# Carsten Peterson

**Email**: carstenp *at* umich *dot* edu

**Office**: East Hall 5840

## About me

Hello, my name is Carsten Peterson. I am a sixth year graduate student at the University of Michigan. I did my undergrad at Yale University. My advisor is 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 my interests are broad and ever-growing: $\{$things I don't like$\}$ $\subset$ $\{$things I don't understand$\}$.

## 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 a recording of a talk I gave to an audience of physics graduate students discusing quantum ergodicity on manifolds and graphs.

Here are slides from a talk I gave at the 2022 Midwest Representation Theory Conference.