.1112/s0025579318000335
Mathematika 65/1 2019-06-06
2018 Friedrich Martin Schneider, Andreas Thom
On Følner sets in topological groups
published pages: 1333-1361, ISSN: 0010-437X, DOI: 10.1112/s0010437x1800708x
Compositio Mathematica 154/7 2019-05-29

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