Department of

Mathematics


Seminar Calendar
for events the day of Friday, September 16, 2016.

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Friday, September 16, 2016

4:00 pm in 345 Altgeld Hall,Friday, September 16, 2016

NIP and Keisler measures

Nigel Pynn-Coates (UIUC Math)

Abstract: Last week, Travis introduced Keisler measures. This week, I will introduce NIP and mention several facts about Keisler measures in NIP structures. The presentation follows Sergei Starchenko's notes on "NIP, Keisler Measures and Combinatorics."

4:00 pm in 241 Altgeld Hall,Friday, September 16, 2016

Poisson Lie Groups, Their Duals and Doubles

Yang Song (UIUC Math)

Abstract: Poisson Lie groups first appeared as the (semi-)classical limit of quantum groups. In this talk, however, we shall not enter the quantum world, but a smooth introduction to Poisson Lie groups, their Lie (bi)algebras , duals and doubles.

4:00 pm in 243 Altgeld Hall,Friday, September 16, 2016

A New Shellability Proof of an Old Identity of Dixon

Ruth Davidson   [email] (UIUC Math)

Abstract: We give a new proof of an old identity of Dixon (1865-1936) that uses tools from topological combinatorics. Dixon's identity is re-established by constructing an infinite family of non-pure simplicial complexes $\Delta(n)$, indexed by the positive integers, such that the alternating sum of the numbers of faces of $\Delta(n)$ of each dimension is the left-hand side of the the identity. We show that $\Delta(n)$ is shellable for all $n$. Then, using the fact that a shellable simplicial complex is homotopy equivalent to a wedge of spheres, we compute the Betti numbers of $\Delta(n)$ by counting (via a generating function) the number of facets of $\Delta(n)$ of each dimension that attach along their entire boundary in the shelling order. In other words, Dixon's identity is re-established by using the Euler-Poincaré relation. No background in topological combinatorics will be assumed for this talk. This is joint work with Augustine O'Keefe and Daniel Parry.