Department of

# Mathematics

Seminar Calendar
for events the day of Monday, February 24, 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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Monday, February 24, 2020

11:00 am in 464 Loomis ,Monday, February 24, 2020

#### Developments in the Bagger-Witten and Hodge line bundles

###### Eric Sharpe (Virginia Tech Physics)

Abstract: This talk will concern advances in understanding explicitly the Bagger-Witten line bundle appearing in four-dimensional N=1 supergravity, which is closely related to the Hodge line bundle on a moduli space of Calabi-Yaus. This has recently been a subject of interest, but explicit examples have proven elusive in the past. In this talk we will outline some recent advances, including (1) a description of the Bagger-Witten line bundle on a moduli space of Calabi-Yau's as a line bundle of covariantly constant spinors (resulting in a square root of the Hodge line bundle of holomorphic top-forms), (2) results suggesting that it (and the Hodge line bundle) is always flat, but possibly never trivial, over moduli spaces of Calabi-Yaus of maximal holonomy and dimension greater than two. We will propose its nontriviality as a new criterion for existence of UV completions of four-dimensional supergravity theories. If time permits, we will explicitly construct an example, to concretely display these properties, and outline results obtained with Ron Donagi and Mark Macerato for other cases.

3:00 pm in 243 Altgeld Hall,Monday, February 24, 2020

#### On symplectic capacities and their blindspots

###### Ely Kerman (Illinois)

Abstract: Symplectic capacities are real-valued symplectic invariants which play an important role in embedding problems. Many fundamental questions concerning their properties remain unresolved in large part because they are difficult to compute. In this talk I will describe some new computations of the capacities defined for star-shaped domains by Gutt and Hutchings. The relevant class of examples is rich enough to yield several new insights into what these capacities can and cannot see. This is a report on joint work with Yuanpu Liang.

3:00 pm in 441 Altgeld Hall,Monday, February 24, 2020

#### An introduction to motivic homotopy theory

###### Brian Shin (Illinois Math)

Abstract: Motivic homotopy is often thought of as the homotopy theory of algebraic varieties. In this expository talk, we'll see exactly what that means. In particular, we'll see how the construction of the category of motivic spaces is a direct algebro-geometric analog of that of the category of spaces. More interestingly, we'll also see how the analogy breaks down.

4:00 pm in 314 Altgeld Hall,Monday, February 24, 2020

#### Digits

###### Frank Calegari (University of Chicago)

Abstract: We discuss some results concerning the decimal expansion of 1/p for primes p, some due to Gauss, and some from the present day. This talk will be accessible to undergraduates.

5:00 pm in 241 Altgeld Hall,Monday, February 24, 2020

Abstract: CEB4