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InvGroGra SIGNED

Asymptotic invariants of discrete groups, sparse graphs and locally symmetric spaces

Total Cost €

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EC-Contrib. €

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Partnership

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 InvGroGra project word cloud

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

preserve    symmetric    gradient    ergodic    estimates    dimer    radius    object    spectral    l2    points    space    essentially    subgroups    plancherel    group    continuous    energy    list    theoretic    arising    tools    minimal    worlds    countable    polynomials    limit    measured    groups    flows    graphings    discrete    statistical    convergence    behavior    matching    serves    random    manifold    models    actions    automata    sofic    free    infinite    suitable    invariant    arbitrary    semisimple    unifying    cellular    girth    emerged    connections    locally    analytic    rank    world    giving    sparse    site    chromatic    equals    chain    volume    invariants    betti    complexes    deficiency    energies    ways    action    theory    language    spaces    profinite    game    initiated    notion    besides    monomer    lebesque    mechanics    probability    geometry    finite    asymptotic    proposes    connection    entropy    connect    graph    ramanujan    sequence    graphs    representation    injectivity    generators    versions    objects    pi   

Project "InvGroGra" data sheet

The following table provides information about the project.

Coordinator
MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET 

Organization address
address: REALTANODA UTCA 13-15
city: Budapest
postcode: 1053
website: http://www.renyi.hu

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

 Coordinator Country Hungary [HU]
 Project website http://www.renyi.hu/InvGroGra
 Total cost 1˙386˙250 €
 EC max contribution 1˙386˙250 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-CoG
 Funding Scheme ERC-COG
 Starting year 2015
 Duration (year-month-day) from 2015-07-01   to  2021-06-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET HU (Budapest) coordinator 1˙386˙250.00

Map

 Project objective

The PI proposes to study the asymptotic behavior of various invariants of discrete groups and their actions, of sparse graphs and of locally symmetric spaces. The game is to connect the asymptotic behavior of an invariant on a sequence of finite models to an analytic invariant on a suitable limit object of the sequence and then use the connection to get new results in both the finite and infinite worlds. The recently emerging notion of invariant random subgroups, initiated by the PI, serves as a unifying language for convergence.

These invariants include the minimal number of generators, deficiency, Betti numbers over arbitrary fields, various spectral and representation theoretic invariants, graph polynomials and entropy. The limit objects arising are invariant processes on groups, profinite actions, graphings, invariant random subgroups and measured complexes. The analytic invariants include L2 Betti numbers, spectral and Plancherel measures, cost and its higher order versions, matching and chromatic measures and entropy per site.

Energy typically flows both ways between the finite and infinite world and also between the different invariants. We list five recent applications from the PI that emerged from such connections. 1) Any large volume locally symmetric semisimple space has large injectivity radius at most of its points; 2) The rank gradient of a chain equals the cost-1 of the profinite action of the chain; 3) Countable-to-one cellular automata over a sofic group preserve the Lebesque measure; 4) Ramanujan graphs have essentially large girth; 5) The matching measure is continuous for graph convergence, giving new estimates on monomer-dimer free energies.

Besides asymptotic group theory and graph theory, the tools of the proposed research come from probability theory, ergodic theory and statistical mechanics. The proposed research will lead to further applications in 3-manifold theory, geometry and ergodic theory.

 Publications

year authors and title journal last update
List of publications.
2018 Fraczyk, Mikolaj; Szumowicz, Anna
On the optimal rate of equidistribution in number fields
published pages: , ISSN: , DOI:
3 2020-04-14
2018 Mészáros, András
Limiting entropy of determinantal processes
published pages: , ISSN: , DOI:
11 2020-04-14
2019 Abért, Miklós; Tóth, László Márton
Uniform rank gradient, cost and local-global convergence
published pages: , ISSN: , DOI:
3 2020-04-14
2018 Péter E. Frenkel
Convergence of graphs with intermediate density
published pages: 3363-3404, ISSN: 0002-9947, DOI: 10.1090/tran/7036
Transactions of the American Mathematical Society 370/5 2020-04-14
2019 Fraczyk, Mikolaj
Growth of mod$-2$ homology in higher rank locally symmetric spaces
published pages: , ISSN: , DOI:
1 2020-04-14
2018 Bencs, Ferenc; Tóth, László Márton
Invariant random subgroups of groups acting on rooted trees
published pages: , ISSN: , DOI:
11 2020-04-14
2019 Mikołaj Frączyk, Jean Raimbault
Betti numbers of Shimura curves and arithmetic three-orbifolds
published pages: 2359-2382, ISSN: 1937-0652, DOI: 10.2140/ant.2019.13.2359
Algebra & Number Theory 13/10 2020-04-14
2018 Elek, Gábor; Grabowski, Łukasz
Almost commuting matrices with respect to the rank metric
published pages: , ISSN: , DOI:
2 2020-04-14
2019 Dorottya Beringer, Ádám Timár
Controllability, Matching Ratio and Graph Convergence
published pages: 1080-1103, ISSN: 0022-4715, DOI: 10.1007/s10955-019-02225-3
Journal of Statistical Physics 174/5 2020-04-14
2016 Miklós Abért, Péter Csikvári, Péter E. Frenkel, Gábor Kun
Matchings in Benjamini–Schramm convergent graph sequences
published pages: 4197-4218, ISSN: 0002-9947, DOI: 10.1090/tran/6464
Transactions of the American Mathematical Society 368/6 2020-04-14
2018 Fraczyk, Mikolaj
Kesten\'s theorem for uniformly recurrent subgroups
published pages: , ISSN: , DOI:
accepted at Ergodic Theory and Dynamical Systems 2020-04-14
2018 Gabor Elek
Amenable purely infinite actions on the non-compact Cantor set
published pages: , ISSN: , DOI:
accepted at Ergodic Theory and Dynamical Systems 2020-04-14
2017 Péter Csikvári
Lower matching conjecture, and a new proof of Schrijver\'s and Gurvits\'s theorems
published pages: 1811-1844, ISSN: 1435-9855, DOI: 10.4171/JEMS/706
Journal of the European Mathematical Society 19/6 2020-04-14
2017 P. Csikvári, P. E. Frenkel, J. Hladký and T. Hubai
Chromatic roots and limits of dense graphs
published pages: , ISSN: 0012-365X, DOI:
Discrete Mathematics 340(5) (2017), pp. 1129–1135 2020-04-14
2017 Miklos Abert
A Spectral Strong Approximation Theorem for Measure Preserving Actions
published pages: , ISSN: 0143-3857, DOI:
Ergodic Theory and Dynamical Systems 2020-04-14
2017 Csikvári, Péter; Lin, Zhicong
Sidorenko\'s conjecture, colorings and independent sets
published pages: P1.2, ISSN: 1077-8926, DOI:
Electronic Journal of Combinatorics 24(1) 2020-04-14
2016 Endre Csóka
On the graph limit question of Vera T. Sós
published pages: 306-311, ISSN: 0095-8956, DOI: 10.1016/j.jctb.2015.09.003
Journal of Combinatorial Theory, Series B 116 2020-04-14
2018 Gábor Elek
Uniformly recurrent subgroups and simple C ⁎ -algebras
published pages: 1657-1689, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2018.01.004
Journal of Functional Analysis 274/6 2020-04-14
2017 Omer Angel, Duncan Dauvergne, Alexander E. Holroyd, Balint Virag
The Local Limit of Random Sorting Networks
published pages: , ISSN: 0294-1449, DOI:
Annales de l\'Institut Henri Poincaré 2020-04-14
2017 Miklos Abert, Tsachik Gelander, Nikolay Nikolov
Rank, combinatorial cost and homology torsion growth in higher rank lattices
published pages: , ISSN: 0012-7094, DOI:
Duke Mathematics Volume 166, Number 15 (2017), 2 2020-04-14
2017 Miklos Abert, Nicolas Bergeron, Ian Biringer, Tsachik Gelander, Nikolay Nikolov, Jean Raimbault, Iddo Samet
On the growth of L^2-invariants for sequences of lattices in Lie groups
published pages: 711-790, ISSN: 0003-486X, DOI: 10.4007/annals.2017.185.3.1
Annals of Mathematics 185/3 2020-04-14

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