Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, September 25, 2013.

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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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Wednesday, September 25, 2013

12:00 pm in Grainger Library, room 335,Wednesday, September 25, 2013

#### To Be Announced

###### Bruce Reznick & David Lebauer (UIUC Math & Energy Biosciences Institute)

Abstract: Two talks will be given: Bruce Reznick, Math, will talk on Non-negative polynomials and sums of squares in theory and (theoretically) in practice, and David Lebauer,Energy Biosciences Institute, will tell us about What we know and what we don't know about ecosystems.

3:00 pm in 347 Altgeld Hall,Wednesday, September 25, 2013

#### Introduction to Quasicategories

###### Sarah Yeakel (UIUC Math)

Abstract: Quasicategories are models for $(\infty,1)$-categories. Our goal is to build intuition for dealing with quasicategories by exploring some examples and some of the usual categorical constructions which apply in the $\infty$-categorical world. In particular, we will discuss how the ordinary category theory is really a part of the higher category theory, and how the new constructions that we give are equivalent to the old ones, when restricted to the ordinary categories. Following chapter one of Higher Topos Theory, we'll start with definitions and hopefully end up with limits and colimits.

3:00 pm in 143 Altgeld Hall,Wednesday, September 25, 2013

#### Grassman Varieties finite and infinite

###### William Haboush (UIUC)

Abstract: I will explain how the set of totally decomposable elements it the r'th exterior power of a vector space of dimension n is a projective variety and that it can be understood as the set of subspaces of dimension r in n space and I will describe the universal bundle. Then I will explain what is to be expected of an infinite dimensional analogue and I will show that it can be represented as a union of varieties each of which is a variety of subspaces of a fixed dimension stabilized by a nilpotent matrix.

4:00 pm in 245 Altgeld Hall,Wednesday, September 25, 2013