MATH Semineri: “Differential systems II”, Waqar Ali Shah (Bilkent Üniversitesi), 13:00 11 Kasım 2026 (EN)

You are cordially invited to the Algebra Seminar organized by the Department of Mathematics.

Speaker: Waqar Ali Shah (Bilkent)

“Differential systems II”

Abstract: In the previous talk, I introduced differential posets and discussed certain implications between the three Miller–Reiner conjectures. In this continuation, I turn to a general framework for studying differential systems: graded, locally finite, bounded-below representations of the first Weyl algebra on which the ∂u-operator has full rank. I will introduce the notion of ramps, which capture the interaction of the up and down maps between two adjacent degrees of a differential system. Under suitable freeness hypotheses on the cokernels, I will sketch the proof of a structure theorem for differential systems over the ring of all algebraic integers. I will also discuss a potential generalization of the Miller–Reiner conjectures in this setting when the freeness hypothesis is relaxed. This is joint work with Shaheen Nazir.

Date: 11 November 2026
Time: 13:00
Place: SA-141