Laplacian Equations from a Representation-Theoretic Point of View
Date/Time:18 Apr 2019 16:00
Venue: S17 #05-12 SR4
Speaker: Tian Fangyang, National University of Singapore
Laplacian Equations from a Representation-Theoretic Point of View
The classical Laplacian equation and wave equation are the basic examples of second order PDE. The fundamental solutions of them, which have been well studied, play an important role in the theory of these equations. A nice feature of these two equations is that the differential operator is invariant under certain classical group, hence one may expect a representation theoretic explanation of these equations.
The (indefinite) Laplacian equations serve as a natural generalization of classical Laplacian equation and wave equation. In this talk, I will follow Howe and Tan’s exposition to discuss the (indefinite) Laplacian equation from a representation-theoretic point of view. We will cover some basic representation theory of (sl(2,R), so(2))-module, Weil representation of \tilde{SL(2,R)}, and the fundamental solutions of the indefinite Laplacian Equation.
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