turkmath.org

The central theme of this talk is related to the problems about the queston "Can we hear the shape of a drum?" that posed by Mark Kac n 1966. The problem has been very popular since 50 years and has led to similar questions in different contexts such as ''Can one hear the shape of a graph associated with the Schrödinger operator?'', ''Can you hear the shape of your throat?'', ''Can you feel the shape of a manifold with Brownian motion?”, ''Can one hear the crack in a beam?'', ''Can one hear into the sun?'', etc. The common point of of these topics is inverse eigenvalue problems or related inverse problems. Expectedly, to find any kind of answer to those problems one needs spectral geometry which yields informaton about geometric shapes from the vibration frequencies they produce.