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Equivariant Log-concavity and Equivariant Kahler Packages (or: Shadows of Hodge Theory)

来源: 09-22

时间: 2022-09-27, TUESDAY 13:30-14:30

地点:Place: Jinchunyuan West Building, Conference Room 3 Zoom meeting ID: 405 416 0815, pw: 111111

组织者:WY CHEN陈伟彦、HH GAO高鸿灏、Y HUANG黄意、JF LIN林剑锋、Y JIANG江怡

主讲人: Tao GUI, CAS AMSS

Abstract: 

This talk aims to advertise a pattern/phenomenon that has emerged in many different mathematical areas during the past decades but is not currently well-understood. I will begin with a broad overview of the Kahler packages (Poincare duality, Hard Lefschetz, and Hodge-Riemann relations) that appear in geometry, algebra, and combinatorics, from the classics of Lefschetz to the recent work of this year's Fields medalist June Huh, in a down-to-earth way. Then I will discuss two new Kahler packages we discovered that are equivariant and have no geometric origin. The equivariant log-concavity in representation theory hints at our discoveries. This talk will be non-technical and accessible to the general audience: nothing will be assumed other than elementary linear algebra. Partly based on joint work with Rui Xiong.

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