Dr. Peter Burton

Assistant Professor

Department of Mathematics and Statistics

University of Wyoming

I am a theoretical mathematician working primarily in ergodic theory, quantum information theory and harmonic analysis on groups. For me, these fields synthesize around the concept of numerical functions on noncommutative structures. I also have a very general interest in computational technology and methods of efficient information processing.

In addition to my appointment in the mathematics department, I am a member of the University of Wyoming's Center for Quantum Information Science and Engineering.

My office on the University of Wyoming campus is Ross Hall 320. Please see below for more information about my work, and feel free to reach out to me at pburton2@uwyo.edu

My CV

Published articles

Bowen, L., Burton, P. - Locally compact sofic groups
- - Isr. J. Math. 251, 239–270 (2023)
  - https://doi.org/10.1007/s11856-022-2431-2
  - https://arxiv.org/abs/2106.09118
Burton, P., Juschenko, K. - The extension problem in free harmonic analysis
- - Ann. Funct. Anal. 13, 43 (2022)
  - https://doi.org/10.1007/s43034-022-00189-2
  - https://arxiv.org/abs/2003.04535
Burton, P. - Statistical constructions in quantum information theory
- - Quantum Stud.: Math. Found. 9, 265–285 (2022)
  - https://doi.org/10.1007/s40509-022-00269-x
  - https://arxiv.org/abs/2103.10995
Bowen, L., Burton, P. - Flexible stability and nonsoficity
- - Trans. Amer. Math. Soc. 373, 4469-448 (2020)
  - https://doi.org/10.1090/tran/8047
  - https://arxiv.org/abs/1906.02172
Bowen, L., Burton, P. - Failure of the L^1 pointwise ergodic theorem for PSL(2,R)
- - Geom. Dedicata. 207, 61–80 (2020)
  - https://doi.org/10.1007/s10711-019-00487-5
  - https://arxiv.org/abs/1901.01299
Burton, P., Kechris, A. - Weak containment of measure-preserving group actions
- - Ergod. Th. & Dynam. Sys. 40, 2681–2733 (2020)
  - https://doi.org/10.1017/etds.2019.26
  - https://arxiv.org/abs/1611.07921
Austin, T., Burton, P. - Uniform mixing and completely positive sofic entropy
- - J. d'Analyse Math. 38, 597–612 (2019)
  - https://doi.org/10.1007/s11854-019-0033-7
  - arxiv.org/abs/1603.09026
Burton, P. - Topology and convexity in the space of actions modulo weak equivalence
- - Ergod. Th. & Dynam. Sys. 38, 2508–2536 (2018)
  - http://doi.org/10.1017/etds.2016.133
  - https://arxiv.org/abs/1501.04079
Burton, P., Kechris, A. - Invariant random subgroups and action versus representation maximality
- - Proc. Amer. Math. Soc. 145, 3961-3971 (2017)
  - https://doi.org/10.1090/proc/13591
  - https://arxiv.org/abs/1608.01331
Burton, P. - Naive entropy of dynamical systems
- - Isr. J. Math. 219, 637–659 (2017)
  - https://doi.org/10.1007/s11856-017-1493-z
  - https://arxiv.org/abs/1503.06360
Burton, P., Tall, F.D. - Productive Lindelöfness and a class of spaces considered by Z. Frolík
- - Topology Appl. 159, 3097-3102 (2012)
  - https://doi.org/10.1016/j.topol.2012.05.022

Preprints

Burton, P., Panangaden, J. - Formulations of Furstenberg's x2 x3 conjecture in complex analysis and operator algebras
- arxiv.org/abs/2410.22701
Burton, P., Eagle, C., Fox, A., Goldbring, I., Harrison-Trainor, M., McNicholl, T., Melnikov, A, Thewmorakot, T. - Computable Gelfand duality
- https://arxiv.org/abs/2402.16672
Burton, P., Chaudkhari, M., Juschenko, K., Muliarchyk, K. - Hyperlinear approximations to amenable groups come from sofic approximations
- arxiv.org/abs/2311.09202
Burton, P. - Synergodic actions of product groups
- arxiv.org/abs/2311.09202