# Carsten Peterson

### Office: East Hall 5840

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

1. 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.
2. S. J. Miller, C. Peterson, C. Sprunger, and R. van Peski, The bidirectional ballot polytope (arxiv version). Integers 18 (2018), #A81.
3. 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.