中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人： 赵鹭天 博士（University of Maryland）
题  目：The Journey Through Nonabelian Hodge Theory: From vector bundles to parahoric torsors
时  间：2023.06.01（星期四），09:00-10:00
地  点：腾讯会议：360-741-098   密码：0601
摘  要：Nonabelian Hodge Theory, a pivotal extension of Hodge theory, bridges the intricate gap between topological, smooth, and holomorphic dimensions. The seminal work of prominent figures like Narasiham, Simpson, and Hitchin made this profound integration possible. Traditionally, these integrations were symbolized by Betti, de Rham, and Dolbeault in the more manageable Abelian case. This naturally led to the question of the identification and integration of nonabelian smooth and holomorphic objects. This talk will guide you through the fascinating history of Nonabelian Hodge Theory, showcasing the evolution of this groundbreaking field and eventually setting the stage for a detailed exploration of nonabelian Hodge for parahoric torsors.
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报告人： 赵鹭天 博士（University of Maryland）
题  目：Nonabelian Hodge Theory of parahoric torsors
时  间：2023.06.08（星期四），09:00-10:00
地  点：腾讯会议：167-134-084   密码：0608
摘  要：A captivating aspect of modern mathematical research has been establishing a bijective correlation between Higgs bundles and local systems over a noncompact Riemann surface. C. Simpson, who ingeniously introduced weighted filtrations for the concerned objects, accomplished this remarkable achievement. Our discussion will extend this correspondence by exploring the relationship between Dolbeault and de Rham moduli spaces for general complex reductive structure groups. In this process, we will employ the powerful language of parahoric group schemes, as originally conceptualized by Bruhat-Tits. This talk is based on our joint efforts with Georgios Kydonakis, Pengfei Huang, and Hao Sun, to enhance the understanding of these correlations.