Algebra and Algebraic Geometry Seminar Spring 2020

Spring 2020 Schedule

date	speaker	title	host(s)
January 24	Xi Chen (Alberta)	Rational Curves on K3 Surfaces	Michael K
January 31	Janina Letz (Utah)	TBD	Daniel and Michael B
February 7	Jonathan Montaño (New Mexico State)	TBD	Daniel
February 14
February 21	Erika Ordog (Duke)	TBD	Daniel
February 28
March 6
March 13
March 20
March 27	Patrick McFaddin (Fordham)	TBD	Michael B
April 3
April 10	Ruijie Yang (Stony Brook)	TBD	Michael K
April 17	Remy van Dobben de Bruyn (Princeton/IAS)	TBD	Botong
April 24
May 1	Lazarsfeld Distinguished Lectures
May 8

Abstracts

Xi Chen

Rational Curves on K3 Surfaces

It is conjectured that there are infinitely many rational curves on every projective K3 surface. A large part of this conjecture was proved by Jun Li and Christian Liedtke, based on the characteristic p reduction method proposed by Bogomolov-Hassett-Tschinkel. They proved that there are infinitely many rational curves on every projective K3 surface of odd Picard rank. Over complex numbers, there are a few remaining cases: K3 surfaces of Picard rank two excluding elliptic K3's and K3's with infinite automorphism groups and K3 surfaces with two particular Picard lattices of rank four. We have settled these leftover cases and also generalized the conjecture to the existence of curves of high genus. This is a joint work with Frank Gounelas and Christian Liedtke.

Janina Letz

Local to global principles for generation time over commutative rings

Abstract: In the derived category of modules over a commutative noetherian ring a complex $G$ is said to generate a complex $X$ if the latter can be obtained from the former by taking finitely many summands and cones. The number of cones needed in this process is the generation time of $X$. In this talk I will present some local to global type results for computing this invariant, and also discuss some applications of these results.