Department of

# Mathematics

Seminar Calendar
for Topology Seminar events the year of Wednesday, July 6, 2022.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      June 2022              July 2022             August 2022
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Friday, February 25, 2022

4:00 pm in 347 Altgeld Hall,Friday, February 25, 2022

#### The Jones Polynomial and its Big Brother, Khovanov Homology

###### Joseph Malionek (UIUC)

Abstract: In this talk, I will acquaint the audience with a link invariant called the Jones Polynomial and one of way of making it much more complicated (but potentially much stronger) called Khovanov Homology. I will go over some key properties of each of these invariants, some example calculations, some big results, and some open problems.

Friday, March 4, 2022

4:00 pm in 347 Altgeld Hall,Friday, March 4, 2022

#### The flux homomorphism for groups of symplectomorphisms

###### Wilmer Smilde (UIUC)

Abstract: On a symplectic manifold, one has two types of symmetries. Namely, the symplectomorphisms, which are diffeomorphisms preserving the symplectic form, and Hamiltonian diffeomorphisms, which are generated by Hamiltonian functions. Every Hamiltonian diffeomorphism is also a symplectomorphism. The flux homomorphisms is a tool that enables us to write the symplectomorphism group as an extension of the Hamiltonian group by a (finite-dimensional) abelian group. In this talk, I will go over the definition of the flux homomorphism, and show some basic properties. The aim is to arrive at some nice and pretty exact sequences. In the end I also hope to explain some important and deep results related to it. The nice thing about the flux homomorphism is that it requires very little experience with symplectic structures, so I hope it is accessible for anyone familiar with differential geometry.

Friday, March 25, 2022

4:00 pm in 347 Altgeld Hall,Friday, March 25, 2022

#### Modular Forms in Geometry and Physics

###### Saaber Pourmotabbed

Abstract: Modular forms appear as generating functions of curve counts and BPS states, partition functions of conformal field theories, in moonshine phenomena, sections of line bundles, spectrums of cohomology theories, elliptic genera of K3 surfaces, and many other interesting cases. In this talk we will look at some examples of where modular forms occur in physics and geometry, why they occur, and their interactions between these different fields.

Friday, April 1, 2022

4:00 pm in 347 Altgeld Hall,Friday, April 1, 2022

#### (Linear) analysis at singularities, infinities, and other things

###### Gayana Jayasinghe

Abstract: How does one make sense of a singularity which can be described in terms of a degenerate Riemannian metric? How does one study operators on a Riemannian manifold with a specific growth at infinity? How can we put this all together to study all sorts of spaces with degeneracies and growth rates and study (pseudo) differential operators, for instance to prove elliptic regularity? How does one study the wave equation with the Weyl Peterson metric and other such fantasies? I'll try and explain how we do this with geometric microlocal analysis.