Nigel Higson教授(The Pennsylvania State University)　によるスーパーグローバルコース数学特別講演会が下記の要領で開催されます。

開催日時：2023年6月29日（木）、30日（金）各日10:30～12:00

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題目：
6/29日
Hypoelliptic equations and noncommutative geometry, I. An introduction to Bismut’s hypoelliptic Laplacian

6/30日
Hypoelliptic equations and noncommutative geometry, II. C*-algebras and hypoellipticity

概要：
In linear partial differential equations, hypoellipticity is the condition that if Df=g, with g smooth, then f is necessarily smooth too. The best-known hypoelliptic equations are the elliptic equations, which are characterized by an isotropy property that can be readily checked point-by-point. More general point-by-point sufficiency criteria for hypoellipticity have been studied, most famously by Lars Hörmander in the 1960’s. Quite recently these criteria have been used to formulate and prove noteworthy new geometric theorems, including extensions of the Atiyah-Singer index theorem. I shall give a survey of some of these developments, in which, perhaps unexpectedly, noncommutative C*-algebras and noncommutative geometry play an important role. Of special interest to a broad audience might be the example of Jean-Michel Bismut's hypoelliptic Laplacian, which is a remarkable family of operators interpolating between the Laplace operator on a Riemannian manifold and the geodesic flow on its tangent bundle.

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