BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kang Zuo/左康 (Universität Mainz) DTSTART:20201227T071500Z DTEND:20201227T081500Z DTSTAMP:20260423T024027Z UID:iccm2020/10 DESCRIPTION:Title: Higgs Bundle in Geometry and Arithmetic A Proposal\nby Kang Zuo/左 康 (Universität Mainz) as part of ICCM 2020\n\n\nAbstract\nThe notion of a Higgs bundle originated from the theory of elementary particles\, more precisely from the notion of the Higgs boson (field) in particle physics. The Yukawa coupling\, named after Hideki Yukawa\, is used in the Standard Model in particle physics to describe the coupling between the Higgs boson s\, a.k.a. the God particle\, and the quarks and leptons. A major developm ent in complex nonabelian Hodge theory was made by Hitchin\, Donadlson\, U hlenbeck-Yau and Simpson in the so-called Hitchin-DonaldsonUhlenbeck-Yau-S impson correspondence\, a powerful tool in complex algebraic/analytic geom etry. In this talk I will raise a proposal for exploring \, exploiting and extending further our newly developed theories of Higgs bundles in algebr aic and arithmetic geometry. We will focus principally on the following tw o programs: • The Shafarevich Program: We work on moduli spaces of polar ized varieties in our approach to (1) the Shafarevich conjecture on the fi niteness of isomorphism classes of families of higher dimensional varietie s and (2) a folklore conjecture on the bigness of the fundamental group of moduli spaces. • p -adic Nonabelian Hodge Theory: We develop and explor e further a theory of Higgs bundles on varieties over p-adic fields. Three directions of applications are (1) to Faltings p-adic Simpson corresponde nce and its relation to Scholze’s OBdR-functor\, (2) revisiting Grothend ieck anabelian geometry via nonabelian Hodge-Tate comparison and (3) to th e construction of motivic local systems over p-adic curves in connections to Drinfeld’s work on the Langlands program via Abe’s solution of Deli gne’s conjecture on p to ` companions. The proposal will therefore demon strate that the concept of Higgs bundle in various generalized settings pl ays a fundamental role in connecting different fields in algebraic geometr y and topology via Yukawacoupling and in arithmetic geomety via p-adic Hig gs de Rham flow\, a p-adic analogue of Yang-Mills-Higgs equation over the archimadean field. Remarkably the both notions originally came from partic le physics and String theory via Calabi-Yau manifolds. I have discussed wi th Steven Lu\, Ruiran Sun and Jinbang Yang on various parts of the proposa l. I thank them very much.\n LOCATION:https://researchseminars.org/talk/iccm2020/10/ END:VEVENT END:VCALENDAR