The abstract Hodge--Dirac operator and its stable discretization
Speaker: Ari Stern, Washington University in St Louis
Abstract: Dirac operators play an important role in linking geometry and topology with the analysis of PDEs. I will discuss a relatively new approach to studying Hodge--Dirac-type operators (due to Axelsson, Keith, and McIntosh, Invent. Math., 2006), which uses an abstract formalism involving nilpotent operators on Hilbert spaces, but which nevertheless preserves many key properties, including the Hodge decomposition. I will then present some recent work (joint with P. Leopardi) on the stable discretization of these operators, with applications to certain problems in "discrete Clifford analysis" and numerical PDEs.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm