University of New Mexico — Algebra and Geometry Seminar

Computing local cohomology modules associated with a subvariety of a smooth variety is a central problem in commutative algebra and algebraic geometry. Recent progress uses the richer structure of mixed-Hodge D-modules. Related D-modules also occur in geometric representation theory, including composition-factor multiplicities of Verma modules described by the Kazhdan–Lusztig theorem. Michael Perlman explains how commutative algebra and Kazhdan–Lusztig theory can be combined to calculate local cohomology supported in Schubert varieties in generalized flag varieties. The classical Grassmannian provides the main example, with possible extensions to determinantal varieties and other Lie types. Attend online via the public Zoom meeting; the organizer publishes the access passcode on the seminar announcement. The talk runs from 15:00 to 15:45 Mountain Daylight Time.

Shikha Bhutani proves the outstanding positive-characteristic cases of the Borisov–Alexeev–Borisov conjecture for geometrically integral ε-klt del Pezzo surfaces over arbitrary fields. Earlier work by Bernasconi and Martin established boundedness except in characteristics 2, 3 and 5, reducing those cases to a uniform estimate for irregularity. The talk establishes that estimate and thereby completes the boundedness result across all positive characteristics.