|Email:||lukas.schimmer (at) gmail.com|
My research mainly focuses on problems in Analysis and Spectral Theory that originate from Mathematical Physics. I study trace formulae, spectral inequalities, Weyl-type asymptotics, resolvent estimates, variational principles and self-adjoint extensions of discrete and continuous differential operators in different geometries. I am especially interested in the investigation of sharp constants in Lieb–Thirring inequalities. Furthermore I am interested in investigating the exchange energy in Density Functional Theory, especially in the context of finding improvements on the Lieb–Oxford inequality.