COGSChicago Operator algebra and Group theory SeminarOrganized by Kate Juschenko and Emily Peters
Past Speakers: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.
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.
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.
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