일정

장소: 서강대학교, K관(김대건관) 101호

일정: 12월 15일 (목)

2:00 ~ 3:00

김정섭 (KIAS)

제목: Projective manifolds with big tangent bundles

초록: After Mori's proof of Hartshorne's conjecture on ample tangent bundles, there are similar questions to characterize a projective manifold $X$ with certain positivity of its tangent bundle $T_X$. For example, a conjecture proposed by Campana and Peternell asks whether the homogeneous varieties are the only Fano manifolds $X$ with nef $T_X$. Recently, there has been some progress on the question of which projective manifolds have big tangent bundles. For example, toric manifolds, and Fano twofolds or some Fano threefolds of higher degree are known to have big tangent bundles. In this talk, I will review the progress, and introduce some examples and non-examples of projective manifolds with big tangent bundles. This talk is based on joint work with Hosung Kim and Yongnam Lee.

3:00 ~ 4:00

박현준 (KIAS)

제목: Counting surfaces on Calabi-Yau 4-folds

초록: Counting curves on Calabi-Yau 3-folds is one of the most central topics in modern enumerative geometry. In this talk, we discuss counting surfaces on Calabi-Yau 4-folds. An interesting new feature is a deep connection to derived algebraic geometry and Hodge theory. As an application, we show that Grothendieck's variational Hodge conjecture holds for (2,2)-classes with non-zero surface counting invariants. This is joint work with Younghan Bae and Martijn Kool.

4:00 ~ 4:15 휴식

4:15 ~ 5:15

홍한솔 (연세대)

제목: The Maurer-Cartan algebra of a Lagrangian and Koszul duality

초록: The Maurer-Cartan algebra of a Lagrangian is the algebra that encodes the deformation of its Floer complex as an A-infinity algebra. I will give a convenient description of the Maurer-Cartan algebra using natural homological algebra language, and relate it with (a version of) Koszul duality for the Floer complex. We will discuss its mirror symmetry interpretation through some concrete geometric examples.