# Carsten Peterson

**Email**: peterson *at* math *dot* upb *dot* de

## About me

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.

## Preprints

- C. Peterson,
*Quantum ergodicity on the Bruhat-Tits building for PGL(3, F) in the Benjamini-Schramm limit* (submitted)

## Publications

- K. Cordwell, M. Hlavacek, C. Huynh, S. J. Miller, C. Peterson, and Y. N. T. Vu,
*Summand minimality and asymptotic convergence of generalized Zeckendorf decompositions* (arxiv version). Res. Number Theory (2018) 4: 43.
- S. J. Miller, C. Peterson, C. Sprunger, and R. van Peski,
*The bidirectional ballot polytope* (arxiv version). *Integers* 18 (2018), #A81.
- S. J. Miller and C. Peterson,
*A geometric perspective on the MSTD question* (arxiv version). Discrete Comput. Geom. 62, 832-855 (2019).

## Other

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.