Talk tiles and abstract

8월 1일

2:30-3:30, 4:00-5:00 조윤형 (IBS) : GELFAND-CETLIN SYSTEMS ON FLAG VARIETIES - I & II

In the first part of this talk, I will introduce Harada-Kaveh’s results on the theory of Newton- Okounkov bodies : For a given projective variety X together with a toric degeneration to X_0, we can associate a completely integrable system on X whose image coincides with the Newton polytope of X_0. In particular, if a polytope △ arises from a Newton-Okounkov body of X, then we can always find a toric degeneration X_0 whose Newton polytope is △.

In the second part, we focus on the case where X is a partial flag variety equipped with a Gelfand- Cetlin system whose image is so called a Gelfand-Cetlin polytope. We will see how X degenerates into Gelfand-Cetlin toric variety, and discuss some topological invariant of X determined by the preimage of vertices of the Gelfand-Cetlin polytope.

8월 2일

11:00-12:00 정승조 (KIAS) : Grassmannians and Newton-Okounkov bodies

I will talk on the Newton-Okounkov bodies for grassmannians. Main reference is K. Rietsch--L. Williams, Cluster duality and mirror symmetry for Grassmannians.

1:30-2:20 신재선 (KAIST) : Okounkov bodies and syzygies on abelian surfaces

The study of how a variety can be embedded in some projective space is an important subject in algebraic geometry, and this is why we study the syzygies of an ample line bundle. A new approach to study the N_p property of an ample divisor on abelian surfaces by using infinitesimal Okounkov body was introduced by Küronya and Lozavanu. In this talk, I will explain their results briefly. Moreover, I will introduce a theorem which extends the result of Lazarsfeld, Pareschi, and Popa on abelian surfaces.  

2:30-3:20 김신영 (KIAS) : Brief introduction to fano horospherical varieties

It seems very useful to practice with concrete example when we study new object. We will briefly introduce the classification of smooth horospherical varieties of Picard number one using colored fan. And then, we will focus on particular horospherical varieties lying in the tangent filtration of the smooth horospherical varieties of Picard number one.

3:40-4:30 황택규 (KIAS) : Kaveh's toric degeneration

 I will explain the toric degeneration constructed by Kaveh. The computation of the Gromov width of flag varieties by Fang-Littelmann-Pabiniak, based on this construction, will be discussed.