Symmetry tricks in spectral geometry

Analysis Seminar: Michael Levitin, Heriot-Watt University. Abstract: We show the use of symmetry tricks in solving two problems of spectral geometry: a partial case $g=2$ of the question "How large can the first eigenvalue be on a surface of genus $g$?" and a modification of Mark Kac's question, "Can one hear the shape of a drum?" The questions (or, rather, our answers) are surprisingly related.