김영락 (Saarland University)

- Title : Ulrich bundles on cubic fourfolds

- Abstract : Ulrich sheaves are one of the most remarkable objects in the study of vector bundles on projective varieties, thanks to their numerous connections and applications. Ulrich complexity for a given projective variety X, originally introduced to measure the complexity of polynomials by Bläser-Eisenbud-Schreyer, is defined as the smallest possible rank for the Ulrich sheaves on X. It is well-known that any hypersurface supports an Ulrich sheaf, however, Ulrich complexity is not very well understood even for cubic hypersurfaces. In this talk, We discuss how to construct Ulrich bundles of small rank on a smooth cubic fourfold. In particular, we focus on the construction of a rank 6 Ulrich
bundle from Lehn-Lehn-Sorger-van Straten sheaves. This is a joint work with D. Faenzi. 

성시학 (IBS-CGP)

- Title: Connected Components in the Hilbert Scheme of Hypersurfaces in Grassmannians

- Abstract: We show that when $d geq 3$, the Hilbert scheme $Hilb_{dT+1-binom{d-1}{2}}(G(k,n))$ has 2 components, even though elements in both components have the same cohomology class. Moreover, we show that the Hilbert scheme associated to the Hilbert polynomial $binom{T+n}{n}-binom{T+n-d}{n}$ in Grassmannian has at most 2 connected components.

유상범 (공주교육대학교)

- Title: Spectral data for principal Higgs bundles over a singular curve

- Abstract: Spectral data for Higgs bundles over a smooth curve has been studied by several mathematicians. The studies in this direction are originated by N.J.Hitchin. Specially, it has contributed to the studies on the fibers of the Hitchin map. In this talk, I will introduce spectral data for Higgs bundles over a smooth curve and over a singular curve, and then present my ongoing project about spectral data for principal Higgs bundles over a singular curve.

이상욱 (숭실대학교)

- Title: Lagrangian Floer theory and orbifold Jacobian algebras

- Abstract: Given an algebraic function, its Jacobian algebra encodes the information of the singularity. There is also a notion of orbifold Jacobian algebras for functions which admit finite (abelian) group actions. We give a construction of an orbifold Jacobian algebra as Floer cohomology of a Lagrangian submanifold which represents homological mirror functor. This talk is based on the joint work with C.-H. Cho.

정승조 (전북대학교)

- Title: On the Bernstein—Sato polynomial and the McKay correspondence
- Abstract: In this talk, I introduce the notion of the Bernstein--Sato polynomials. Main focus of this talk is one for hypersurface singularities and its relation with other invariants of the singularities. 
If time permits, I overview the notion for hypersurfaces in singular varieties and present a possible interpretation via the McKay correspondence. 

좌동욱 (KIAS)

- Title: Fukaya category of Landau-Ginzburg orbifolds and its application

- Abstract: Landau-Ginzburg orbifolds are a particular type of germ of isolated singularities W : C^n → C with a finite group action G preserves W. I will explain a construction of Fukaya-type categories for a pair (W, G) and its application to Berglund-Hubsch homological mirror symmetry. The relation to categorical replacement of divisors will be stressed. This is a joint work with Cheol-hyun Cho and Wonbo Jeong.

황준묵 (IBS-CCG)

- Title: Unbendable rational curves of Cartan type
- Abstract: A nonsingular rational curve in a complex manifold of dimension n is unbendable if its normal bundle is isomorphic to O(1)^p + O^(n-1-p) for some nonnegative integer p. Well-known examples are general minimal rational curves on uniruled projective manifolds. We study a natural distribution on the deformation space of such rational curves, concentrating on the case of p=1 and n = 5, which is the simplest nontrivial situation. In this setting, the families of unbendable rational curves  fall  essentially into  two classes: Goursat type or Cartan type, depending on the growth vectors of the distributions. We show that the family of lines on a general quartic 5-fold is of Cartan type, in the proof of which the projective geometry of varieties of minimal rational tangents plays a key role. This is a joint-work with Qifeng Li. 

Hsuan-Yi Liao (KIAS)

- Title: A CFO approach to derived differential geometry

- Abstract: A main motivation of developing derived differential geometry is to deal with singularities arising from zero loci or intersections of submanifolds. Both zero loci and intersections can be considered as fiber products of manifolds. Thus, we extend the category of differentiable manifolds to a larger category in which one can consider "homotopy fiber products" of manifolds. We approach this problem by using curved L-infinity algebras and categories of fibrant objects. The talk is mainly based on a joint work with Kai Behrend and Ping Xu.