Time: 11:30
Speaker: (Western)
Title: "Learning Seminar"
Room: MC 107

Abstract: We continue on: ---The index problem for elliptic PDE's, characteristic classes via Chern-Weil theory, ---Miraculous cancellations, Getzler's supersymmetric proof of the Atiyah-Singer index theorem, special cases: Gauss-Bonnet-Chern, Hirzebruch signature theorem, and Riemann-Roch, --- Approach via path integrals and quantum mechanics.

Time: 15:30
Speaker: Lyudmila Korobenko (McMaster University)
Title: "Orlicz Sobolev inequalities for infinitely degenerate metrics and regularity of solutions to associated equations"
Room: MC 107

Abstract: The talk is concerned with regularity of weak solutions to second order infinitely degenerate elliptic equations. It is known that regularity of weak solutions can be studied by studying properties of certain metric spaces associated to the operator, namely, subunit metric spaces. The problem arising in the infinitely degenerate case is that the measures of subunit balls are non doubling. As a consequence many classical tools such as Sobolev-type inequalities become unavailable. We show that in certain cases a weaker version of Sobolev inequality can be established which allows to perform Moser iterations to obtain boundedness and continuity of weak solutions.