2018 Symposium in Algebraic Geometry

 

 

대수기하 심포지엄

 

 

 

December 25-27, 2018                                     Libero Hotel, Busan, Korea

Title/Abstract Home > Title/Abstract

 

김현규 (이화여자대학교)

- Title: Deformation quantization of cluster varieties from Riemann surfaces

- Abstract: I will introduce the notion of deformation quantization of a variety with Poisson structure. I will explain examples for Fock-Goncharov cluster varieties, especially those arising from punctured surfaces which are closely related to Teichmueller spaces. I will explain known results, and some open problems.

 

박진형 (KIAS CMC)

- Title: Local positivity of divisors and Newton-Okounkov bodies

- Abstract: A Newton-Okounkov body is a convex subset in Euclidean space associated to a divisor (or more generally a graded linear series) on a variety with respect to an admissible flag. First, I show what kind of local numerical properties of divisors are precisely encoded in Newton-Okounkov bodies (this is joint work with Sung Rak Choi and Joonyeong Won). Then I explore the connection of the Seshadri constants and Newton-Okounkov bodies. Especially, I give simpler proofs of the results previously obtained by Küronya-Lozovanu and Choi-Hyun-Park-Won (this is joint work with Jaesun Shin).

 

조창연 (IBS)

- Title: Proper base change for lcc étale sheaves of spaces

- Abstract: In this talk, I'll generalize the proper base change theorem in étale cohomology to space-valued sheaves, and provide two applications to the étale homotopy theory: the profinite étale homotopy type functor commutes with finite products and the symmetric powers of proper schemes over a separably closed field, respectively. In particular, the commutativity of the étale fundamental groups with finite products will be extended to all higher homotopy groups. In the applications, we'll see the advantage of the infinity categorical approach in étale homotopy theory over the model categorical one.

 

황원태 (KIAS)

- Title: Automorphism groups of (simple) polarized abelian surfaces over finite fields

- Abstract: Let X be an abelian surface over a field k. It is known that X is either simple or isogenous to a product of two elliptic curves over k. It is then natural to consider automorphisms of X over k. In general, the group Aut_k X of automorphisms of X over k is not finite. Hence, we might be led to consider the classification of finite subgroups of Aut_k X in a suitable sense. In such a classification, the notion of a “polarized abelian surface” could be more appropriate.

In this talk, we mainly focus on such classifications for the case when X is simple. After introducing some basic facts related to our goal, we first recall a result of Birkenhake and Lange regarding the classification of finite subgroups of the automorphism group of a simple abelian surface X over C that is maximal in the isogeny class of X. The classification is somewhat simple. Afterwards, we give a classification of finite groups that can be realized as the full automorphism group of a simple polarized abelian surface over a finite field in a similar sense to that of Birkenhake and Lange. Time permitting, we briefly consider the case of X being non-simple.

 

이철규 (KIAS)

- Title: A construction of multiplicity class from Hesselink stratification

- Abstract: In this talk, we will define the multiplicity class of hypersurfaces and construct it from the Hesselink stratification of a Hilbert scheme.

 

이상현 (KIAS)

- Title: Algebraic reduced genus one Gromov-Witten Invariants and comparison theorem for complete intersections in projective spaces

- Abstract: In this talk, we review the past works on reduced genus one Gromov-Witten invariants, studied by A. Zinger and other researchers. We suggest notion of algebraic reduced Gromov-Witten Invariants for complete intersections in projective spaces and explain the proof of the comparison theorem, comparing ordinary genus one Gromov-Witten invariants and Reduced Gromov-Witten Invariants. This is a joint work with Jeongseok Oh (Arxiv arXiv:1809.10995).