Speaker: Prof. Bohan Fang (Beijing International Center for Mathematical Research)
Time: 10:30-11:30am May 29, 2024 (Wednesday)
Place: MCM410
Title: Oscillatory integrals in mirror symmetry
Abstract: I will describe the oscillatory and period integrals on the B-side of mirror symmetry. They correspond to Gromov-Witten primary and descendant invariants of Gamma-modified twisted Chern classes of the mirror coherent sheaves. The cycles for integration correspond to these mirror sheaves by homological mirror symmetry, and one may obtain higher genus invariants if using correct higher genus B-model integrands. I will explain some examples in the setting of toric mirrors and Gross-Hacking-Keel mirror LG models, and discuss application to Gamma conjectures in the toric setting.
Speaker: Prof. Qizheng Yin (Beijing International Center for Mathematical Research)
Time: 16:30-17:30 May 29, 2024 (Wednesday)
Place: MCM410
Title: Cohomological and motivic aspects of compactified Jacobian fibrations
Abstract: Beauville showed using Fourier transforms that the Chow ring/motive of an abelian variety admits a natural, multiplicative decomposition. I will explain how Beauville's theory can be extended to certain abelian fibrations with singular fibers. One notable consequence of this extension is a proof of the P=W conjecture in nonabelian Hodge theory. In this talk I will focus on aspects beyond P=W, and discuss some related open questions. Joint work in progress with Davesh Maulik and Junliang Shen.
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