Dr. Peter Burton

Postdoctoral research associate

Department of Mathematics

Iowa State University

My research interests are centered on ergodic theory and its connections with other areas of mathematics, in particular group theory and quantum information theory. Please see below for more information about my work, and feel free to reach out to me at pburton@iastate.edu

I am organizing the logic and computability seminar at Iowa State during Spring 2023 - see here for the calendar.

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., 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