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Carsten Peterson

Email: clhpeterson1870 at gmail dot com

About me

I am a postdoc at Institut de Mathématiques de Jussieu - Paris Rive Gauche at Sorbonne University working with Farrell Brumley in the Automorphic Forms group. I am currently supported by an NSF postdoctoral fellowship. Previously I was funded by the Cofund MathInGreaterParis fellowship. Before that I was a postdoc at Paderborn University in the Spectral Analysis group of Tobias Weich as part of the Collaborative Research Center on Integral Structures in Geometry and Representation Theory (specifically projects B3 and B4). I graduated in Spring 2023 from University of Michigan where my advisor was Ralf Spatzier.

My research interests center around geometry and analysis on symmetric spaces and buildings, as well as their quotients by discrete subgroups. I like to use tools from many areas including representation theory, spectral theory, homogeneous dynamics, polytopal geometry, and combinatorics. One of my main research interests is higher rank quantum (unique) ergodicity.

Preprints

  1. C. Arends, C. Peterson, and T. Weich, Resonances on geometrically finite graphs. 30 pages. in preparation (preprint available upon request).
  2. F. Brumley, S. Marshall, J. Matz, and C. Peterson, Quantum ergodicity in the Benjamini-Schramm limit on locally symmetric spaces. 61 pages.
  3. C. Peterson, The discrete wave equation with applications to scattering theory and quantum chaos. 46 pages.
  4. C. Peterson, Quantum ergodicity on the Bruhat-Tits building for $\text{PGL}(3, F)$ in the Benjamini-Schramm limit. 71 pages.

Publications

  1. C. Peterson, A degenerate version of Brion's formula (arxiv version). Adv. Math. 486 (2026). Paper #110732. 54 pages.

Publications based on undergraduate research

  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 my CV.

Here are slides from a colloquium that I gave at University of Utah on quantum ergodicity in the Benjamini-Schramm limit in higher rank.

Here are slides from a talk I gave in the Combinatorics, Arithmetic, and Geometry seminar at IMJ-PRG on the degenerate Brion's formula.

Here is a recording of a virtual talk I gave at UC San Diego.

Here is a recording of a talk I gave to an audience of physics graduate students.