Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, December 5, 2018.

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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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1  2  3                      1          1  2  3  4  5
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Wednesday, December 5, 2018

3:00 pm in 241 Altgeld Hall,Wednesday, December 5, 2018

#### $\ell^2$ Betti numbers of countable Borel equivalence relations: Part 4

###### Ruiyuan (Ronnie) Chen (UIUC Math)

Abstract: We will continue to discuss Gaboriau's 2002 paper "Invariants $\ell^2$ de relations d'équivalence et de groupes" from a descriptive set-theoretic point of view. In this second talk, we will discuss Borel fields of sets and structures (in particular, simplicial complexes and Hilbert spaces) over a countable Borel equivalence relation, and how to measure their "Borel cardinality" using Tarski's theory of cardinal algebras.

4:00 pm in 2 Illini Hall,Wednesday, December 5, 2018

#### Tiered UFD

###### Justin Kelm (UIUC Math)

Abstract: We proved the proporty that a strongly tiered UFD will satisfy.

4:00 pm in 245 Altgeld Hall,Wednesday, December 5, 2018

#### Orders of infinities: asymptotic valued differential fields

###### Nigel Pynn-Coates (UIUC Math)

Abstract: Asymptotic valued differential fields go back to work of Hardy and are motivated by comparing the asymptotic behaviour of solutions to differential equations. I will introduce valued differential fields and discuss some of this history. We will see how versions of l’Hôpital’s Rule show up as key properties in the subject. Along the way, I will draw some pictures to illustrate the topology of valued fields. Time permitting, I may mention some of my results or ongoing work.