Department of

# Mathematics

Seminar Calendar
for events the day of Friday, September 25, 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, September 25, 2020

1:00 pm in Zoom link sent to mailing list,Friday, September 25, 2020

#### To Be Announced

###### Mary Angelica Gramcko-Tursi   [email] (UIUC Math)

Abstract: TBA

4:00 pm in Zoom,Friday, September 25, 2020

#### Framed Cobordism and the Homotopy Groups of Spheres

###### Brian Shin

Abstract: The computation of the homotopy groups of spheres has dominated the minds of homotopy theorists since the 1930s. To this day, much is still not known about these groups. In this expository talk, I'd like to discuss one of the earliest approaches to understanding these groups: the geometry of framed cobordisms. Please contact basilio3 (at) illinois (dot) edu for Zoom details.

4:00 pm in Zoom (email ruiyuan at illinois for info),Friday, September 25, 2020

#### Characterizing companionability for expansions of o-minimal theories by a dense, proper subgroup

###### Alexi Block Gorman (UIUC Math)

Abstract: Recent works in model theory have established natural and broad criteria concerning the existence of model companions and the preservation of certain neostability properties when passing to the model companion. In this talk, we restrict our attention to the o-minimal setting. By doing so, we can isolate the sort of necessary and sufficient condition that can be elusive in more general settings. The central result is a full characterization for when the expansion of a complete o-minimal theory by a unary predicate that picks out a dense, divisible subgroup has a model companion. We will discuss examples both in which the predicate is an additive subgroup, and in which it is a mutliplicative subgroup. The o-minimal setting allows us to provide a full and geometric characterization for companionability, with a particularly elegant dividing line when the group operation is multiplication. We conclude with a brief discussion of neostability properties, and give examples that illustrate the lack of preservation for properties such as strong, NIP, and NTP2, though there are also examples for which some or all three of those properties hold.