Dec 06, 2016
Tuesday
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09:15 AM - 09:30 AM
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Welcome
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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09:30 AM - 10:30 AM
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Weak forms of amenability for CAT(0) cubical groups
Erik Guentner (University of Hawaii at Manoa)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
A group which act properly on a CAT(0) cubical complex, while not necessarily amenable, satisfies several weak forms of amenability: such a group is a-T-menable, weakly amenable and K-theoretically amenable. In the talk, based on joint work with J. Brodzki and N. Higson, I will describe a proof of K-amenability which finds its roots in earlier work of P. Julg and A. Valette on groups acting on trees. I will focus on the geometric constructions involved, and will keep the analytic complications to a minimum
- Supplements
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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Irreducible group actions by affine isometries on Hilbert spaces
Bachir Bekka (Université de Rennes 1)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Important classes of locally compact groups are characterized by their actions by affine isometries on Hilbert spaces (groups with Kazhdan's property, a-T-menable groups aka groups with the Haagerup property). We will be interested on the question of irreducibility of such actions, in the sense that the only non empty closed invariant affine subspace is the whole space. This notion was extensively studied in a recent joint work of T. Pillon, A. Valette and myself. We will report on this work as well as on some further results. Special attention will be paid to affine actions whose linear part is a factorial representation, that is, a representation which generates a factor in the von Neumann algebra sense
- Supplements
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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Kazhdan sets in groups and equidistribution properties
Catalin Badea (Université de Lille I (Sciences et Techniques de Lille Flandres Artois))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We will present some results about Kazhdan sets in topological groups using functional and harmonic analysis methods. We will discuss in particular a question, raised by Shalom, about Kazhdan sets and equidistribution properties. This is joint work with Sophie Grivaux
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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03:30 PM - 04:30 PM
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Quasi-isometric rigidity of fundamental groups of compact 3–manifolds.
Peter Haissinsky (Université d'Aix-Marseille (AMU))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
The talk will focus on the following results: a finitely generated group quasi-isometric to the fundamental group of a compact 3–manifold or to a finitely generated Kleinian group contains a finite index subgroup isomorphic to the fundamental group of a compact 3–manifold or to a finitely generated Kleinian group
- Supplements
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04:30 PM - 06:20 PM
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Reception
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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Dec 07, 2016
Wednesday
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09:30 AM - 10:30 AM
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Sublinearly bilipschitz maps, hyperbolic and nilpotent groups
Yves Cornulier (Centre National de la Recherche Scientifique (CNRS))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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Box spaces, expanders, and rigidity
Anastasia Khukhro (Université de Neuchâtel)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We will present a new construction of a box space of a free group which does not contain coarsely embedded expanders, but does not embed coarsely into Hilbert space. We will also describe a new rigidity result for box spaces of finitely presented groups, and give some applications. This is joint work with Thiebout Delabie
- Supplements
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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Sofic mean length
Hanfeng Li (University at Buffalo (SUNY))
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- Location
- SLMath: Atrium
- Video
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- Abstract
For a unital ring R, a length function on left R-modules assigns a (possibly infinite) nonnegative number to each module being additive for short exact sequences of modules. For any unital ring R and any group G, one can form the group ring RG of G with coefficients in R. The modules of RG are exactly R-modules equipped with a G-action. I will discuss the question of how to define a length function for RG-modules, given a length function for R-modules. An application will be given to the question of direct finiteness of RG, i.e. whether every one-sided invertible element of RG is two-sided invertible. This is based on joint work with Bingbing Liang
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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03:30 PM - 04:30 PM
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Finite embeddability of groups and its applications to geometry and topology
Guoliang YU (Texas A & M University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We will introduce the concept of finite embeddability of groups and discuss its applications to non-rigidity of topological manifolds and the moduli space of positive scalar curvature metrics. A certain secondary invariant of elliptic operators plays a crucial role in these applications. This is joint work with Shmuel Weinberger and Zhizhang Xie
- Supplements
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Dec 08, 2016
Thursday
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09:30 AM - 10:30 AM
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Equicontinuous actions of semisimple Lie groups
Uri Bader (Weizmann Institute of Science)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Every fixed-point-free isometric action of a semisimple Lie group G is proper.
I will explain this in my talk. Later I will elaborate on further generalizations of this fact.
For example, the image of G under any continuous homomorphism into a topological group is closed. Another application is given by describing explicitly the WAP compactification of G (a notion that will be defined in the talk). The latter will be related to the decay property of matrix coefficients of reflexive representations.
The talk will be based on a joint work with Tsachik Gelander
- Supplements
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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Glueing together copies of amenable groups
Kate Juschenko (Northwestern University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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Superintrinsic synthesis in fixed point properties
Masato Mimura (Tohoku University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
The following natural question arises from Shalom's innovational work (1999, Publ.IHES) on Kazhdan's property (T). ``Can we establish an `intrinsic' criterion to synthesize relative fixed point properties into the whole fixed point property without assuming `Bounded Generation'?'' This talk is aimed to present a resolution to this question in the affirmative. Our criterion works for ones with respect to certain classes of Busemann Non-Positively Curved spaces. It, moreover, suggests a further step toward constructing super-expanders from finite simple groups of Lie type.
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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03:30 PM - 04:30 PM
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Strong boundedness and distortion in transformation groups
Kathryn Mann (Cornell University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Higman’s embedding theorem says that any countable group can be embedded in a group generated by two elements. The relative version of this asks: given a countable subgroup H of a large group G, does H always lie in a finitely generated subgroup of G? (Of course, the answer should depend on G). This talk will answer this question for some interesting classes of groups, and discuss the related notions of strong boundedness (the property that every action of G by isometries on any metric space has all orbits bounded) and strong distortion. Far from pathological examples, the groups we consider are all groups of homeomorphisms or diffeormophisms of manifolds; where boundedness and distortion of subgroups of homeomorphisms can say something about the dynamics of their actions on the manifold. This is new joint work with F. Le Roux
- Supplements
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Dec 09, 2016
Friday
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09:30 AM - 10:30 AM
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A nice trick involving amenable groups
Martin Kassabov (Cornell University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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L_p-compression of wreath products and some related groups
Tianyi Zheng (University of California, San Diego)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We show a formula relating the L_p-compression exponent of a group and its wreath product with a cyclic group for p in [1, 2]. The argument extends the Markov type method introduced by Naor and Peres. Using wreath product as ingredients, we construct finitely generated amenable groups with arbitrary prescribed L_p compression exponent in the interval [0,1]. This can be viewed as an elementary amenable analogue of a result of Arzhantseva, Drutu and Sapir. Joint with Jeremie Brieussel
- Supplements
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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On spectra of Koopman, groupoid and quasi-regular representations
Rostislav Grigorchuk (Texas A & M University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Given an action of a countable group on a probability measure space by a measure class preserving transformations one can associate a three types of unitary representations: Koopman representation, groupoid representation, and uncountable family of quasi-regular representations defined for each orbit of the action. If additionally an element of a group algebra over the field of complex numbers is given then the corresponding operators associated with each of these representations are defined. We show that there is a strong relation between spectra of them (in the form of equality or containment). More information is known in the case when the measure is invariant or the action is Zimmer amenable (hyperfinite). The result has interpretation in the terms of weak containment of unitary representations. We illustrate the use of this result and of the corresponding techniques (based the Schreier graphs approach), and show how to compute the spectrum of the Cayley graph of the first group of intermediate growth constructed by the speaker in 1980. The talk is based on a joint paper with A.Dudko
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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03:30 PM - 04:30 PM
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Amenability, group C*-algebras and operator spaces
Gilles Pisier (Texas A & M University)
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- Location
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- Video
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- Abstract
We will review several results and open problems relating amenability to two properties of group C* algebras introduced or studied by E. Kirchberg, namely the local lifting property (LLP) and the weak expectation property (WEP).
- Supplements
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