清华主页 EN
导航菜单

Counting sheaves on K3 surfaces in 3 folds and 4 folds

来源: 09-22

时间:Fri.,15:30-16:30 Sept. 22, 2023

地点:Zoom ID: 455 260 1552 PW: YMSC; Venue Tsinghua West Stepping Classroom 清华大学西阶梯教室

组织者:Caucher Birkar 曲三太, 陈炳仪

主讲人:Artan Sheshmani BIMSA

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/


返回顶部
相关文章
  • Algebraic Geometry Seminar | QQ-Fano 3-folds

    Abstract:Non-singular Fano 3-folds were classified by Fano, Iskovskikh, Mori and Mukai, and are known to fall into 107 deformation families that are fairly well studied. The Mori category of projective 3-folds with terminal singularities is considerably more diverse. For many purposes, it is enough to concentrate on varieties with terminal orbifold points 1/r(1,a,r-a) as the only singular poin...

  • From curve counting on Calabi-Yau 4-folds to quasimaps for quivers with potentials

    AbstractI will start by reviewing an old joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten, Gopakumar-Vafa and stable pair invariants on compact Calabi-Yau 4-folds. For non-compact CY4 like local curves, similar invariants can be studied via the perspective of quasimaps to quivers with potentials. In a joint work in progress with Gufang Zhao, we define a virtual count fo...