Chicago Operator algebra and Group theory Seminar

Organized by Kate Juschenko and Emily Peters


Adam Marcus, Yale University "Controlling Eigenvalues (at least in theory) part 2"
Thursday, November 21, 4pm.

Abstract: In the late 80's and early 90's Bourgain and Tzafriri published a series of influential papers regarding the Kadison--Singer problem. One result from that work in particular has been used effectively in a number of areas is what has come to be known as "Restricted Invertibility." I will show how the method of interlacing polynomials can be used to reprove this result with asymptotically sharp constants. Then I will discuss how those same proof techniques were extended in the proof of Kadison--Singer.

Past speakers:

Collin Bleak, University of St Andrews. "De Bruijn Automorphisms of the Full Shift"
Thursday, October 23, 2pm. Linguistics Department Seminar Room (2016 Sheridan Road).
(joint seminar with Northwestern Algebra Seminar)

Abstract: We investigate a set of groups {SBC_n}. Each group SBC_n sits very naturally in the full group of automorphisms of {0,1, ... , n-1}^Z, the full shift on n letters, and is somehow a very natural object. Still, the structure of each group SBC_n, at least initially, was quite a mystery.
These groups' elements are describable as finite transducers, and so the groups SBC_n are linked strongly to the rational group R introduced by Grigorchuk, Nekrashevych, and Suschanskii. Furthermore, the group SBC_n corresponds precisely to the outer automorphism group of the generalized Higman-Thompson group G_{n,1} = V_n.
In this talk, we exploit a connection with De Bruijn graphs to begin to explore the structure of the groups SBC_n. Amongst other results, we will show that for m eq n, SBC_m is not isomorphic to SBC_n, and we will also show that for n>2, the groups SBC_n are infinite, locally finite groups (and hence are not finitely generated).
This talk features work from two separate projects involving collaborators Y. Maissel, A. Navas, and P. Cameron.

Yash Lodha, Cornell. "A new solution to the von Neumann-Day problem for finitely presented groups." 15 October 2014.

Abstract: In this talk, I will describe a finitely presented subgroup of s group of piecewise projective homeomorphisms of the real line. This in particular provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian free subgroup. The example is moreover torsion free. A portion of this is joint work with Justin Moore. Higher finiteness properties will be discussed if time permits.

Darren Creutz, Vanderbilt. "Operator Algebraic Superrigidity for Lattices and Commensurators." 3 December 2013.

Robin Tucker-Drob, Rutgers. "Shift-minimal groups, fixed price 1, and the unique trace property." 11 December 2013.