Geometry & Geometric Analysis Seminar
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and UT Arlington to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
The next meeting of GAGA will be Thursday, August 22 from 4 to 5 pm in Tucker Technology (TUC) 243. Zhaoting Wei from Texas A&M-Commerce will speak on The Grothendieck-Riemann-Roch Theorem, Superconnections, and Index Theorems. You can also attend via Zoom.
Abstract: It is well-known that the Hirzebruch-Riemann-Roch theorem in algebraic geometry is a special case of the Atiyah-Singer index theorem. In this talk I will present a proof of the Grothendieck-Riemann-Roch theorem for coherent sheaves on compact complex manifolds as a special case of the family version of the Atiyah-Singer index theorem. In more details, we first give a Chern-Weil construction of characteristics forms of coherent sheaves in terms of antiholomorphic flat superconnections, and then give a heat-kernel proof of Grothendieck-Riemann-Roch theorem. This is a joint work with Jean-Michel Bismut and Shu Shen.