Algebra and Algebraic Geometry Seminar Fall 2023

The seminar normally meets 2:30-3:30pm on Fridays, in the room VV B223.

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Fall 2023 Schedule

date	speaker	title	host/link to talk
September 15	Joshua Mundinger	Quantization in positive characteristic	local
November 17	Purnaprajna Bangere	Syzygies of adjoint linear series on projective varieties	Michael K

Abstracts

Joshua Mundinger

Quantization in positive characteristic

In order to answer basic questions in modular and geometric representation theory, Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties in positive characteristic. These are certain noncommutative algebras over a field of positive characteristic which have a large center. I will discuss recent work describing how to construct an important class of modules over such algebras.

Purnaprajna Bangere

Syzygies of adjoint linear series on projective varietiess

Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. After the pioneering work of Mark Green on curves, numerous attempts have been made to extend some of these results to higher dimensions. It has been proposed that the syzygies of adjoint linear series L=K+mA, with A ample is a natural analogue for higher dimensions to explore. The very ampleness of adjoint linear series is not known for even threefolds. So the question that has been open for many years is the following (Question): If A is base point free and ample, does L satisfy property N_p for m>=n+1+p? Ein and Lazarsfeld proved this when A is very ample in 1991. In a joint work with Justin Lacini, we give a positive answer to the original question above.