Research Interests

My research interests are in probability theory and statistical mechanics. I'm particularly interested in the lace expansion, spin systems, random spatial permutations, non-Markovian random walks, cluster expansions and their combinatorics, and models of excluded volume such as branched polymers, hard spheres, nematic rods, and hard-core lattice gases. For more information, see my research statement.


In Preparation

  • A. Hammond, T. Helmuth, "Directed Spatial Permutations on Asymmetric Tori".
  • D. Brydges, T. Helmuth, M. Holmes, "The Continuous-time Lace Expansion".

Preprints

  • R. Bauerschmidt, T. Helmuth, A. Swan, "Dynkin isomorphism and Mermin--Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process", 16 pp. [arXiv]
  • A. Hammond, T. Helmuth, "Self-attracting self-avoiding walk", 34 pp. [arXiv]

Published

  • T. Helmuth, "Dimensional reduction for generalized continuum polymers", J. Stat. Phys., 165(24), 24-43, 2016. [arXiv]
  • T. Helmuth, "Loop-weighted walk", Ann. Inst. Henri Poincaré Comb. Phys. Interact., 3, 55-119, 2016. [arXiv]
  • T. Helmuth, "Ising model observables and non-backtracking walks", J. Math. Phys. 55(8), 1--28, 2014. [arXiv]
  • T. Helmuth, G. Patrick, "Two rolling disks or spheres", Discrete Contin. Dynam. Systems Ser. S 3(1), 129--140.
  • T. Helmuth, R. Spiteri, J. Szmigielski, "One-dimensional magnetotelluric inversion with radiation boundary conditions", Canad. Appl. Math. Quart. 15(4), 419--444.

Talks

Upcoming

  • Probability seminar, KTH Royal Institute of Technology, Apr. 23, 2018.
  • London Probability Seminar, Univ. College London, May 10, 2018.
  • Probability Seminar, Univ. of Bath, May 24, 2018.
  • Horowitz Seminar, Univ. Tel Aviv, June 18, 2018.

Past

  • Stochastics Seminar, TU Budapest, Mar. 29, 2018.
  • Probability Seminar, Univ. of Cambridge, Mar. 6, 2018.
  • Statistical Mechanics Seminar, Univ. of Warwick, Feb. 22, 2018.
  • Probability Seminar, Univ. of Bristol, Oct. 20, 2017.
  • Stochastics Seminar, Univ. Nacional Autónoma de México, Aug. 9, 2017.
  • Mathematical Physics and Probability Seminar, Univ. of California, Davis, May 10, 2017.
  • Probability Seminar, Univ. of California, Berkeley, May 3, 2017.
  • Stochastics Seminar, Univ. of Utah, Apr. 7, 2017.
  • Mathematical Physics and Probability Seminar, Univ. of California, Davis, Nov. 30, 2016.
  • Mathematics Colloquium, Univ. of Oregon, Oct. 10, 2016.
  • Bay Area Discrete math day #33, held at Univ. of California, Davis, Oct. 1, 2016.
  • Algebra-Geometry-Combinatorics Seminar, San Francisco State Univ., Sep. 14, 2016.
  • Mathematical Physics and Probability Seminar, Univ. of California, Davis, Jun. 1, 2016.
  • Trends in Mathematical Crystallization Workshop, Univ. of Warwick, May 4, 2016.
  • Applied Math and Mathematical Physics Seminar, Univ. of Saskatchewan, Dec. 21, 2015.
  • Stochastics Seminar, Univ. Bonn, Jul. 16, 2015.
  • Expansion Methods in Statistical Mechanics Workshop, Utrecht Univ., Jul. 3, 2015.
  • CRC 1060 Seminar, Univ. Bonn, Jun. 16, 2015.
  • Center of Mathematical Sciences & Applications Seminar, Harvard, Apr. 23, 2015.
  • Mathematical Physics and Probability Seminar, Univ. of California, Davis, Nov. 17, 2014.
  • Probability Seminar, Univ. of Kansas, Nov. 12, 2014.
  • Probability Seminar, Univ. of California, Berkeley, Oct. 29, 2014.
  • PIMS Summer School in Probability, Univ. of British Columbia, Jun. 20, 2014.
  • EPSRC Symposium on Statistical Mechanics: Gradient Random Fields, Univ. of Warwick, May 27, 2014.
  • Feza Gürsey Summer School in Mathematical Physics, Feza Gürsey Institute, Jun. 25, 2012.
  • PIMS Summer School in Probability, Univ. of British Columbia, Jun. 14, 2012.
  • Discrete Math Seminar, Univ. of British Columbia, Mar. 27, 2012.
  • Applied Math and Mathematical Physics Seminar, Univ. of Saskatchewan, Dec. 20, 2011.