Speaker: Insong Choe (Konkuk University)
Title: Review on moduli of orthogonal bundles over hyperelliptic curves
Abstract: I'll review the Ramaman's paper "Orthogonal and spin bundles over hyperelliptic curves" (Proc. Indian Acad. Sci. v.90 (1981) pp.151-166), which generalizes the famous paper of Desale and Ramanan on moduli of rank 2 bundles over hyperelliptic curves. The main topic of this paper is the Fano variety of the intersection of two quadrics.

Speaker: Jinwon Choi (Sookmyung Women's University)
Title: Fulton-MacPherson configuration space of and wall-crossing
Abstract: Motivated by Landau-Ginzburg/Calabi-Yau correspondence by  and  wall-crossing in quasimap theory, we study the geometry of Fulton-MacPherson configuration space by wall-crossing. In this talk, I will describe the  and  wall crossing. In the case relevant to the Fulton-MacPherson space, each wall-crossing is given by a blowup. This gives a new construction of the Fulton-MacPherson configuration space. This is joint work with Young-Hoon Kiem.

Speaker: Kiryong Chung (Kyungpook National university)
Title: Geometry of moduli spaces of rational curves in linear sections of Grassmannian Gr(2, 5)
Abstract: In this talk, I prove that the moduli spaces of rational curves of degree at most 3 in linear sections of the Grassmannian Gr(2, 5) are all rational varieties. We also study their compactifications and birational geometry. This is joint work with J. Hong and S. Lee.

Speaker: Donghoon Hyeon (Seoul National University)
Title: Commuting nilpotents modulo simultaneous conjugation and Hilbert scheme
Abstract: Pairs of commuting nilpotent matrices have been extensively studied, especially from the view point of quivers. But the space of commuting nilpotents modulo simultaneous conjugation has not received any attention at all although it has a definite moduli theory flavor. Unlike the case of commuting nilpotents paired with a cyclic vector, the GIT is not well behaved in this case. I will explain how a 'moduli space' can be constructed as a homogeneous space, and show that it is isomorphic to an open subscheme of a punctual Hilbert scheme. Over the field of complex numbers, thus constructed space is diffeomorphic to a direct sum of twisted tangent bundles over a projective space. Time permitting, I will also explain how the new development in GIT (of affine spaces modulo solvable groups) might possibly treat this case and produce a moduli space as a GIT quotient. This is a joint work with W. Haboush.

Speaker: Byeongho Lee (NIMS)
Title: Moduli spaces, Frobenius manifolds, and integrable systems
Abstract: The Deligne-Mumford compactifications of the moduli spaces of rational curves with marked points have natural topological operad structure via gluing morphisms. After taking their homologies, it becomes an algebraic one. A formal Frobenius manifold is nothing but an algebra over this operad. Given a Frobenius manifold, it is a natural question to extend to a higher genus analogue. For semisimple Frobenius manifolds, Dubrovin-Zhang approached this problem from the viewpoint of integrable systems. On the other hand, Givental has another approach that is more geometric. He also claimed that the two are equivalent. We want to compare them against each other.

Speaker: Sanghyeon Lee (Seoul National University)
Title: Moduli space of Stable Maps in Moduli of Vector bundles on algebraic curve with fixed determinant
Abstract: A. M. Castravet Classified moduli of maps  with arbitrary degree, where N is a moduli space of stable rank 2 vector bundles on an algebraic curve X, with fixed determinant. Stable map space can be considered as a compactification. Degree 1 case was studied by V. Munoz, Degree 2 case was studied by Y.-H. Kiem. I'll introduce some results about degree 3 case. This is a joint work with Kiryong Chung.

Speaker: Yongnam Lee (KAIST)
Title: Dominant rational map from a very general surface in a hyperplane section of high degree in Fano threefolds
Abstract: In this talk, we present some results obtained by combining Hodge theoretical and deformation methods. In particular, we show that there is no dominant rational map from a very general surface of degree to any nonrational surface unless the map is birational. Similar results hold for a hyperplane section of high degree in some Fano threefolds. This is joint work with Gian Pietro Pirola.

Speaker: Wanmin Liu (IBS-CGP)
Title: Two Facets of Birational Geometries of Moduli Space of Sheaves over Surface
Abstract: Denote M the moduli space of twisted-Gieseker semi-stable sheaves with fixed topology over a surface S. The birational geometry of M is packaged into Mori wall-chamber structures inside the effective cone Eff(M) of divisors. On the other side, by enlarging the category of coherent sheaves to its derived category, the moduli space M could also be thought of as Bridgeland moduli space  for the stability condition  in a very special chamber (called large volume limit) inside stability manifold Stab(S). One then changes stability conditions in the Bridgeland wall-chambers inside Stab(S), and get birational models of M. The two facets of birational geometries are linked by Bayer-Macri's line bundle theory, from Stab(S) to Eff(M). In the two talks, I will review such theory and report some recent progress for S being the Hirzebruch surface.

Speaker: Hanbom Moon (Fordham University)
Title: A computational approach to the F-conjecture
Abstract: The F-conjecture is a long-standing conjecture on the structure of the nef cone of the moduli space of (pointed) curves. In this talk, I will explain how one can translate the-invariant version of the conjecture into a feasibility problem in polyhedral geometry, which is purely computational. The main ingredients are the graphical algebra in classical invariant theory, embeddings into toric varieties, and the tropical compactification. Also I will propose a stronger statement which might be true for the genus zero case in general, and give some evidences. This is a joint work with David Swinarski.

Speaker: Sang-Bum Yoo (POSTECH)
Title: Higgs Hecke cycles and stable rank 2 twisted Higgs bundles on a curve
Abstract: Let X be a smooth complex projective curve of genus  and let L be a line bundle on X. Let M be the moduli space of semistable rank 2 L-twisted Higgs bundles with trivial determinant on X. In this talk we construct a cycle, which is called Higgs Hecke cycle. Then we introduce the main result that there is an isomorphism between the stable locus of M and an open dense locus of the moduli space of Higgs Hecke cycles. Further we present an investigation of degeneracy loci of Higgs fields from which rational curves arise in the moduli space of Higgs Hecke cycles.