김호일 (경북대)

- Title: Hodge structures on generalized complex manifolds

- Abstract: Generalized complex structures have been introduced in physical society and rigorously described mathematically by Hitchin, Gualtieri and others. They are the combinations of complex structures and symplectic structures, so that they are very useful to understand both structures in one language, in particular in mirror symmetry. In this talk we desribe Hodge structures on generalized (super) complex manifolds, which is an on-going project.

오정석 (KIAS)

- Title: Quasimap theory and Gauged Linear Sigma Model.

- Abstract: Quasimap theory is introduced by Ciocan-Fontanine, Kim, and Maulik. It turns out that it is the one of most important ingredient to study Gromov-Witten theory by several works of different groups. We briefly discuss the status of Gromov-Witten theory and quasimap theory as well as its importance. Also, we discuss how it can be related to GLSM.

정대웅 (충북대)

- Title: Counting Lagrangian subbundles via GW invariants

- Abstract: Let W be a general stable symplectic vector bundle of rank 2n and degree d over a smooth projective curve of genus g. Let LQ(e;W) be the Lagrangian Quot scheme parametrizing Lagrangian subsheaves of degree -e. In this talk I will explain  a joint work with I. Choe and G. Hithcing. Our results can be summarized as follows: We first prove that LQ(e;W) is generically smooth and irreducible of expected dimension if e is sufficiently large. Secondly,  based on this result, we find an explicit formula for the number of maximal Lagrangian subbundles when the Lagrangian Quot scheme under consideration has a zero dimension

원준영 (IBS)

- Title: K-stability for Fano variety

- Abstract: We introduce some invariants for K-stability of Fano variety and survey recent related results.

정예원 (KAIST)

- Title: Moduli of second fundamental forms of a nonsingular intersection of two quadrics

- Abstract: In 1979, Griffiths and Harris raised a question on the moduli of second fundamental forms of a projective complex submanifold of codimension two. We will report on our study of the question for complete intersections of two quadrics.

권혁민 (S-Core(삼성 SDS 자회사))

- Title: Terminating Euclidean algorithm for a non-Noetherian Bézout domain and its applications

- Abstract: In this talk, we show that a non-Noetherian Bézout domain, k[y] + x · k(y)[x] over a field k, has terminating Euclidean algorithm. As its application, an algorithm to find the normal form of any matrix in GL2(k[y] + x · k(y)[x]) is suggested. Because k[x, y] ⊂ k[y] + x · k(y)[x], that algorithm can naturally calculate the normal form of any matrix in GL2(k[x, y]). That normal forms have information related to two dimensional polynomial automorphisms. And we apply the Euclidean algorithm to give a realization algorithm for matrices in SL2(k[y] + x · k(y)[x]) also.

박경동 (IBS)

- Title: Ulrich bundles on the Fano 3-fold $V_5$

- Abstract: The Fano 3-fold $V_5$ is a unique smooth Fano 3-fold of Picard number 1, degree 5 and index 2. Also, it can be described as a generic codimension 3 linear section of the Grassmannian Gr(2, 5). After introducing Ulrich bundles as interesting classes of vector bundles on smooth projective varieties, I will discuss quiver representations to describe the moduli spaces of Ulrich bundles on $V_5$. This is a joint work with Kyoung-Seog Lee.