Title & Abstract

Day 1 (Nov 9, RM225) - The first talk will be in 254.

  • 2:00 LI QIFENG : A characterization of Symplectic and odd Symplectic Grassmannians, and their deformation rigidity

During the study of deformation rigidity of rational homogeneous spaces of Picard number one, Hwang and Mok develop the theory of varieties of minimal rational tangents (VMRT). In the theory of VMRT, one of the main problems is to recognize certain varieties from its VMRT, firstly studied by Mok and then by Hwang and Hwang-Hong etc. It turns out that in principle the deformation rigidity could be obtained as a corollary of the characterization by VMRT. In this talk, we will discuss the characterization of Symplectic and odd Symplectic Grassmannians by their VMRT's. We will also discuss their deformation rigidity, while the deformation rigidity of Symplectic Grassmannians was obtained by Hwang and Mok in a more complicated way. This is a joint work with Jun-Muk Hwang.

  • 3:30 CHUNG KIRYONG : Toward computation of the cohomology ring of the moduli space of the pure sheaves on del Pezzo surfaces

The geometry of the moduli space of sheaves on $\mathbb{P}^2$ has been studied in various viewpoints, for instance curve counting, the strange duality conjecture, and birational geometry via Bridgeland stability. For small degree cases, it was possible to classify all rational contractions and compute the cohomology ring of the moduli space.

In this talk, we consider the next simplest case of a quadric surface. We construct a flip between the moduli space of sheaves and a projective bundle, and show that their common blown-up space is the moduli space of stable pairs. In principle, this enable us to compute the cohomology ring of the moduli space from that of the projective bundle.

  • 4:30 GONGYO YOSHINORI : On Kollár’s injectivity theorem on globally F-regular varieties

We discuss the Kollár type injectivity theorem for cohomologies of adjoint bundles on globally F-regular varieties


Day 2 (Nov 10, RM225)

  • 11:00 KIM HYUNKYU: Quantization of cluster varieties

A cluster variety is a scheme obtained by gluing split algebraic tori along certain birational maps called mutation, defined and studied by Fock and Goncharov. An important example of a cluster variety is birational to some version of the Teichmuller space of a Riemann surface. Quantization replaces the tori by quantum tori, and the birational maps by non-commutative maps. I will introduce basic notions and constructions about these topics.

  • 2:00 HU YONG : On minimal 3-folds of general type which are fibred by $(1,2)$-surfaces

We answer an open problem raised in 2008 and prove that, for any minimal 3-fold $X$ of general type with the geometric genus $\geq 5$, the $4$-canonical map $\varphi_{4,X}$ is non-birational if and only if $X$ is birationally fibred by $(1,2)$-surfaces. The statement does not hold for those with the geometric genus $\leq 4$. This is a joint work with Meng Chen.

  • 3:00 JUNG SEUNG-JO : Cubic fourfolds and K3 surfaces: general overview

This talk gives a general overview on the beautiful relationship between cubic fourfolds and K3 surfaces. Mainly I review a recent construction of stability conditions on Kuznetsov categories by Bayer--Lahoz--Macrí--Stellari and its applications. If I can prove something meaningful during my holiday, I will present it as well.