Monday 13th of March 2023, 15:15-16:15 in HG03.085
Aquerman Yanes
An Introduction to Index Theory.
Index theory is an area in the intersection of analysis, topology and geometry which is prominently used to study the global aspects of (elliptic) differential operators on manifolds. In this talk we shall introduce the classical notion of the index of a Fredholm operator and construct some examples. We lay out the general theory on compact manifolds and explore the analytic side of the Gauss-Bonnet theorem for surfaces, given by the index of a Dirac operator defined thereupon. If time permits, we will also explore some of the more modern approaches and problems in the area, which use techniques in \(C^*\)-algebras, K(K)-theory and representation theory.