Morse Theory and van Hove Singularities - part 2
The local behaviour of a certain class of differentiable functions obeys strong constraints due to the global topology of their domain, with several important implications for dispersion relations in solid-state physics, for which periodic boundary conditions require reciprocal space to have a nontrivial global topology. This talk should provide a physically intuitive overview of Morse Theory, the mathematics underlying the surprising connection of global topology to local behaviour, and the striking experimental predictions of van Hove singularities, a phenomenon in crystallographic optical absorption spectra.
The content will be less biophysical/soft matter than usual and more oriented towards analytic solid state theory, and also may also be interesting to particle theorists.
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..