Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 21, 2020.

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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, February 21, 2020

2:00 pm in 447 Altgeld Hall,Friday, February 21, 2020

#### Novikov conjecture for groups generated by coarsely embeddable groups under extensions and admissible limits

###### Zhizhang Xie (Texas A&M)

Abstract: I will talk about some recent work on the strong Novikov conjecture for groups generated by coarsely embeddable groups under extensions and admissible limits. Here we say a group $G$ is an admissible limit of a family of groups $\{ G_i \}$ if the following is satisfied: for any finite subset $F$ of $G$, there exists $n$ such that the preimage of $F$ in $G_i$ injects into $G$ for all $i > n$. This talk is based on my joint work with Jintao Deng and Guoliang Yu.

4:00 pm in 341 Altgeld Hall,Friday, February 21, 2020

#### Julia Robinson and Hilbert's Tenth Problem

###### (UIUC Math)

Abstract: Julia Robinson was the first woman elected to the mathematical section of the National Academy of Sciences, and the first woman to become president of the American Mathematical Society. While tracing Robinson's contribution to the solution of Hilbert's tenth problem, the film illuminates how her work led to an unusual friendship between Russian and American colleagues at the height of the Cold War.

4:00 pm in 141 Altgeld Hall,Friday, February 21, 2020

#### Unifying Galois Theories with Categorification

###### Robert (Joseph) Rennie (UIUC)

Abstract: Since its inception nearly two centuries ago, what we call "Galois Theory" (say in an undergraduate algebra course) has led to many analogous results, and thus attained the status of a sort of metatheorem. In Galois' case, this concept was applied to fields, yielding an equivalence between some lattice of field extensions and a lattice of subgroups of a corresponding "galois group" ... under certain conditions. Later on, the same concept was shown to be present in Topology, with extensions being replaced by their dual notion of covering spaces, and the galois group being replaced by the fundamental group... again, under certain conditions. Even later, Galois' results for fields were generalized to arbitrary rings, introducing new associated data along the way. In this talk, we explore the process of formally unifying all of these "Galois Theories" into one Galois Principle, with the aim of developing an intuition for identifying some of its infinite use-cases in the wilds of Math (e.g. Algebra, Topology, and Logic). Along the way, I aim to discuss explicitly and to motivate categorification to the working mathematician using the results of this talk as concrete examples.

5:00 pm in 245 Altgeld Hall,Friday, February 21, 2020