Colloquia/Fall18: Difference between revisions
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===September 4: Isaac Goldbring (UIC) === | ===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. | |||
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Revision as of 17:12, 1 September 2015
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.