Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 19, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2016          February 2016            March 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2       1  2  3  4  5  6          1  2  3  4  5
3  4  5  6  7  8  9    7  8  9 10 11 12 13    6  7  8  9 10 11 12
10 11 12 13 14 15 16   14 15 16 17 18 19 20   13 14 15 16 17 18 19
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24 25 26 27 28 29 30   28 29                  27 28 29 30 31
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Friday, February 19, 2016

2:00 pm in 445 Altgeld Hall,Friday, February 19, 2016

#### Amenability and group C* algebras

###### Anthony Sanchez (UIUC Math)

Abstract: A group G is amenable if it can be equipped with a left invariant mean. It turns out that amenability is characterized by the equivalence of certain C* algebras that we can build from G. These C* algebras carry the information about unitary representations of G. The purpose of this talk is to introduce the audience to some ideas from functional analysis by proving one direction of this characterization. Consequently, the only pre-requisites is some familiarity with functional analysis.

4:00 pm in 241 Altgeld Hall,Friday, February 19, 2016

#### Yoneda Lemma and the Fundamental Group

###### Nima Rasekh (UIUC Math)

Abstract: The goal of this talk is to show how category theory relates to the fundamental group. We will first gloss over the basics of those two concepts and then we will introduce the overarching idea which relates these two: Higher Category Theory. Finally, we will see how everything in this world is connected. No particular knowledge of category theory is assumed.

4:00 pm in 345 Altgeld Hall,Friday, February 19, 2016

#### Some results on strongly summable ultrafilters

###### David Fernandez Breton (University of Michigan)

Abstract: A strongly summable ultrafilter is an ultrafilter on $\omega$ that has a base of sets of the form FS(X), where FS(X) denotes the set of all numbers that can be obtained as the sum of finitely many distinct elements of X. These ultrafilters relate to Hindman's Theorem in much the same way that Ramsey ultrafilters relate to Ramsey's Theorem. In this talk, I will present some fairly recent results concerning strongly summable ultrafilters. Some of these results involve algebraic properties of these ultrafilters as elements of the Cech-Stone compactification of the additive semigroup of natural numbers, while others relate to the investigation of whether these ultrafilters exist under certain set-theoretic hypothesis.