Aug 22, 2016
Monday

09:00 AM  09:15 AM


Welcome

 Location
 SLMath: Eisenbud Auditorium
 Video


 Abstract
 
 Supplements



09:15 AM  10:30 AM


Mapping class groups and Out(F_n)
Mladen Bestvina (University of Utah)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
I am planning to briefly describe these two classes of groups, their most important properties, and spaces on which they act. I will try to explain how these different spaces fit together in a form of a dictionary relating the two theories. I will finish by listing some of the outstanding problems in the two subjects
 Supplements


10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:30 PM


Hyperboliclike behaviour of groups
Koji Fujiwara (Kyoto University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
I will discuss properties, techniques and examples related to hyperboliclike groups.
For example, contracting geodesics, weakly proper discontinuous/acylindrical group actions.
Then I explain the construction of projections complexes and mention some of its applications
 Supplements


12:30 PM  02:30 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



02:30 PM  03:20 PM


Topological dimension of the boundaries of some hyperbolic Out(Fn)graphs
Camille Horbez (Université de Paris XI)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
A theorem of BestvinaBrombergFujiwara asserts that the mapping class group of a hyperbolic surface of finite type has finite asymptotic dimension; its proof relies on an earlier result of BellFujiwara stating that the curve complex has finite asymptotic dimension. The analogous statements are still open for Out(Fn). In joint work with Mladen Bestvina and Ric Wade, we give a first hint towards this, by obtaining a bound (linear in the rank n) on the topological dimension of the Gromov boundary of the graph of free factors of Fn (as well as some other hyperbolic Out(Fn)graphs).
 Supplements


03:20 PM  03:50 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



03:50 PM  04:40 PM


Hyperbolic group extensions
Spencer Dowdall (Vanderbilt University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
William Thurston's seminal construction of a hyperbolic 3manifold fibering over the circle gave the first example of a Gromov hyperbolic surfacebycyclic group. This breakthrough sparked a flurry of activity, and there has subsequently been much progress towards developing a general theory of hyperbolic group extensions. In this talk I will review some of this basic theory  including combination theorems for ensuring a group extension is hyperbolic and structural theorems about general hyperbolic extensions  and then discuss my work with Sam Taylor studying hyperbolicity in the specific context of free group extensions. For instance, we use the geometry of Outer space to show that every purely atoroidal subgroup of Out(F_n) that quasiisometrically embeds into the free factor complex gives rise to a hyperbolic extension of F_n
 Supplements



Aug 23, 2016
Tuesday

09:00 AM  10:30 AM


The geometry of CAT(0) spaces
Ruth Charney (Brandeis University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The talk will begin with a brief history of CAT(0) geometry, including some longstanding open problems. Then I will discuss more recent developments and areas of current interest, including the theory of CAT(0) cube complexes and the interplay between CAT(0) geometry and hyperbolic geometry
 Supplements


10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:30 PM


Special cube complexes and the virtual Haken conjecture
Jason Manning (Cornell University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
This will be an expository talk on the theory of special cube complexes and their application in resolving the virtual Haken conjecture
 Supplements


12:30 PM  02:30 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



02:30 PM  03:20 PM


Counting loxodromics for hyperbolic actions
Samuel Taylor (Yale University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
Consider a nonelementary action by isometries of a hyperbolic group G on a hyperbolic metric space X. Besides the action of G on its Cayley graph, some examples to bear in mind are actions of G on trees and quasitrees, actions on nonelementary hyperbolic quotients of G, or examples arising from naturally associated spaces, like subgroups of the mapping class group acting on the curve graph.
We show that the set of elements of G which act as loxodromic isometries of X (i.e those with sinksource dynamics) is generic. That is, for any finite generating set of G, the proportion of Xloxodromics in the ball of radius n about the identity in G approaches 1 as n goes to infinity. We also establish several results about the behavior in X of the images of typical geodesic rays in G. For example, we prove that they make linear progress in X and converge to the boundary of X. This is joint work with I. Gekhtman and G. Tiozzo
 Supplements


03:20 PM  03:50 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



03:20 PM  03:50 PM


Poster Session

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



03:50 PM  04:40 PM


The poset of acylindrically hyperbolic structures on a group
Denis Osin (Vanderbilt University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
For every group G, we introduce the set of acylindrically hyperbolic structures on G, denoted AH(G). One can think of elements of AH(G) as cobounded acylindrical Gactions on hyperbolic spaces considered up to a natural equivalence.Elements of AH(G) can be ordered in a natural way according to the amount of information they provide about the group G. We will discuss some basic questions about the poset structure of AH(G) as well as more advanced results about the existence of maximal acylindrically hyperbolic structures and rigidity phenomena
 Supplements


04:40 PM  06:20 PM


Reception

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements




Aug 24, 2016
Wednesday

09:00 AM  10:30 AM


Recognizing 3manifold groups by their finite quotients
Alan Reid (Rice University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
This talk will be focused on the problem of: to what extent can the fundamental groups of compact 3manifolds be distinguished by the finite quotients of their fundamental groups.
The talk will highlight examples (e.g. the figure eight knot complement) and introduce ideas and techniques used in attacking the problem
 Supplements


10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:30 PM


Surface subgroups
Henry Wilton (Center for Mathematical Sciences)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
A surface group is the fundamental group of a closed surface of nonpositive Euler characteristic. A great deal of recent energy in geometric group theory has focussed on finding surface subgroups in various classes of groups of geometrical interest, especially wordhyperbolic groups. I will survey recent developments, highlights of which include Kahn—Markovic’s solution of the Surface Subgroup conjecture for Kleinian groups and Calegari—Walker’s discovery of surface subgroups in random groups
 Supplements



Aug 25, 2016
Thursday

09:00 AM  10:30 AM


Amenability and fixed point properties
Cornelia Drutu (University of Oxford)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
A fundamental dichotomy in the theory of infinite groups is the one between amenable groups and groups with Kazhdan's Property (T). In this talk I shall overview versions of these two opposite properties, connections to actions on nonpositively curved spaces and on Banach spaces, to other geometric features of the groups, and to expander graphs. I shall also mention what is known in the setting of random groups and that of important classes of infinite groups (e.g. lattices, mapping class groups, Out(F_n) etc)
 Supplements


10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:30 PM


Decision problems
Martin Bridson (University of Oxford; Clay Mathematics Institute )

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The (non)existence and complexity of algorithms has been a central theme in combinatorial and, later, geometric group theory since their inception, with low dimensional topology providing both motivation and a significant field of application. In this talk I will review some of the milestones in the development of decision problems in group theory, highlighting the geometry behind them. I shall then survey the current state of the art, with an emphasis on applications to geometry and topology and including decision problems for profinite groups
 Supplements


12:30 PM  01:30 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



01:30 PM  02:20 PM


Random groups and largescale geometry
John Mackay (University of Bristol)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
Probabilistic methods have been used highly successfully in graph theory over the past 70 years, with two different flavors of approach. First, such methods are used to show the existence of graphs with some pathological properties that are hard to explicitly construct. Second, random or typical graphs are studied in their own right as interesting and important objects.
In Gromov's 1987 paper on hyperbolic groups, he described how many typical finitely presented groups are hyperbolic. Since then a variety of authors have studied random groups, again with the two approaches above: building exotic counterexamples (notably Gromov's construction of a finitely presented group that does not coarsely embed into Hilbert space), and the study of properties of typical finitely presented groups in a variety of models (notably Gromov's density model).
In this talk we'll survey this history and discuss some work, in part joint with Cornelia Drutu, which takes steps towards distinguishing the quasiisometry types of random groups
 Supplements


02:30 PM  03:20 PM


Proper affine actions of rightangled Coxeter groups
Fanny Kassel (Institut des Hautes Études Scientifiques (IHES))

 Location
 SLMath:
 Video

 Abstract
The Auslander Conjecture states that all discrete groups acting properly and cocompactly on R^n by affine transformations should be virtually solvable. In 1983, Margulis constructed the first examples of proper (but not cocompact) affine actions of nonabelian free groups. It seems that until now all known examples of irreducible proper affine actions were by virtually solvable or virtually free groups. I will explain that any rightangled Coxeter group on k generators admits a proper affine action on R^{k(k1)/2}. This is joint work with J. Danciger and F. Guéritaud.
 Supplements


03:30 PM  03:50 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements




Aug 26, 2016
Friday

09:00 AM  10:30 AM


Arithmetic groups: geometry and cohomology
Kevin Wortman (University of Utah)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
 
 Supplements


10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:30 PM


Homological stability, representation stability, and FImodules
Thomas Church (Stanford University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
Homological stability is the classical phenomenon that for many natural families of moduli spaces the homology groups stabilize. Often the limit is the homology of another interesting space; for example, the homology of the braid groups converges to the homology of the space of selfmaps of the Riemann sphere. Representation stability makes it possible to extend this to situations where classical homological stability simply does not hold, using ideas inspired by asymptotic representation theory. I will give a broad survey of homological stability and a gentle introduction to the tools and results of representation stability, focusing on its applications in topology.
 Supplements


12:30 PM  02:30 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



02:30 PM  03:20 PM


Extending to Lie algebras some results on subdirect products of groups
Conchita Martinez Perez (Universidad de Zaragoza)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
Since Baumslag and Roseblade discovered that finitely presented subgroups of a product of two free groups must be virtually a product of free groups there has been an intensive research on properties of subdirect products of groups mainly focusing on the homological and homotopical properties, including the celebrated 123 Theorem by Bridson, Howier, Miller and Short. In this talk we will discuss how to extend some of these results to Lie algebras.
This is a joint work with Dessislava Kochloukova
 Supplements


03:20 PM  03:50 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



03:50 PM  04:40 PM


Monster groups acting on CAT(0) spaces
Rémi Coulon (Université de Rennes I)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
Since the beginning of the 20th century, infinite torsion groups have been the source of numerous developments in group theory: Burnside groups Tarski monsters, Grigorchuck groups, etc. From a geometric point of view, one would like to understand on which metric spaces such groups may act in a non degenerated way (e.g. without a global fixed point).
In this talk we will focus on CAT(0) spaces and present two examples with rather curious properties. The first one is a nonamenable finitely generated torsion group acting properly on a CAT(0) cube complex. The second one is a nonabelian finitely generated Tarskilike monster : every finitely generated subgroup is either finite or has finite index. In addition this group is residually finite and does not have Kazdhan property (T).
(Joint work with Vincent Guirardel)
 Supplements


