Hello, my name is Carsten Peterson. I am currently a postdoc at Paderborn University as part of the Collaborative Research Center on Integral Structures in Geometry and Representation Theory (specifically projects B3 and B4). In Fall 2024 I will be at Laboratoire d'Analyse, Géométrie et Applications at Université Sorbonne Paris Nord as part of the Cofund MathInGreaterParis program.
I graduated in Spring 2023 from University of Michigan where my advisor was Ralf Spatzier. My current focus is in the direction of quantum ergodicity, which relates ergodicity of a dynamical system with equidistribution of the eigenfunctions of the corresponding Laplace operator. More specifically I am working on "quantum ergodicity on Bruhat-Tits buildings". Bruhat-Tits buildings are simplicial complexes built from semisimple algebraic groups over non-archimedean local fields. They may be interpreted as non-archimedean analogues of symmetric spaces of non-compact type. The simplest examples of these buildings are infinite regular trees. More generally I am interested in analogies between symmetric spaces and affine buildings, as well as connections between representation theory, spectral theory, and dynamics.
Here is my CV.
Here are slides from a talk that I gave at Johns Hopkins in December 2023.
Here is a poster that I presented at the IMJ-PRG 2023 Summer School on Microlocal and probabilistic methods in geometry and dynamics.
Here is a recording of a talk I gave to an audience of physics graduate students discusing quantum ergodicity on manifolds and graphs.