Professor Alan D Sokal, BA MA PhD

Room 800
Tel: 020-7679-2844
E-mail: sokalmath.ucl.ac.uk
Fax: 020-7383-5519

Research Interests

Statistical mechanics, combinatorics

My research centers on topics at the interface between mathematical physics (notably statistical mechanics and quantum field theory) and combinatorics, together with a strong dose of probability and complex analysis. In particular, I am interested in the real and complex zeros of combinatorially defined polynomials such as the Tutte polynomial (and its specializations such as the chromatic polynomial and the flow polynomial), and their relation to phase transitions in statistical mechanics. Some of this work leads to the investigation of "classical" problems in complex analysis.

I am also interested in developing, analyzing and applying Markov-chain Monte Carlo algorithms for problems in statistical physics. This involves methods of probability theory along with large-scale computation.

Examples of recent papers include:

1) A.D. Sokal, The multivariate Tutte polynomial (alias Potts model)
for graphs and matroids, review paper presented at the 2005
British Combinatorial Conference

http://arxiv.org/abs/math.CO/0503607

2) A.D. Scott and A.D. Sokal, The repulsive lattice gas,
the independent-set polynomial, and the Lovasz local lemma,
J. Stat. Phys. 118, 1151-1261 (2005)

http://arxiv.org/abs/cond-mat/0309352

3) Y.-B. Choe, J. Oxley, A.D. Sokal and D.G. Wagner,
Homogeneous multivariate polynomials with the half-plane property,
Adv. Appl. Math. 32, 88-187 (2004)

http://arxiv.org/abs/math.CO/0202034

4) A.D. Sokal, Chromatic roots are dense in the whole complex plane,
Combin. Probab. Comput. 13, 221-261 (2004)

http://arxiv.org/abs/cond-mat/0012369