Weakly Commensurable Groups
Andrei Rapinchuk, University of Virginia
Location: Stevenson 5211
The notion of weak commensurability (of Zariski-dense subgroups of semi-simple algebraic groups) was introduced in the ongoing joint work with Gopal Prasad on length-commensurable and isospectral locally symmetric spaces. We were able to determine when two arithmetic subgroups are weakly commensurable. This led to various geometric results, some of which are related to the famous question "Can one hear the shape of a drum?" Tea at 3:30 pm in SC 1425.
The Brouwer Fix-Point Theorem
Yago Antolin Pichel, Vanderbilt University
Location: Stevenson 1206
Play Hex, Prove Brouwer
Graduate Student Tea
Location: Stevenson 1425
Lattices in Amenable Groups
Tsachik Gelander, Hebrew University and Weizmann Institute
Location: Stevenson 1310
Let G be a locally compact amenable group. We discuss the question whether every closed subgroup of finite covolume in G is cocompact. Joint work with U. Bader, P.E. Caprace and S. Mozes.
Reduction to Type II in Dynamical Systems
Kamran Reihani, Vanderbilt University
Location: Stevenson 1432
The talk reports on a frequently used strategy that seems to be useful when some sort of "type-III" phenomena prevent the existence of invariant structures for dynamical systems. The approach is called "reduction to type II" (in analogy with the reduction of type-III factors to type II in the theory of von Neumann algebras). It involves some extension of the dynamical system in such a natural way that the resulting system is large enough to carry the desired invariant structure. We will discuss a few examples in geometry, topology, and measure theory. The reduction process in the measurable case naturally involves Tomita-Takesaki theory, and the computations are based on a joint work with Bill Paschke.