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报告题目：Derived deformation rings and cohomology of locally symmetric spaces
Yichang Cai is a lecturer at the College of Mathematics and Physics, Wenzhou University. He obtained his PhD in June 2021 from Université Sorbonne Paris Nord under the supervision of Prof. Jacques Tilouine. His main area of interest lies in number theory, especially in deformation theory.
It has been observed by Venkatesh that the cohomology of locally symmetric spaces with integral coefficients has some additional homotopical structures. In the paper [Derived Galois Deformation Rings] by Galatius and Venkatesh, the authors introduced homotopical generalizations of universal deformation rings, and proved a homotopical version of the "R=T" type statement, thus providing an explanation of those additional structures. In this talk, we will explain the idea of Galatius and Venkatesh, and generalize their main theorem by removing certain assumptions. In particular, the congruences inside the localized Hecke algebra are allowed.