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.
Speaker Intro
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). Between 2020 and 2023, I jointly held the visiting professor position at Institute for the Mathematical Sciences of the Americas at University of Miami, where I was part of the research collaboration program on "Hodge theory and its applications". During the past 5 years while at Harvard CMSA I have been a visiting professor at Harvard Physics department (2020-2021), and an Associate Professor of Mathematics at Institut for Mathematik (formerly the Center for Quantum Geometry of Moduli Spaces) at Aarhus University in Denmark (2016-2022). 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. In joint work with Shing-Tung Yau (BIMSA, YMSC, Tsinghua, Harvard Math, Harvard CMSA, and Harvard Physics departments), Cody Long (Harvard Physics), and Cumrun Vafa (Harvard Math and Physics departments) I worked on geometry moduli spaces of sheaves with non-homolomorphic support and their associated non-BPS (non-holomorphic) counting invariants. In 2019 I recieved IRFD "Research Leader" grant (approx 1M USD) on my project "Embedded surfaces, dualities and quantum number theory". The project has additionally been co-financed by Harvard University CMSA (Approx total. 400K USD).
Detail of IRFD "Research Leader" grant: https://dff.dk/en/grants/research-leaders-2018.
