노현호 (충남대) 

Title: Tautological relation on Picard stack.

Abstract: Tautological relation on the moduli space of stable curves were studied by several method. I will reveiw the method used by Pandharipande-Pixton to prove the tautological relation on the moduli space of stable curvse using stable quotient. I will explain how to extend the result to get tautological relations on relative Picard stack over the moduli space of stable curves by constructing the stable quotient over Picard stack. After this I will explain how to get the result on the Picard stack which extends the original form of tautological relation given by Faber and Zagier. This talk is based on the joint work in progress with Younghan Bae.

박경동 (경상국립대)

Title: Deformation rigidity of the double Cayley Grassmannian 

Abstract: The double Cayley Grassmannian is a (unique) smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group G2, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bi-octonions. We show the rigidity of the double Cayley Grassmannian under Kähler deformations. This means that for any smooth projective family of complex manifolds over a connected base of which one fiber is isomorphic to the double Cayley Grassmannian, all other fibers are isomorphic to the double Cayley Grassmannian. This is a joint work with Shin-young Kim. 

오정석 (서울대)

이기선 (Clemson University)

Title: Numerical certification, certified homotopy tracking, and beyond

Abstract: A certified algorithm produces both a solution and a certificate of correctness for a specific problem. Numerical certification focuses on these certified algorithms as they apply to results obtained through numerical methods in algebraic geometry. In this talk, we review the emergence of numerical certification within the realm of numerical algebraic geometry and introduce certified homotopy tracking as one of its key methods. We also overview its applications, from enumerative geometry to algebraic vision. This presentation is based on joint work with S, where S ranges over a large set.

이석주 (IBS-CGP)

Title: Irregular Hodge filtration and applications to mirror symmetry.

Abstract: In the first part of this talk, I will briefly introduce the de Rham cohomology of a Landau–Ginzburg model, a pair consisting of a smooth quasi-projective variety and a regular function on it. This cohomology, known as twisted de Rham cohomology, is equipped with a natural filtration called the irregular Hodge filtration, first introduced by P. Deligne for curves and later generalized to higher dimensions by J. D. Yu. In the second part, I will discuss an application to mirror symmetry. For a mirror pair of Landau–Ginzburg models, the usual mirror duality of Hodge numbers can be extended to the duality of irregular Hodge numbers. In joint work with Andrew Harder, we show that this duality holds for a large class of mirror pairs known as Clarke mirror pairs. Our main technical tool is tropicalization, which is also of independent interest for computing irregular Hodge numbers.

이용남 (KAIST/IBS-CCG)

Title: Morphisms from a very general hypersurface

Abstract: In this talk, we will talk about a non-binational surjective morphism from a very general hypersurface X  to a normal projective variety Y. We first show Y is a Fano variety if the degree of the morphism is bigger than a constant C where C depends on the dimension and degree of X. Next we prove an optimal upper bound of the morphism which is degree of X provided that Y is factorial, degree of the morphism is prime and bigger than a constant E where E depends only on the dimension of X. Also we will show that Y is a projective space under some conditions. This is a joint work with Yujie Luo and De-Qi Zhang.

임우남 (연세대)

Title: P=C conjecture for the moduli space of one-dimensional sheaves on the plane

Abstract: Study of the moduli space of one-dimensional sheaves on P^2 was initiated by Simpson and Le Potier 30 years ago. This classical moduli space has an application to Gopakumar-Vafa theory related to counting curves in a Calabi-Yau 3-fold, known as local P^2. The main ingredient for this application is so-called the perverse filtration associated to the degenerate abelian fibration of the moduli space. I will explain the P=C conjecture which predicts that the perverse filtration is equal to the Chern filtration coming from a generator/relation description of the cohomology ring. This is a joint work with Kononov, Moreira, Pi.

장성욱 (IBS-CCG)

Title: Existence of anticanonical minimal models

Abstract: For decades, there were tremendous achievements in the theory of MMP (short for minimal model program). For instance, we can run a 3-dimensional MMP and we know that it eventually terminates. Furthermore, for now, we can run any MMP for an lc pair. However, we do not know whether the MMP terminates or not, in general. The MMP, in short, is a sequence of birational maps which makes a canonical divisor closer to a nef divisor. If the canonical divisor is pseudoeffective and the MMP terminates, then we obtain a minimal model whose canonical divisor is nef. We are interested in an anticanonical divisor. We want to find a model whose anticanonical divisor is nef. In this talk, we will explain how the theory of MMP is applied to obtain an anticanonical minimal model and will show what conditions guarantee the existence of anticanonical minimal models.

조용화 (경상국립대)

Title: Double point divisors and their positivity properties

Abstract: In his famous article "What can be computed in algebraic geometry?", Mumford studied the non-isomorphic locus of a general projection of a smooth projective variety onto a hypersurface. This locus is endowed with a natural divisorial structure, hence the name "double point divisor". In the same article, Mumford proved that the double point divisors from the general outer projections form a base point free linear system. Moreover, this linear system turned out to be ample except for some special cases (known as Roth varieties) as shown by Ilic. In this talk I will explain joint work with Jinhyung Park, in which we proved that the aforementioned linear system is very ample except for the Roth varieties.

한창호 (고려대)

Title: Seminormal curves, compactified Jacobians, and the extended Torelli map

Abstract: It is well-known that the Torelli map, that turns a smooth curve of genus g into its Jacobian (a principally polarized abelian variety of dimension g), extends to a map from the Deligne—Mumford moduli of stable curves to the moduli of semi-abelic varieties by Alexeev. Moreover, it is also known that the Torelli map does not extend over the alternative compactifications of the moduli of curves as described by the Hassett—Keel program, including the moduli of pseudostable curves (can have nodes and cusps but not elliptic tails). But it is not yet known whether the Torelli map extends over alternative compactifications of the moduli of curves described by Smyth; what about the moduli of curves of genus g with seminormal singularities? As a joint work in progress with Jesse Kass and Matthew Satriano, I will describe moduli spaces of curves with seminormal singularities (with topological constraints) and describe how far the Torelli map extends over such spaces into the Alexeev compactifications.