Determining the complexity of Kazhdan-Lusztig varieties

Abstract: Kazhdan-Lusztig varieties are defined by ideals generated by certain minors of a matrix, which are chosen by a combinatorial rule. These varieties are of interest in commutative algebra and Schubert varieties. Each Kazhdan-Lusztig variety has a natural torus action from which one can construct a cone. The complexity of this torus action can be computed from the dimension of the cone and, in some sense, indicates how close the variety is to the toric variety of the cone. In joint work with Maria Donten-Bury and Irem Portakal we address the problem of classifying which Kazhdan-Lusztig varieties have a given complexity. We do so by utilizing the rich combinatorics of Kazhdan-Lusztig varieties.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

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