Dongmin Gang (Seoul National University)

Title: 3D rank-0 N=4 SCFTs, rational chiral algebras and modular functions

Abstract: I will talk about newly discovered connections among 3D rank-0 N=4 superconformal field theories, rational chiral algebras, and modular functions.

Shuai Guo (Peking University)

Title: On the BCOV’s Feynman rule for multi-parameter Calabi-Yau threefolds

Abstract: BCOV’s Feynman rule is a conjectural algorithm for computing the higher genus Gromov-Witten invariants of the Calabi-Yau threefolds. In this talk, I will try to explain the applications of mixed field theory to this conjecture. This is based on the joint work in progress with H.-L. Chang, J. Li, W.-P. Li and Y. Zhou

Hansol Hong (Yonsei Unversity)

Title: Blowups of surfaces and the mirror superpotential

Abstract: Any log Calabi-Yau surface $X$ can be expressed as a nontoric blowup of a toric surface up to a modification of the boundary divisor.

Using this, one can construct a special Lagrangian torus fibration on $X$ with nodal fibers, which results In the cluster structure on its SYZ mirror. 

I will first describe its mirror potential in terms of combinatorial data on the associated scattering diagram, and examine how its critical loci are affected by blowups.

In particular, we will see that the blowup creates exactly one nondegenerate `geometric’ critical point of the potential.

This is mirror to the analogous fact about the quantum cohomology of $X$ that can be shown applying the result of Bayer.

Heeyeon Kim (KAIST)

Title:  Path integral derivations of K-theoretic Donaldson invariants

Abstract: I will discuss the partition function of 5d N=1 supersymmetric Yang-Mills theory compactified on X x S1, where X is a smooth, compact, oriented four-manifold. After the topological twist on X, the partition function can be identified with the so-called K-theoretic Donaldson invariants, which is the index of the Dirac operator on moduli spaces of instantons. We evaluate the invariants via the five-dimensional path integrals and reproduce/generalize the results recently obtained by Gottsche-Nakajima-Yoshioka and Gottsche-Kool-Williams.

Tsung-Ju Lee (National Cheng Kung University)

Title: On the periods for Calabi--Yau fractional complete intersections

Abstract: In this talk, I will introduce the notion of Calabi--Yau fractional complete intersections and study their B-model, i.e., the period integrals, via GKZ systems. In the present case, the GKZ system is completeand the periods are completely characterized by the system. As an application, we can give a close formula for the periods of Calabi--Yau arising from double covers over IP^3 branched along 8 hyperplanes.

Seung-Joo Lee (IBS-CTPU)

Title: Landscape, Swampland and Geometry

Abstract: Many instances have recently been found on the intriguing interplay between string landscape and algebraic geometry via the so-called swampland conjectures. In this talk, we will exemplify such an interplay. Specifically, by addressing certain universal properties of compact elliptic Calabi-Yau (d+1)-folds, we will test certain conjectures out for all possible effective QFT models of F-theory in (real) D=10-2d dimensions. In particular, several results will be discussed on non-vanishing of specific enumerative invariants, as well as characterization of geometries at infinite distance in the moduli space. 

Sungjay Lee (KIAS)

Title: Exact Supersymmetric Partition Functions and Mirror Symmetry

Abstract:  *TBA

Bong Lian (Brandeis University)

Title: Fractional Complete Intersections

Abstract: We will consider a class of (typically) singular Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler, Gauss and Legendre, who considered 2-fold covers of branched over 4 points. Two-fold covers of branched over 6 lines have been studied more recently by many authors, including Matsumoto, Sasaki, Yoshida and others, mainly from the viewpoint of their moduli spaces and their comparisons. I will outline a higher dimensional generalization from the viewpoint of mirror symmetry, and discuss the Riemann-Hilbert problem for periods of these singular varieties. The new insight here is the idea of `abelian gauge fixing' and `fractional complete intersections' that leads to a new interpretation of those classical results. The idea further points to a construction of large class of Calabi-Yau mirror pairs.
The lecture is based on joint work with S. Hosono, T.-J. Lee, M. Romo, L. Santilli, H. Takagi, S.-T. Yau. 

Sungwoo Nam (Postech)

Title: Sheaves on surfaces from 5D rank 2 theories

Abstract: The geometry of moduli of sheaves on a surface has been studied extensively from many perspectives. In this talk, motivated by five-dimensional supersymmetric field theories, I’ll describe how some singular surfaces (rank 2 surfaces in 5D theories) can be viewed as smooth objects in the category of Deligne-Mumford stacks. Adopting Nironi’s work on moduli of sheaves on stacks, I’ll explain how we can define moduli spaces of sheaves on these stacks, leading to a definition of genus 0 Gopakumar-Vafa invariants and Hilbert schemes of points. Then I’ll discuss how to compute topological invariants of some moduli spaces, producing some of Gholampour-Jiang-Kool’s calculation on rank 1 sheaves on weighted projective stacks as a special case.

Hyeonjun Park (KIAS)

Title: Virtual Lagrangian cycles

Abstract: Donaldson-Thomas invariants of Calabi-Yau 4-folds are defined through recently developed virtual Lagrangian cycles associated to (-2)-shifted symplectic derived moduli spaces. In this talk, we discuss various properties of these virtual Lagrangian cycles in the perspective of shifted symplectic geometry. We first provide a virtual pullback formula for Lagrangian correspondences and use it to compute Hilbert scheme invariants. We then construct reduced virtual cycles for counting surfaces via (-1)-shifted closed 1-forms and show that they can detect the variational Hodge conjecture. We also revisit cosection localization via virtual Lagrangian cycles for (-2)-shifted twisted cotangent bundles. We finally explain deformation invariance in terms of the exactness of the symplectic forms.

Artan Sheshmani (BIMSA/Harvard)

Title: BV differentials and Derived Lagrangian intersections in moduli spaces of surfaces on Fano and CY threefolds.  
Abstract: We elaborate on construction of a derived Lagrangian intersection theory on moduli spaces of divisors on compact Calabi Yau threefolds. Our goal is to compute deformation invariants associated to a fixed linear system of divisors in CY3. We degenerate the CY3 into a normall crossing singular variety composed of Fano threefolds meeting along a K3. The deformation invariance arguments, together with derived Lagrangian intersection counts over the special fiber of the induced moduli space degeneration family, provides one with invariants of the generic CY fiber. This is report on several joint projects in progress with Ludmil Katzarkov, Tony Pantev, Vladimir Baranovsky and Maxim Kontsevich.  

Xin Wang (KIAS)

Title: 5D Wilson Loops and Topological Strings

Abstract: Geometric engineering provides a rich class of 5D supersymmetric gauge theories with eight supercharges, arising from M-theory compactification on non-compact Calabi-Yau threefolds. The counting of BPS states in the low-energy gauge theory is determined by the degeneracies of M2-branes wrapping holomorphic two-cycles in the Calabi-Yau threefold X. These degeneracies can also be calculated from the (refined) topological strings on the same manifold X. In this talk, I will explore the BPS spectrum of the 5D gauge theory with the insertion of a half-BPS Wilson loop operator, which is a charged object under the one-form symmetry. Utilizing M-theory realization, we derive the BPS expansion of the expectation value of the Wilson loop operator in terms of BPS sectors. It is found that the BPS sectors can be realized and computed from topological string theories. In the unrefined limit, the BPS sectors act as generating functions for Gromov-Witten invariants on compact (semi)-Fano threefolds constructed from X. We further conjecture the refined holomorphic anomaly equations for the VEVs of the Wilson loop operators. These equations can completely solve the refined BPS invariants of Wilson loops for local  and local .

Yaoxiong Wen (KIAS)

Title: Seiberg-like duality for resolutions of determinantal varieties

Abstract: In this talk, I will discuss the genus-zero Gromov-Witten theory of two different resolutions of determinantal varieties termed the PAX and PAXY resolutions. We realize the resolutions as each lying in a quiver bundle, and show that the respective quiver bundles are related by mutation. We conjecture that generating functions of genus-zero Gromov-Witten invariants for the two resolutions are related by a specific cluster change of variables.  We prove a version of the conjecture when the determinantal variety lies in a GIT quotient. Along the way, we obtain a quantum Thom-Porteous formula for determinantal varieties and prove a Seiberg-like duality statement for certain quiver bundles. This talk is based on the in-progress work with Mark Shoemaker and Nathan Priddis.