Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Fall 2015

Go to next semester, Spring 2016.

date	speaker	title	host(s)
September 4	Isaac Goldbring (UIC)	On Kirchberg's embedding problem	Andrews/Lempp
September 11	Doron Puder (IAS)	Word-Measures on Groups	Gurevich
September 18	Izzet Coskun (UIC)	The geometry of points in the plane	Erman
September 25	Abbas Ourmazd (UW-Milwaukee)		Mitchell
October 2
October 9	Igor Mezic (UC Santa Barbara)		Budisic, Thiffeault
October 16	Hadi Salmasian (Ottawa)		Gurevich
October 23	Wisconsin Science Festival.
October 30	Ruth Charney (Brandeis)		Dymarz
November 6	Reserved *S
November 13	Reserved *T
November 20	Reserved
November 27	University Holiday	No Colloquium
December 4	Reserved
December 11	Reserved

Abstracts

September 4: Isaac Goldbring (UIC)

Title: On Kirchberg's embedding problem

Abstract: In his seminal work on the classification program for nuclear C*-algebras, Kirchberg showed that a particular C*-algebra, the Cuntz algebra O2, plays a seminal role. Subsequent work with Chris Phillips showed that O2 also plays a prominent role in regards to the wider class of exact C*-algebras, and this led Kirchberg to conjecture that every C*-algebra is finitely representable in O2, that is, is embeddable in an ultrapower of O2. The main goal of this talk is to sketch a proof of a local finitary reformulation of this conjecture of Kirchberg. The proof uses model theory and in particular the notion of model-theoretic forcing. No knowledge of C*-algebras or model theory will be assumed. This is joint work with Thomas Sinclair.

September 11: Doron Puder (IAS)

Title: Word-Measures on Groups.

Abstract: Let w be a word in the free group on k generators, and let G be a finite (compact) group. The word w induces a measure on G by substituting the letters of w with k independent uniformly (Haar) chosen random elements of G and evaluating the product. Questions about word-measures on groups attracted attention in recent years both for their own sake and as a tool to analyze random walks on groups.

We will explain some properties of word-measure, give examples and state conjectures. We will also talk about recent results regarding word-measures on symmetric groups and word-measures on unitary groups.

September 18: Izzet Coskun (UIC)

Title: The geometry of points in the plane

Abstract: Grothendieck's Hilbert scheme of points is a smooth compactification of the configuration space of points in the plane. It has close connections with combinatorics, representation theory, mathematical physics and algebraic geometry. In this talk, I will survey some of the basic properties of this beautiful space. If time permits, I will discuss joint work with Arcara, Bertram and Huizenga on codimension one subvarieties of the Hilbert scheme.