Titles and abstracts

Sami Assaf — Title: Superb Crystals
Abstract: Demazure crystals are certain extremal subsets of highest weight crystals which give a combinatorial skeleton of Demazure modules. In certain special cases, Kashiwara’s tensor product rule for crystals gives a combinatorial realization of excellent filtrations for tensor products of Demazure modules. However, not all tensor products of Demazure crystals result in unions of Demazure crystals. This reflects the fact that not all tensor products of Demazure modules admit excellent filtrations. Polo conjectured tensor products of Demazure modules always admit superb filtrations, wherein successive quotients are Schubert modules. In evidence of this, I recently proved certain products of Demazure characters expand nonnegatively into Schubert characters. In this talk, we introduce a new family of extremal subsets of highest weight crystals and show how they might give a crystal-theoretic model for Polo’s conjecture. 

Pablo Boixeda-Alvarez — TBA

Jon Brundan — Title: Categorification of quantum symmetric pairs
Abstract: Given a symmetrizable Cartan matrix $(a_{i,j})_{i,j \in I}$, Lusztig's algebra $\mathbf{f}$, which is half of a Drinfeld-Jimbo quantum group, has generators $\theta_i\:(i \in I)$ subject to the quantum Serre relations. An elementary algebraic way to "categorify" this algebra was introduced nearly 20 years ago by Khovanov, Lauda and Rouquer, based on a new family of algebras called quiver Hecke algebras. The quantum Serre relation gets replaced by a split exact complex whose Euler characteristic recovers the original relation. Another remarkable family of quantum algebras are the quasi-split iquantum groups introduced by Letzter, generalized by Kolb, and studied further by Bao and Wang (who introduced this terminology). They include ordinary Drinfeld-Jimbo quantum groups as a special case. The definition requires the additional data of an involution $\tau$ of the Cartan matrix. When defined by generators and relations, there is again just one required relation, which is similar to the quantum Serre relation but with the $0$ on the right hand side replaced by a complicated lower order term. I will explain how to categorify quasi-split iquantum groups in a uniform way, leading to a categorical explanation for the mysterious extra term in the iSerre relation. This is based on joint work with Weiqiang Wang and Ben Webster.

Ben Elias — TBA

Monica Garcia — TBA

Eduardo Gonzalez — TBA

Cris Negron — TBA

Khoa Nguyen — TBA

Julia Pevstova — Title: The Balmer spectrum of local dualizable representations of a finite group.
Abstract: Let G be a finite group, and k a field of positive characteristic p. The stable category of representations of G over k is a well-studied entity whose Balmer spectrum was effectively computed by Benson, Carlson and Rickard in 1997. If one fixes a prime ideal in the Balmer spectrum and zooms in to the category of all representations of G supported only at that specific ideal, one discovers many interesting phenomena.  I’ll describe the ``small” (= dualizable) objects in that category, calculate their spectrum, and draw parallels with completions in commutative algebra. Joint work with D. Benson, S. Iyengar, H. Krause.

Raphael Rouquier — TBA

Eric Rowell — TBA

Nick Rozenblyum — TBA

Leonid Rybnikov — TBA

Vasu Tewari — TBA

Oleksandr Tsymbaliuk — TBA

Yaolong Shen — TBA

Chelsea Walton — Title: Representations of braided categories.
Abstract: In the talk, I'll discuss recent work with Robert Laugwitz and Milen Yakimov, and with Harshit Yadav, on module categories over braided finite tensor categories. This will be based on the articles, ArXiv/2307.14764 and ArXiv/2411.18453, and I'll aim to keep this down-to-earth.