Coherent sheaves, superconnection, and the Riemann-Roch-Grothendieck formula.

• 主讲人：Shu Shen (IMJ-PRG)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2023-04-27 21:00 - 2023-04-27 22:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/C7DCC1DD2C9C640F862DE94FD472BFC5
Valid Until: 2027-05-31 23:59

 

Abstract: In this talk, I will explain a construction of Chern character for coherent sheaves on a closed complex manifold with values in Bott-Chern cohomology. I will also show a corresponding Riemann-Roch-Grothendieck formula, which holds for general holomorphic maps between closed non-Kahler manifolds. Our proof is based on two fundamental objects: the superconnection and the hypoelliptic deformations. This is a joint work with J.-M. Bismut and Z. Wei arXiv:2102.08129.

 

Bio: Shu Shen is a lecturer at Sorbonne University and a researcher at IMJ-PRG. He received his MA at Ecole Polytechnique in 2010 and PhD at Paris-Sud University in 2014. He had research and postdoc experiences at Max-Plank (Bonn), Humboldt University and Paris-Sud University. Shen’s main research interests are geometry and analysis of manifolds. https://webusers.imj-prg.fr/~shu.shen/