Department of

# Mathematics

Seminar Calendar
for events the day of Friday, September 29, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, September 29, 2017

12:00 pm in 243 Altgeld Hall,Friday, September 29, 2017

#### To Be Announced

###### Fernando Roman Garcia (UIUC)

3:00 pm in 341 Altgeld Hall,Friday, September 29, 2017

#### Bott-Samelson varieties and combinatorics

###### Laura Escobar (UIUC)

Abstract: Schubert varieties parametrize families of linear spaces intersecting certain hyperplanes in C^n in a predetermined way. In the 1970’s Hansen and Demazure independently constructed resolutions of singularities for Schubert varieties: the Bott-Samelson varieties. In this talk I will describe their relation with associahedra. I will also discuss joint work with Pechenick-Tenner-Yong linking Magyar’s construction of these varieties as configuration spaces with Elnitsky’s rhombic tilings. Finally, based on joint work with Wyser-Yong, I will give a parallel for the Barbasch-Evens desingularizations of certain families of linear spaces which are constructed using symmetric subgroups of the general linear group.

4:00 pm in 345 Altgeld Hall,Friday, September 29, 2017

#### "Borel circle squaring" by Marks and Unger: Part 3

###### Anush Tserunyan (Illinois Math)

Abstract: In the previous talk of this series, we built a real valued Borel flow by taking the average of the "relative" matchings over each connected component. In the current talk, I'll describe how to obtain an integer valued Borel flow out of a real valued one, which is the main difficulty of the whole proof. Getting a Borel matching from an integer valued Borel flow is much easier and we will do so if time permits.

4:00 pm in 241 Altgeld Hall,Friday, September 29, 2017

#### Framed cobordisms in algebraic topology

###### Pedro Mendes De Araujo (UIUC)

Abstract: The Thom-Pontryagin construction was the first machinery developed to compute homotopy groups of spheres, in terms of framed cobordism classes of manifolds embedded in Euclidean space. Although much less successful at that than the algebraic machinery developed later, it has the advantage of being highly geometric and intuitive. In this talk, which will hopefully be fun, full of pictures, and requiring little more than an acquaintance with manifolds (and a high tolerance to geometric hand waving), we'll look at how it can be used to compute pi_{n+1} S^n. On the way, we'll give a very explicit proof of the Freudenthal suspension theorem.