Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 12, 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  4  5  6                1  2  3                      1
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Monday, November 12, 2018

3:00 pm in 243 Altgeld Hall,Monday, November 12, 2018

#### Beyond semitoric

###### Susan Tolman (Illinois)

Abstract: A compact four dimensional completely integrable system $f \colon M \to \mathbb{R}^2$ is semitoric if it has only non-degenerate singularities, without hyperbolic blocks, and one of the components of $f$ generates a circle action. Semitoric systems have been well studied and have many nice properties; for example, the fibers $f^{-1}(x)$ are connected. Unfortunately, although there are many interesting examples of semitoric systems, the class has some limitations. For example, there are blowups of $S^2 \times S^2$ with Hamiltonian circle actions that cannot be extended to semitoric system. We show that, by allowing certain degenerate singularities, we can expand the class of semitonic systems but still prove that $f^{-1}(x)$ is connected. We hope that this class will be large enough to include not only all compact four manifolds with Hamiltonian circle actions, but more generally all complexity one spaces. Based on joint work with D. Sepe.

3:00 pm in 345 Altgeld Hall,Monday, November 12, 2018

#### Modalities and Blakers-Massey

###### Joseph Rennie (UIUC Math)

Abstract: In this talk, I’ll introduce modality from a logical standpoint, then explore the interpretation within the logic of spaces provided by recent Type Theories. I’ll present the recent generalization of Blakers-Massey theorems to arbitrary higher toposes as well as some applications to homotopy theory.

4:00 pm in 245 Altgeld Hall,Monday, November 12, 2018

#### Enumerative Algebraic Geometry, String Theory, and Modular Forms

###### Sheldon Katz   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: String Theory in physics has interacted strongly with many areas of pure mathematics over the past 30 years, bringing new insights along with it, leading to provable theorems. Among these areas of mathematics are algebraic geometry and number theory. In this talk, I give a high level overview of the interaction of string theory, algebraic geometry, and number theory together with some illustrative examples involving enumerative geometry and modular forms.

5:00 pm in 241 Altgeld Hall,Monday, November 12, 2018

#### Cheeger inequalities for arbitrary Hermitian matrices

###### Michael Jarret (Perimeter)

Abstract: We study graph Laplacian of maximal degree and the corresponding wighted Cheeger constant.