Speaker:	Lutian Zhao (Kavli IPMU)
Title:	Parahoric Higgs bundle and Related Geometry
Date (JST):	Fri, Oct 18, 2024, 15:30 - 17:00
Place:	Seminar Room B
Abstract:	We will explore the geometry of the moduli space of parahoric Higgs bundles. The journey begins with Simpson's pioneering work on non-abelian Hodge theory for vector bundles with filtrations, which provided a framework for understanding these objects as Higgs bundles on open surfaces. In parallel, the concept of parahoric group schemes, introduced by Bruhat and Tits, established a new geometric foundation for constructing these bundles. These locally compact groups play a crucial role in the formation and properties of parahoric bundles. At the core of the discussion is the definition and properties of the moduli space of parahoric Higgs bundles, building on the foundational contributions of Balaji and Seshadri. We analyze the geometric structure of this moduli space, its singularities, and its connections to more classical moduli spaces of vector bundles and principal G-bundles. Finally as a work in progress, we want to relate this structure to the Langlands program, particularly through the lens of topological mirror symmetry. We discuss conjectures connecting the moduli space of parahoric Higgs bundles to dual objects in the geometric Langlands correspondence, and how these connections might yield new insights in both algebraic geometry and number theory. This is ongoing work with Georgios Kydonakis, Hao Sun and Pengfei Huang.

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