Mini-course on Approximable Triangulated Categories
作者： Professor Amnon Neeman
时间： 2024-08-19
阅读：
Mini-course on Approximable Triangulated Categories
主讲人: Professor Amnon Neeman (University of Milan)
题目: Approximable triangulated categories
时间: August 19-26, 2024
August 19、22、25, 9:00-11:00(AM)
August 20、23、26, 14:30-16:30(PM)
地点: Main Campus (at HuaYuanQiao)Teaching Building No.2, Room 627
School of Mathematical Sciences, Capital Normal University, Beijing
摘要:
Motivated by certain conjectures in algebraic geometry, the speaker developed a theory called approximable triangulated categories. And, somewhat unexpectedly, the theory has turned out to be applicable in surprising directions, some quite unrelated to the origin in algebraic geometry.Roughly speaking the idea is to borrow techniques, from the world of real analysis, and use them on triangulated categories. As we said in the last paragraph: given how strange this approach is, it is remarkable how powerful the methods have turned out to be.
By now the author has written seven manuscripts on the subject, some quite long. And others have joined in, there is interesting recent work by Sun and Zhang, as well as by Biswas, Chen, Manali-Rahul, Parker and Zheng.
In this series of lectures we will try to run through the highlights.
主讲人简介:
Amnon Neeman is an Emeritus professor in Australian National University, and now a professor in University of Milan. He was elected as a fellow of Australian Academy of Science in 2005, and was awarded Australian Laureate Fellow in 2011. In 2023, he was awarded an Advanced Grant of over 1 million euro from European Research Council. He was an invited speaker at ICM 2022.
Professor Neeman has produced a body of very profound and important work in the core mathematical disciplines of algebraic geometry, topology and K-theory. He has promoted developments in triangulated categories and their applications. His results on the K-theory of triangulated categories were startlingly original, and completely changed the subject. Neeman’s foundational work, extending the Brown representability theorem, has rendered techniques more powerful; applications include his new treatment of Grothendieck duality. Neeman has made notable contributions to algebraic geometry, especially geometric invariant theory. He has contributed importantly to the interplay of analytic and algebraic invariants of manifolds. Recently, he developed the theory of approximable triangulated categories which has turned out to be powerful in algebraic geometry and representation theory by solving sorts of famous conjectures.His work has been very influential.
