Spring 2018 GGD Workshop

Date: Saturday, March 3, 2018

Location: Purdue University


Speakers:

Schedule: All talks will be located in room 175 of the Mathematical Sciences Building.

Times below are given in Eastern Time.

10:30-11:30 Welcome, Coffee and Pastries

11:30-12:30 Talk 1, He

12:30-2:00 Lunch

2:00-3:00 Talk 2, Ho

3:00-3:30 Coffee break

3:30-4:30 Talk 3, Eskin

4:30-5:30 Farewells


Parking and Local Info:

The University Street Parking Garage (coded PGU on the searchable campus map) is directly across the street from the Mathematical Sciences Building. No permit is required on weekends.

Wifi is available via eduroam for participating institutions or publicly accessible via "attwifi".

GGD Day Spring 2018



Organizers:

This GGD workshop is funded with the support of the U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 "RNMS: GEometric structures And Representation varieties" (the GEAR Network).

Titles and Abstracts (pdf)


Alex Eskin (3:30-4:30)
On stationary measure rigidity and orbit closures for actions of non-abelian groups

Abstract: I will describe joint work in progress with Aaron Brown, Federico Rodriguez-Hertz and Simion Filip. Our aim is to find some analogue, in the context of smooth dynamics, of Ratner's theorems on unipotent flows. This would be a (partial) generalization of the results of Benoist-Quint and my work with Elon Lindenstrauss in the homogeneous setting, the results of Brown and Rodriguez-Hertz in dimension 2, and my results with Maryam Mirzakhani in the setting of Teichmuller dynamics.

Yan Mary He (11:30-12:30)
Topology of the shift locus via the big mapping class group
Abstract: The shift locus of (monic centered) complex polynomials
of degree d > 1 is the set of polynomials whose filled-in Julia set
contains no critical points. Traversing a loop in the shift locus gives
rise to a holomorphic motion of Cantor Julia sets, which can be
extended to a homeomorphism of the plane minus a Cantor set up
to isotopy. Then there is a well-defined monodromy representation
from the fundamental group of the shift locus to the mapping class
group of the plane minus a Cantor set. In this talk, I will discuss the
image and the kernel of this map as well as the presentation of the
fundamental group. This is joint work with J. Bavard, D. Calegari, S.
Koch and A. Walker
Turbo Ho (2:00-3:00)
The word problem of a group as formal languages
Abstract: The word problem of a group G = <S> can be defined as the set of formal words in S* that represent the identity in G. When viewed as formal languages, this gives a strong connection between classes of groups and classes of formal languages. For example, Anisimov showed that a group is finite if and only if its word problems is regular, and Muller and Schupp showed that a group is virtually-free if and only if its word problem is context-free. 
Recently, Salvati showed that the word problem of Z^2 is multiple context-free. Afterwards, Kropholler and Spriano show that the class of groups with multiple context-free word problems is closed under amalgamated free products over finite groups. Gilman, Kropholler, and Schleimer showed that most nilpotent groups, RAAGs, and hyperbolic three-manifold groups do not have multiple context-free word problem. In this talk, we will discuss a generalization of Salvati’s result that Z^n has multiple context-free word problem.






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