Search Research Symposium Abstracts

Stability of line bundles and deformed-Hermitian-Yang Mills equation for some elliptic surfaces

Donaldson and Uhlenbeck-Yau established the classical result that on a compact Kahler manifold, an irreducible holomorphic vector bundle admits a Hermitian metric solving the Hermitian-Yang-Mills equation if and only if the vector bundle is Mumford-Takemoto stable. Motivated by the characterization of supersymmetric B-branes in string theory and mirror [Read More...]

Presenter: Yun Shi, Brandeis University
Authors: Tristan Collins, Jason Lo, Yun Shi, Shing-Tung Yau
Symposium Year: 2023
Session: Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]
Presentation Time: September 30, 2023; 2:00 pm

Parabolic induction and parity sheaves for classical groups.

Parity sheaves are some constructible complexes defined on some stratified space where the strata satisfies some parity vanishing conditions. They are introduced by Carl Mautner, Daniel Juteau and Geordie Williamson in 2014. In characteristic $0$ they coincide with the intersection cohomology complexes but in positive characteristic they are new and [Read More...]

Presenter: Tamanna chatterjee, University of Notre Dame
Authors: Pramod N. Achar, Tamanna Chatterjee
Symposium Year: 2023
Session: Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]
Presentation Time: September 30, 2023; 2:50 pm

Additive Invariants of Open Petri Nets

We classify all additive invariants of open Petri nets: these are $\mathbb{N}$-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems: one for open Petri nets and one for monically open Petri nets (i.e. open Petri nets whose interfaces are specified by [Read More...]

Presenter: Layla Sorkatti, Southern Illinois University
Authors: Benjamin Merlin Bumpus, Sophie Libkind, Jordy Lopez Garcia, Layla Sorkatti, Samuel Tenka
Symposium Year: 2023
Session: Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]
Presentation Time: September 30, 2023; 3:40 pm

Homological Mirror Symmetry for Theta Divisors

Symplectic geometry is a relatively new branch of geometry. However, a string theory-inspired duality known as “mirror symmetry” reveals more about symplectic geometry from its mirror counterparts in complex geometry. M. Kontsevich conjectured an algebraic version of mirror symmetry called “homological mirror symmetry” (HMS) in his 1994 ICM address. [Read More...]

Presenter: Catherine Cannizzo, UC Berkeley
Authors: Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu, Catherine Cannizzo
Symposium Year: 2023
Session: Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]
Presentation Time: October 1, 2023; 9:45 am

Spectral Sequence for Relative Contact Homology via Winding along a Binding and Applications

There is a spectral sequence converging to symplectic cohomology of an affine variety whose E1-page consists of symplectic cohomology of the complement of a hypersurface in the affine variety. We will talk about a contact (as well as S1-equivariant) version of the spectral sequence and provide applications including the invariants of fibered knots and the [Read More...]

Presenter: Dahye Cho, Yonsei University
Symposium Year: 2023
Session: Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]
Presentation Time: October 1, 2023; 10:35 am

Cherednik algebras, Hilbert schemes and mirabolic D-modules

Under the Gordon-Stafford functor, every filtered representation of the type A rational Cherednik algebra corresponds to an equivariant coherent sheaf on the Hilbert scheme of points on the plane. Under the decategorification of this functor, the images of the finite-dimensional representations are closely related to the knot superpolynomials as conjectured [Read More...]

Presenter: Xinchun Ma, UChicago
Symposium Year: 2023
Session: Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]
Presentation Time: October 1, 2023; 2:00 pm

Diving Deeper into Supercuspidal Representations

Reeder-Yu introduced certain low positive depth supercuspidal representations of $p$-adic groups called $\textit{epipelagic}$ representations. These representations generalize the simple supercuspidal representations of Gross-Reeder, which have the lowest possible depth. Epipelagic representations also arise in recent work on the Langlands correspondence; [Read More...]

Presenter: Prerna Agarwal, LSU
Symposium Year: 2023
Session: Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]
Presentation Time: October 1, 2023; 2:50 pm