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)	Hindman's theorem and idempotent types	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: Hindman's theorem and idempotent types

Abstract: For a set A of natural numbers, let FS(A) denote the set of sums of finitely many distinct elements of A. A set B of natural numbers is said to be an IP set if B contains FS(A) for some infinite set A. A central result in combinatorial number theory is Hindman's theorem, which states that if one finitely colors an IP set, then at least one of the colors is an IP set. The slickest proof of this result uses idempotent ultrafilters. Di Nasso suggested a model-theoretic generalization of idempotent ultrafilters, aptly named idempotent types, and asked in what completions of PA idempotent types exist. In this talk, I will show that Hindman's theorem is actually equivalent to the existence of idempotent types in all countable complete extensions of PA. This is joint work with Uri Andrews.

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.