September 2 - December 20, 2013
Organizers: Alexander Kechris, Katrin Tent, Anatoly Vershik
Description: The goal of the program was to study and link universality phenomena in different areas of pure mathematics. These areas included model theory, combinatorics, descriptive set theory, group theory, dynamical systems, especially ergodic theory and topological dynamics, random matrices and representation theory. In this way we promoted interactions in an unprecedented way between these different areas.
Universality is a pervasive notion in mathematics, and is suggestive of useful analogies between different areas. Examples are Fraïssé theory in logic, universal graphs in combinatorics, the universal Urysohn space in topology, universality in algebraic geometry, and so on. We considered it important to initiate a discussion of universality as a global phenomenon in mathematics, and brought together some of the main contributors.
The main reason for studying universal objects is that they may act as a frame of reference for what kind of results to expect, what kind of objects might exist and how homogeneous certain structures are. If a class of structures allows universal objects, studying these objects yields important insights into the class of structures and on individual structures of this class. Universal objects often serve both as examples for and counterexamples to theorems and conjectures. They are typically very homogeneous and reflect all properties that may or may not be realized. Model theory provides techniques for constructing and studying such objects. Also constructing a structure by a 'random' process often leads to the universal object of a certain class. Therefore, we obtained feedback in both directions from the universal object to random processes and conversely.
Associated Events:
- Trimester Seminar
- Mini Courses
- Workshop on Homogeneous Structures
- Special Seminar on Universality of moduli spaces and geometry
The Apostles Peter and Paul Domenikos Theotokopoulos (El Greco) 1587-92. Printed by permission of The State Hermitage Museum, St. Petersburg, Russia
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| No. | Author(s) | Title | Preprint | Publication |
| 2013c01 | Zalesski, A. E. | On the Steinberg character of an orthogonal group over a finite field | 1310.4440 | J. Algebra Appl. 13(7) (2014), 46. https://doi.org/10.1142/S0219498814500339 |
| 2013c02 | Wesolek, P. | Conjugacy class conditions in locally compact second countable groups | 1310.1561 | Proc. Amer. Math. Soc. 144(1) (2016), 399–409. https://doi.org/10.1090/proc/12645 |
| 2013c03 | Mildenberger, H. | Finitely many near-coherence classes of ultrafilters | 1404.7350 | |
| 2013c04 | Garbulińska-Wȩgrzyn, J.; Kubiś, W. | A universal operator on the Gurariĭ space | 1310.2380 | J. Operator Theory. 73(1) (2015), 143–158. https://doi.org/10.7900/jot.2013oct09.1999 |
| 2013c05 | Jasiński, J.; Laflamme, C.; Nguyen Van Thé, L.; Woodrow, R. | Ramsey precompact expansions of homogeneous directed graphs | 1310.6466 | Electron. J. Combin. 21(4) (2014), 31. https://doi.org/10.37236/3840 |
| 2013c06 | Bogachev, L. V. | Unified derivation of the limit shape for multiplicative ensembles of random integer partitions with equiweighted parts | 1111.3311 | Random Structures Algorithms. 47(2) (2015), 227–266. https://doi.org/10.1002/rsa.20540 |
| 2013c07 | Evans, D. M.; Tsankov, T. | Free actions of free groups on countable structures and property (T) | 1312.5140 | Fund. Math. 232(1) (2016), 49–63. https://doi.org/10.4064/fm232-1-4 |
| 2013c08 | Sabok, M. | Automatic continuity for isometry groups | 1312.5141 | J. Inst. Math. Jussieu. 18(3) (2019), 561–590. https://doi.org/10.1017/s1474748017000135 |
| 2013c09 | Vershik, A. M. | Intrinsic metric on graded graphs, standardness, and invariant measures | 1312.7239 | J. Math. Sci. (transl.). 200(6) (2014), 677–681. https://doi.org/10.1007/s10958-014-1958-0 |
| 2013c10 | Bartošová, D.; Kwiatkowska, A. | Lelek fan from a projective Fraïssé limit | 1312.7514 | Fund. Math. 231(1) (2015), 57–79. https://doi.org/10.4064/fm231-1-4 |
| 2013c11 | Ben Yaacov, I.; Tsankov, T. | Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups | 1312.7757 | Trans. Amer. Math. Soc. 368(11) (2016), 8267–8294. https://doi.org/10.1090/tran/6883 |
| 2013c12 | Bodirsky, M.; Pinsker, M.; Pongrácz, A. | Reconstructing the topology of clones | 1312.7699 | Trans. Amer. Math. Soc. 369(5) (2017), 3707–3740. https://doi.org/10.1090/tran/6937 |
| 2013c13 | Doucha, M. | Metrically universal abelian groups | 1312.7683 | Trans. Amer. Math. Soc. 369(8) (2017), 5981–5998. https://doi.org/10.1090/tran/7059 |
| 2013c14 | Hubička, J.; Nešetřil, J. | Bowtie-free graphs have a Ramsey lift | 1402.2700 | Advances in Applied Mathematics. 96 (2018), 286-311. https://doi.org/10.1016/j.aam.2017.12.005 |
| 2013c15 | Fiala, J.; Hubička, J.; Long, Y. | Universality of intervals of line graph order | 1402.3736 | European J. Combin. 41 (2014), 221–231. https://doi.org/10.1016/j.ejc.2014.04.008 |
| 2013c16 | Bogachev, L. V. | Limit shape of random convex polygonal lines: even more universality | 1111.3529 | J. Combin. Theory Ser. A. 127 (2014), 353–399. https://doi.org/10.1016/j.jcta.2014.07.005 |
| 2013c17 | Doucha, M. | Non-abelian group structure on the Urysohn universal space | 1403.3277 | Fund. Math. 228(3) (2015), 251–263. https://doi.org/10.4064/fm228-3-3 |
| 2013c18 | Melleray, J.; Nguyen Van Thé, L.; Tsankov, T. | Polish groups with metrizable universal minimal flows | 1404.6167 | Int. Math. Res. Not. IMRN. (5) (2016), 1285–1307. https://doi.org/10.1093/imrn/rnv171 |
| 2013c19 | Ben Yaacov, I.; Kaïchouh, A. | Reconstruction of separably categorical metric structures | 1405.4177 | J. Symb. Log. 81(1) (2016), 216–224. https://doi.org/10.1017/jsl.2014.80 |
| 2013c20 | Cherlin, G. | Henson graphs and Urysohn-Henson graphs as Cayley graphs | Funct. Anal. Appl. 49(3) (2015), 189–200. https://doi.org/10.1007/s10688-015-0103-2 |
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| 2013c21 | Koshevoy, G. | Cluster monomials in ℂ[GLn/N], a simplicial fan in the cone of semi-standard Young tableaux, and the Lusztig basis | 1411.3569 | |
| 2013c22 | Grigoryev, D.; Koshevoy, G. | Complexity of tropical Schur polynomials | J. Symbolic Comput. 74 (2016), 46–54. https://doi.org/10.1016/j.jsc.2015.05.005 |
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| 2013c23 | Ben Yaacov, I.; Henson, C. W. | Generic orbits and type isolation in the Gurarij space | 1211.4814 | Fund. Math. 237(1) (2017), 47–82. https://doi.org/10.4064/fm193-3-2016 |
| 2013c24 | Vershik, A. | The problem of describing central measures on the path spaces of graded graphs | 1408.3291 | Funct. Anal. Appl (transl.).48(4) (2014), 256–271. https://doi.org/10.1007/s10688-014-0069-5 |
| 2013c25 | Towsner, H. | σ-algebras for quasirandom hypergraphs | 1312.4882 | Random Structures Algorithms. 50(1) (2017), 114–139. https://doi.org/10.1002/rsa.20641 |
| 2013c26 | Ackerman, N.; Freer, C.; Nešetřil, J.; Patel, R. | Invariant measures via inverse limits of finite structures | 1310.8147 | European J. Combin. 52 (2016), 248–289. https://doi.org/10.1016/j.ejc.2015.07.006 |
| 2013c27 | Ackerman, N.; Freer, C.; Kwiatkowska, A.; Patel, R. | A classification of orbits admitting a unique invariant measure | 1412.2735 | Ann. Pure Appl. Logic. 168(1) (2017), 19–36. https://doi.org/10.1016/j.apal.2016.08.003 |
| 2013c28 | Mwesigye, F.; Truss, J. K. | Finitely coloured ordinals | ||
| 2013c29 | Glasner, E. | RP[d] is an equivalence relation: An enveloping semigroup proof | 1402.3135 | |
| 2013c30 | Glasner, E.; Megrelishvili, M. | Eventual nonsensitivity and tame dynamical systems | 1405.2588 | |
| 2013c31 | Ben Yaacov, I.; Ibarlucía, T.; Tsankov, T. | Eberlein oligomorphic groups | 1602.05097 | Trans. Amer. Math. Soc. 370(3) (2018), 2181–2209. https://doi.org/10.1090/tran/7227 |
| 2013c32 | Henson, C. W.; Raynaud, Y. | Asymptotically Hilbertian modular Banach spaces: examples of uncountable categoricity | 1606.03122 | Comment. Math. 56(1) (2016), 119–144. https://doi.org/10.14708/cm.v56i1.1231 |
| 2013c33 | Evans, D. M.; Ghadernezhad, Z.; Tent, K. | Simplicity of the automorphism groups of some Hrushovski constructions | 1312.3430 | Ann. Pure Appl. Logic. 167(1) (2016), 22–48. https://doi.org/10.1016/j.apal.2015.09.002 |
| 2013c34 | Glasner, E.; Gutman, Y.; Ye, X. | Higher order regionally proximal equivalence relations for general minimal group actions | 1706.07227 | Adv. Math. 333 (2018), 1004–1041. https://doi.org/10.1016/j.aim.2018.05.023 |
| Name | Affiliation |
| Andrey Alpeev | Saint-Petersburg State University |
| Dana Bartosova | University of Sao Paolo |
| Oleg Belegradek | Istanbul Bilgi University |
| Itaï Ben Yaacov | Université Claude Bernard Lyon 1 |
| Manuel Bodirsky | CNRS / LIX, Ecole Polytechnique |
| Leonid Bogachev | University of Leeds |
| Gregory Cherlin | Rutgers University |
| Michal Doucha | Polish Academy of Sciences |
| David Evans | University of East Anglia |
| Valentin Ferenczi | Universidade de São Paulo |
| Cameron Freer | Massachusetts Institute of Technology (MIT) |
| Pavel Galashin | Saint-Petersburg State University |
| Zaniar Ghadernezhad | Westfälische Wilhelms-Universität Münster |
| Moshe Shmuel Glasner | Tel Aviv University |
| Dmitry Grigoryev | Université Lille 1 |
| Yonatan Gutman | University of Cambridge |
| C. Ward Henson | University of Illinois |
| Jan Hubicka | Charles University in Prague |
| Tomás Ibarlucía | Université Claude Bernard Lyon 1 |
| Itay Kaplan | Universität Münster |
| Michael Kapovich | University of California |
| Adriane Kaïchouh | Université Claude Bernard - Lyon 1 |
| Ulrich Kohlenbach | TU Darmstadt |
| Gleb Koshevoy | CEMI RAS |
| Wieslaw Kubis | Academy of Sciences of the Czech Republic |
| Aleksandra Kwiatkowska | Universität Bonn |
| Claude Laflamme | University of Calgary |
| Stéphane Laurent | Université de Strasbourg |
| Julie Linman | University of Colorado at Boulder |
| Yangjing Long | Max Planck Institute for Mathematics in the Sciences |
| László Lovász | Eötvös Loránd University |
| Hugh Dugald Macpherson | University of Leeds |
| Barnaby Martin | |
| Julien Melleray | Université Lyon 1 |
| Heike Mildenberger | Albrecht-Ludwigs-Universität Freiburg |
| Benjamin D. Miller | Universität Münster |
| Jaroslav Nesetril | Charles University in Prague |
| Lionel Nguyen Van Thé | Université d'Aix-Marseille |
| Piotr Niemiec | Jagiellonian University |
| Andre Nies | University of Auckland |
| Javier de la Nuez Gonzalez | WWU Münster |
| Alexey Ostrovskiy | Universität der Bundeswehr München |
| Daniel Palacín | Universität Münster |
| Rehana Patel | Olin College of Engineering |
| Fedor Petrov | Steklov Mathematical Institute RAS |
| Michael Pinsker | Technische Universität Wien |
| András Pongrácz | Laboratoire d'Informatique de l'École Polytechnique |
| Yves Raynaud | UPMC |
| Matatyahu Rubin | Ben Gurion University |
| Rizos Sklinos | Universität Münster |
| Miodrag Sokic | California Institute of Technology |
| Slawomir Solecki | University of Illinois |
| Katrin Tent | Universität Münster |
| Stevo Todorcevic | University of Toronto |
| Henry Towsner | University of Pennsylvania |
| John Truss | University of Leeds |
| Todor Tsankov | Université Paris Diderot |
| Slawomir Turek | Uniwersytet Jana Kochanowskiego w Kielcach |
| Anatoly Vershik | St. Petersburg Department of Steklov Institute of Mathematics |
| Dimitris Vlitas | University of Athens |
| Phillip Wesolek | University of Illinois at Chicago |
| Jay Williams | Caltech |
| Joshua Wiscons | Universität Münster |
| Alexandre Zalesski | University of East Anglia |
| Boris Zilber | University of Oxford |
This list does not include people who only participated in workshops.
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