SWAG 10 - 일정

박진형(서강대학교) 1:30-2:20

Asymptotic vanishing of syzygies of algebraic varieties

Abstract: About ten years ago, Ein-Lazarsfeld showed the asymptotic nonvanishing theorem of syzygies of algebraic varieties. Their result roughly says that almost all "asymptotic syzygies" of algebraic varieties are nonvanishing, and they conjectured that the remaining "asymptotic syzygies" are vanishing. This suggests that the minimal free resolutions of the graded section rings of line bundles on a projective variety have a surprisingly uniform asymptotic shape as the positivity of the line bundles grows. In this talk, we confirm Ein-Lazarsfeld's conjecture on vanishing of asymptotic syzygies of algebraic varieties. We first prove the conjecture for the case of products of projective spaces, and then following Raicu's argument, we deduce the general case from this special case.

2.김인균(연세대학교) 2:40-3:30
An introduction to log canonical thresholds

The log canonical threshold is an important invariant. Let (X, D) be a pair. Then the log canonical threshold provide a way of measuring how singular X and D are.

In this talk, we study the definition, some properties of the log canonical threshold and examples. And we introduce some applications of log canonical thresholds. Finally we study the Hodge ideal which is a generalization of the multiplier ideal.

3.김유식(부산대학교) 3:40-4:30

Mirror symmetry of polygon spaces.

The main topic of this talk is 3D polygon spaces. I will highlight the importance of 3D polygon spaces in the aspect of mirror symmetry and Lagrangian Floer theory. Especially, I will focus on the interaction between bending systems, construction of cluster varieties, and computation of disk potential functions.