Cohomology in algebra, geometry, physicsand statistics

Triangular decoupling of systems of differential equations, with application to separation of variables on Schwarzschild spacetime

Certain tensor wave equations admit a complete separation of variables on the Schwarzschild spacetime (static, spherically symmetric black hole), resulting in complicated systems of radial mode ODEs. The spectral theory of these systems has important applications to the stability analysis electromagnetic and gravitational perturbations of the black hole. However, almost none of the important questions about the radial mode equations can be answered in their original form. I will discuss a drastic simplification of these ODE systems to sparse upper triangular form that is directly susceptible to spectral analysis. Essential to this simplification are geometric properties of the original tensor wave equations, ideas from homological algebra and from the theory of ODEs with rational coefficients. Based on [arXiv:1711.00585, 1801.09800].

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We shall start   at 11:00  for coffee.

Meeting ID: 982-2069-8442
 Join URL: https://cesnet.zoom.us/j/98220698442