InvGroGra SIGNED
Asymptotic invariants of discrete groups, sparse graphs and locally symmetric spaces
Total Cost €
0EC-Contrib. €
0Partnership
0Views
0InvGroGra 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.
Project "InvGroGra" data sheet
The following table provides information about the project.
| Coordinator |
MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Organization address contact info |
| 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.
| # | ||||
|---|---|---|---|---|
| 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 |
|---|---|---|---|
| 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, Åukasz Almost commuting matrices with respect to the rank metric published pages: , ISSN: , DOI: |
2 | 2020-04-14 |
| 2019 |
Dorottya Beringer, Ãdám 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 |
Are you the coordinator (or a participant) of this project? Plaese send me more information about the "INVGROGRA" project.
For instance: the website url (it has not provided by EU-opendata yet), the logo, a more detailed description of the project (in plain text as a rtf file or a word file), some pictures (as picture files, not embedded into any word file), twitter account, linkedin page, etc.
Send me an email (fabio@fabiodisconzi.com) and I put them in your project's page as son as possible.
Thanks. And then put a link of this page into your project's website.
The information about "INVGROGRA" are provided by the European Opendata Portal: CORDIS opendata.