Department of

Mathematics

Seminar Calendar
for events the day of Friday, December 2, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, December 2, 2016

4:00 pm in 243 Altgeld Hall,Friday, December 2, 2016

Intersecting Families of Permutations

Michelle Delcourt   [email] (UIUC)

Abstract: Enumerating families of combinatorial objects with given properties and describing the typical structure of these objects are fundamental problems in extremal combinatorics. In this talk, we will investigate intersecting families of discrete structures in various settings, determining their typical structure as the size of the underlying ground set tends to infinity. Our new approach outlines a general framework for a number of similar problems; in particular, we prove analogous results for hypergraphs, permutations, and vector spaces using the same technique. This is joint work with József Balogh, Shagnik Das, Hong Liu, and Maryam Sharifzadeh.

4:00 pm in 345 Altgeld Hall,Friday, December 2, 2016

The $n$-simplex as a projective Fraïssé limit

Aristotelis Panagiotopoulos (UIUC Math)

Abstract: Classical Fraïssé theory has played a key role in the study of dynamics of automorphism groups of countable structures. Projective Fraïssé theory, introduced by Irwin and Solecki, captures the dense dynamics of homeomorphism groups of compact metrizable spaces. In this talk, we express the $n$-simplex as a projective Fraïssé limit. In the process, we develop further the combinatorial counterpart to PL-topology known as stellar theory. We use this development to show that any simplicial map between two triangulations of the $n$-simplex that is a near-homeomorphism and fixes the ($n+1$)-many spanning vertexes is a factor of some very simple map generated by selections. Recall that a map from the $n$-simplex to the $n$-simplex is a near-homeomorphism if it is the uniform limit of a sequence of homeomorphisms.
This is a joint work with Sławomir Solecki.