Date: Saturday, March 3, 2018Location: Purdue UniversitySpeakers:- Alex Eskin (U Chicago)
- Yan Mary He (U Chicago)
- Turbo Ho (Purdue)
Times below are given in Eastern Time. 10:30-11:30 11:30-12:30 12:30-2:00 2:00-3:00 3:00-3:30 3:30-4:30 4:30-5:30
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".
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) (3:30-4:30)Alex EskinOn stationary measure rigidity and orbit closures for actions of non-abelian groupsAbstract: 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. (11:30-12:30)Yan Mary HeTopology of the shift locus via the big mapping class group`Abstract: The shift locus of (monic centered) complex polynomials`
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. |