Convergence of Star Products on \(T^*G\)
Monday, 23.10.23, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1
Star products can be seen as a generalization of a symbol calculus for differential operators. In fact, for cotangent bundles, the global symbol calculus yields a star product of a particular kind. While formal star products have been studied in detail with deep and exciting existence and classification theorems, convergence of the formal star products is still a widely open question. Beside several (classes of) examples, not much is known. In this talk I will focus on a particular class of examples, the cotangent bundles of Lie groups, where a nice convergence scheme has been established. I will try to avoid the technical details as much as possible and focus instead on the principal ideas of the construction. The results are joint work with Micheal Heins and Oliver Roth.
Witten deformation for non-Morse functions and gluing formulas
Monday, 30.10.23, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
Witten deformation is a versatile tool with numerous applications in\nmathematical physics and geometry. In this talk, we will focus on the analysis\nof Witten deformation for a family of non-Morse functions, leading to a new\nproof of the gluing formula for analytic torsions. Then we could see that the\ngluing formula for analytic torsion can be reformulated as the Bismut-Zhang\ntheorem for non-Morse functions. Furthermore, this approach can be extended to\nanalytic torsion forms, which also provides a new proof of the gluing formula\nfor analytic torsion forms.