Abstract

We discuss the enumerative geometry of moduli spaces of sheaves with 2 dimensional support on K3 surfaces in K3-fibered threefolds and 4 folds. The reason to study such specific geometric setups is that these often provide computable invariants which govern deep information about geometry of moduli spaces of solutions to N=2 Super Yang-Mills theory on K3 surfaces, when the base surface is allowed to have deformations in ambient 3 folds or 4 folds. On the other hand the partition functions of these invariants, when set up suitably, have often outstanding properties, such as Mock modularity property, which allows computing all the invariants from only a few low degree invariants, using certain recursive relations induced by the mock modular form. This is based on earlier joint work with Amin Gholampour, and Yukinobu Toda, as well as recent ongoing discussions with Jeongseok Oh.

About the speaker

Artan Sheshmani BIMSA

I am a Professor of Pure Mathematics, specialized in Algebraic Geometry, Differential Geometry and Mathematics of String Theory. I am a Professor at Yanqi Lake Beijing Institute of Mathematical Sciences and Applications in Beijing, as well as a senior personnel (Professor) at Simons Collaboration Program on Homological Mirror Symmetry at Harvard University Center for Mathematical Sciences and Applications (CMSA), and an Affiliate Faculty Member at Harvard University- MIT IAiFi (Institute for Articial Intelligence and Fundamental Interactions). My work is mainly focused on Gromov Witten theory, Donaldson Thomas theory, Calabi-Yau geometries, and mathematical aspects of String theory. I study geometry of moduli spaces of sheaves and curves on Calabi Yau spaces, some of which arise in the study of mathematics of string theory. In my research I have worked on understanding dualities between geometry of such moduli spaces over complex varieties of dimension 2,3,4 and currently I am working on extension of these projects from derived geometry and geometric representation theory point of view.

Homepage：

https://bimsa.net/people/artansheshmani/