SLMath · Fall 2026
Organizers: Erika Beserra and Yuanning Zhang.
Welcome! This is the webpage for the SLMath graduate student seminar and mini workshops in Fall 2026.
Fridays, 10–11 am · Eisenbud Auditorium, SLMath.
Abstract. We will introduce the negative half of the quantum group, discuss a positivity question, and walk through the idea of the proof of positivity of the canonical bases through categorification via KLR algebras. If there is remaining time, we will introduce cyclotomic quotients of KLR algebras, and their generalizations, KLRW algebras.
Marco Giustetto
Abstract.We will give a (very) quick overview of Morel's theory of 𝔸1-coverings and discuss some of its applications — for instance, motivic knots. We will then introduce 𝔸1-n-coverings, present a classification theorem for them — analogous to the topological classification of coverings — and give a variety of examples. Finally, we will answer a question of Morel on a geometric criterion for recognizing 𝔸1-coverings between schemes over a field. This is based on joint work with Thor Wittich.
Mini Workshop
Abstract. The Kazhdan Lusztig isomorphism, which relates the affine Hecke algebra of a p-adic group to the equivariant K-theory of the Steinberg variety of its Langlands dual, played a key role in the proof of the Deligne Langlands conjecture on the classification of tamely ramified irreducible representations. For a spherical variety X, we can construct two modules over the affine Hecke algebra: the first by considering Iwahori invariant functions on X, and the second using relative Langlands duality and equivariant K-theory. It is natural to expect a relationship between these modules. I will discuss this relationship for X = GL₂ₙ/Sp₂ₙ and its application to the study of distinguished representations.
Geometric Representation Theory and 3d Mirror Symmetry workshop (October 5–9).
Ansuman Chandra Bardalai
Abstract. The almost-commuting stack is the moduli of triples (g,X,q), where g is a group element, X is a Lie algebra element, and q is a scalar, such that g−1Xg = qX. We compute the dg-algebra of G∨-invariant functions on the almost-commuting stack as a graded dg-algebra over k[q,1/q]. In other words, we calculate the pushforward of the structure sheaf to Gm/Gm. Away from roots of unity, this k[q,1/q]-dga agrees with O(T∨)W[q,1/q], while at q = 1, there are derived corrections with nonzero grading degree. Unlike the related work of Li-Nadler-Yun on the multiplicative commuting stack, or of BenZvi-Chen-Helm-Nadler on coherent Springer theory, our approach does not require any form of Bezrukavnikov's equivalence. Instead, the primary technical input is a categorification of the Schur orthogonality relations / Hirzebruch-Riemann-Roch theorem, which is extracted from an adjointability criterion for doubly oplax-twisted topological field theories.
Motivic Homotopy Theory: Connections and Applications workshop (October 19–23).
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All seminars must take place in the Eisenbud Auditorium this week.
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SLMath is closed for Thanksgiving (November 26–27).
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