An irregular Deligne-Simpson problem and Cherednik algebras

Abstract

The Deligne-Simpson problem asks for a criterion of the existence of connections on an algebraic curve with prescribed singularities at punctures. We give a solution to a generalization of this problem to G-connections on P^1 with a regular singularity and an irregular singularity (satisfying a condition called isoclinic). Here G can be any complex reductive group. Perhaps surprisingly, the solution can be expressed in terms of rational Cherednik algebras. This is joint work with Konstantin Jakob.

About the speaker

Zhiwei Yun joined MIT as a Professor since January 2018. Yun received his Bachelor’s degree from Peking University in 2004, and the PhD degree from Princeton University in 2009, under the supervision of R.MacPherson. Yun’s research is at the crossroads between algebraic geometry, number theory, and representation theory. He studies geometric structures aiming at solving problems in representation theory and number theory, especially those in the Langlands program.

Yun received the 2012 SASTRA Ramanujan Prize, the 2013 Packard Fellowship, and the 2016 Morningside Silver Medal of Mathematics given by the International Congress of Chinese Mathematicians. In December 2017, Yun and Wei Zhang received the 2018 New Horizons Breakthrough Prize in Mathematics. Yun was an invited speaker at ICM 2018. In 2019, Yun received the Gold Medal of Mathematics by the International Congress of Chinese Mathematics (formerly the Morningside Gold Medal). He was also selected to be Fellow of the AMS. In 2020, Zhiwei received a Simons Investigatorship in Mathematics.