Department of

# Mathematics

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

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2016           September 2016          October 2016
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1  2  3  4  5  6                1  2  3                      1
7  8  9 10 11 12 13    4  5  6  7  8  9 10    2  3  4  5  6  7  8
14 15 16 17 18 19 20   11 12 13 14 15 16 17    9 10 11 12 13 14 15
21 22 23 24 25 26 27   18 19 20 21 22 23 24   16 17 18 19 20 21 22
28 29 30 31            25 26 27 28 29 30      23 24 25 26 27 28 29
30 31


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.