# Research Interests

My research interests are in probability theory and statistical mechanics, as well as related aspects of combinatorics. Particular interests include the lace expansion and its applications, models of random loops and spatial permutations, non-Markovian random walks, cluster expansions and their combinatorics, branched polymers, and models of excluded volume such as hard spheres, nematic rods, and hard-core lattice gases.

# In Preparation

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

# Preprints

**A. Hammond, T. Helmuth**, "Self-attractive Self-avoiding Walk",*preprint,*34 pp. [Available]

# 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**, Univ. of California, Berkeley, May 3, 2017.**Mathematical Physics and Probability Seminar**, Univ. of California, Davis, May 10, 2017.

## Past

**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.