Andrés Larrain Hubach (University of Dayton, Ohio)
Joint online scientific meeting with the American University of Beirut, Lebanese University in Fanar, and the University of Potsdam in the framework of the cooperation:
AT THE CONFLUENCE OF GEOMETRY, ANALYSIS AND MATHEMATICAL PHYSICS
Abstract: The grading technique is a trick used to analyze the supertrace of the heat kernel of a geometric Dirac operator. In this talk, I will review the fundamental aspects of this idea and its use in the proof of the local index theorem. If there is time left, we will discuss how to modify the grading to give an elementary computation of the leading term of an asymptotic expansion of a certain heat kernel constructed from a Dirac operator associated to tensor powers of a holomorphic line bundle over a complex manifold.
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