Search Research Symposium Abstracts

Applications of geometric representation theory to link homology*

The motivation behind this work in progress is to unify different approaches to Khovanov-Rozansky triply graded link homology, HHH. By an old theorem of Markov links up to isotopy is equivalent to braids up to the so called Markov moves. Hence, braid group actions, which already play a central role in geometric representation theory, provides a natural [Read More...]

Presenter: Tina Kanstrup, UMass Amherst
Symposium Year: 2022
Session: Geometric and Categorical Aspects of Representation Theory and Related Topics
Presentation Time: June 18, 2022; 10:15 am

Relating the Specht and sl_3 web bases

An important topic in representation theory is understanding the relationship between different bases for the same representation. In this talk, we discuss our work showing upper triangularity of the change-of-basis matrix between the sl_3 web basis and Specht basis for irreducible symmetric group representations of three-row rectangular shape. Specht bases [Read More...]

Presenter: Heather M. Russell, University of Richmond
Authors: Heather M. Russell & Julianna S. Tymoczko
Symposium Year: 2022
Session: Geometric and Categorical Aspects of Representation Theory and Related Topics
Presentation Time: June 18, 2022; 11:05 am

Homological mirror symmetry for the universal centralizers

I will present my recent result on homological mirror symmetry for the universal centralizer (a.k.a Toda space) associated with a complex semisimple Lie group. The A-side is a partially wrapped Fukaya category on the universal centralizer, and the B-side is the category of coherent sheaves on the categorical quotient of the dual maximal torus by the Weyl [Read More...]

Presenter: Xin Jin, Boston College
Symposium Year: 2022
Session: Geometric and Categorical Aspects of Representation Theory and Related Topics
Presentation Time: June 18, 2022; 3:20 pm

Parity sheaves on graded Lie algebras

Let $G$ be a complex, connected, reductive, algebraic group, and $\chi: \mathbb{C}^\times \to G$ be a fixed co-character that defines a grading on $\mathfrak{g},$ the Lie algebra of $G$. Let $G_0$ be the centralizer of $\chi(\mathbb{C}^\times).$ Here I will talk about $G_0$-equivariant parity sheaves on the $n$-graded piece, $\mathfrak{g}_n.$ For the first [Read More...]

Presenter: Tamanna Chatterjee, University of Georgia
Authors: Tamanna Chatterjee
Symposium Year: 2022
Session: Geometric and Categorical Aspects of Representation Theory and Related Topics
Presentation Time: June 18, 2022; 4:10 pm

The geometry and combinatorics of 3-row Springer fibers*

The Springer fiber of a matrix $X$ is a subvariety of the flag variety consisting of the flags fixed by $X$. One of the classical examples of geometric representation theory shows that their cohomology admits a representation of the symmetric group (or the Weyl group, in general Lie type). Like Schubert varieties, the geometry of Springer fibers is deeply [Read More...]

Presenter: Julianna Tymoczko, Smith College
Symposium Year: 2022
Session: Geometric and Categorical Aspects of Representation Theory and Related Topics
Presentation Time: June 19, 2022; 9:15 am

A quasi-Poisson structure on the multiplicative Grothendieck-Springer resolution*

The Grothendieck-Springer resolution of a semisimple complex group G carries a canonical Poisson structure whose symplectic leaves are affine bundles over the flag variety. This structure is obtained by Hamiltonian reduction of the cotangent bundle T*G with respect to the action of a Borel. We construct a multiplicative counterpart to this setting by [Read More...]

Presenter: Ana Balibanu, Harvard University
Authors: Ana Balibanu, Maxence Mayrand
Symposium Year: 2022
Session: Geometric and Categorical Aspects of Representation Theory and Related Topics
Presentation Time: June 19, 2022; 10:05 am

B_2 Foams and Web Homology

Closed webs in Kuperberg's B_2 spider evaluate to Laurent polynomials in q with integer coefficients. We will discuss ongoing work on the categorification of the graphical calculus for so_5 webs using decorated web cobordisms or [Read More...]

Presenter: Mrudul Thatte, Columbia University
Symposium Year: 2022
Session: Geometric and Categorical Aspects of Representation Theory and Related Topics
Presentation Time: June 19, 2022; 10:05 am