中科院数学与系统科学研究院
数学研究所
代数几何研讨班
报告人：Dr. Ho Quoc Phu(Institute of Science and Technology Austria)
题 目：Factorization homology in arithmetic and topology
时 间：2020.12.18（星期五）, 16:00-17:00
地 点：数学院南楼N204
Zoom 会议：692 7468 0663 密码：484075
摘 要：Inspired by conformal field theory and vertex operator algebras, factorization homology was invented by Beilinson and Drinfeld and further developed by Ayala, Francis, Gaitsgory, Lurie, and others. Unlike usual homology theories, factorization homology yields multiplicative invariants of geometric objects, similar to zeta functions and knot invariants. In recent years, the theory has emerged as a powerful tool to study problems in diverse areas of mathematics, from number theory over function fields, such as Gaitsgory--Lurie's celebrated proof of the Weil's Tamagawa number 1 conjecture, to knot theory and quantum topology, such as Gunningham--Jordan--Safronov's recent proof of Witten's finiteness conjecture for skein modules, to many other advances in the Geometric/Betti Langlands program, pioneered by Ben-Zvi, Gaitsgory, and Nadler.In this talk, I will give a quick introduction to the subject, with emphasis on topics closest to my interests. Then I will outline my own previous, current, and future research projects. These revolve around applying factorization homology ideas and techniques to the study of homological stability phenomena and the topology of mapping spaces, including the solutions to various questions of Vakil--Wood and Farb--Wolfson--Wood, and categorical traces of Hecke categories, with possible links to the Betti Langlands program.
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