Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, February 26, 2019.

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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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Tuesday, February 26, 2019

11:00 am in 345 Altgeld Hall,Tuesday, February 26, 2019

#### What we know so far about "topological Langlands Correspondence"

###### Andrew Salch (Wayne State University)

Abstract: I'll give a survey of some relationships between Galois representations and stable homotopy groups of finite CW-complexes which suggest the possibility of "topological Langlands correspondences." I'll explain what such correspondences ought to be, what their practical consequences are for number theory and for algebraic topology, and I'll explain the cases of such correspondences that are known to exist so far. As an application of one family of known cases, I'll give a topological proof of the Leopoldt conjecture for one particular family of number fields. Some of the results in this talk are joint work with M. Strauch.

12:00 pm in 243 Altgeld Hall,Tuesday, February 26, 2019

#### Congruence subgroups in genus one

###### Autumn Kent (U Wisconsin)

Abstract: I’ll discuss a proof of Asada’s theorem that mapping class groups of punctured tori have the congruence subgroup property.

1:00 pm in Altgeld Hall,Tuesday, February 26, 2019

#### n-dependent groups and fields

Abstract: NIP theories are the first class of the hierarchy of n-dependent structures. The random n-hypergraph is the canonical object which is n-dependent but not (n-1)-dependent. Thus the hierarchy is strict. But one might ask if there are any algebraic objects (groups, rings, fields) which are strictly n-dependent for every n? We will start by introducing the n-dependent hierarchy and present all known results on n-dependent groups and fields. These were (more or less) inspired by the above question.

2:00 pm in 243 Altgeld Hall,Tuesday, February 26, 2019

#### 2-connected hypergraphs with no long cycles

###### Ruth Luo (Illinois Math)

Abstract: The Erdős–Gallai theorem gives an upper bound for the maximum number of edges in an $n$-vertex graph with no cycle of length $k$ or longer. Recently, many analogous results for $r$-uniform hypergraphs with no Berge cycle of length $k$ or longer have appeared. In this talk, we present a result for $2$-connected hypergraphs without long Berge cycles. For $n$ large with respect to $r$ and $k$, our bound is sharp and is significantly stronger than the bound without restrictions on connectivity. This is joint work with Zoltán Füredi and Alexandr Kostochka.

3:00 pm in 243 Altgeld Hall,Tuesday, February 26, 2019

#### Pure cohomology of multiplicative quiver varieties

###### Thomas Nevins (UIUC)

Abstract: Multiplicative quiver varieties are certain quasiprojective algebraic varieties, defined by Crawley-Boevey and Shaw, associated to quivers. Examples include many moduli spaces of surface group representations (with punctures), a.k.a. moduli spaces of connections on punctured surfaces. I will introduce the basics of these varieties and explain joint work with McGerty that describes generators of the Hodge-theoretically "pure" part of their cohomology rings.

4:00 pm in 245 Altgeld Hall,Tuesday, February 26, 2019

#### Altgeld-Illini Renovation/Building Project Feedback Session

Abstract: This feedback session will focus on office space. Everyone is encouraged attend and the committee would like to hear from graduate students, non-tenure track instructors and lecturers and postdocs, in addition to faculty.