Third Year Major Oral: Index Theorem for Hypoelliptic Operators

Abstract: Israel Gelfand asked, "Is there a topological formula for the analytic index of an elliptic operator on a compact manifold?" Michael Atiyah and Isadore Singer, in 1963,  answered this question by giving the Atiyah-Singer Index theorem. Their result brings together the ideas in analysis, geometry, and topology. Lars Hörmander, in 1971, proved that the Atiyah-Singer index formula can be applied to hypoelliptic operators of the type $(p, \delta)$. This talk will discuss developments in the index theory of (certain)hypoelliptic operators on contact manifolds. I will also talk about its generalization to filtered manifolds.

Advisor: Xiang Tang