报告题目：A nonabelian Hodge correspondence for filtered G-local systems

报告人：黄鹏飞, Heidelberg University

时间： 2023年2月24日（周五）16:30-17:30

腾讯会议：437-8994-6832

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https://meeting.tencent.com/dm/X2h5StJN8cqQ

摘要：Local systems can be studied through the monodromies of algebraic vector bundles with regular integrable connections by the celebrated Riemann-Hilbert correspondence of Deligne. This equivalence was put by Simpson into his tame nonabelian Hodge correspondence through incorporating parabolic structures (i.e. weighted filtrations) at the divisors, resulting a correspondence between filtered local systems and parabolic Higgs bundles. However, when the structure group is generalized from GLn(C) to an arbitrary complex reductive G, due to some monodromy issues, it will be failed to achieve a satisfactory correspondence by considering parabolic structures merely. Finding the correct objects that correspond to filtered G-local systems is an interesting problem. In this talk, we will follow Boalch's idea of parahoric Bruhat-Tits's group scheme theory to provide a complete tame nonabelian Hodge correspondence that involves filtered G-local systems. If time permits, the wild correspondence will be mentioned as well. Based on recent joint work with G. Kydonakis, H. Sun and L. Zhao, and with H. Sun.