Proposed reading projects.
Project 1: On the chromatic polynomial and cluster expansions. Read: A. Sokal, "Bounds on the complex zeros of (di)chromatic polynomials and Potts-model partition functions." Combin. Probab. Comput. 10 (2001), no. 1, 41--77.
Project 2: Recent improvements on cluster expansion techniques and application to chromatic polynomials. Read: R. Fernandez and A. Procacci, "Cluster expansion for abstract polymer models. New bounds from an old approach." Comm. Math. Phys. 274 (2007), no. 1, 123--140, AND from the same authors "Regions without complex zeros for chromatic polynomials on graphs with bounded degree." Combin. Probab. Comput. 17 (2008), no. 2, 225--238.
Project 3: Hierarchical models. Read: Lecture 2 of Park City/IAS course by D. Brydges, "Lectures on the renormalisation group".
Project 4: Hierarchical models. Read: P. Collet and J.-P. Eckmann, "The epsilon-expansion for the hierarchical model". Comm. Math. Phys. 55 (1977), no. 1, 67--96.
Project 5: Hierarchical models. Read: K. Gawedzki and A. Kupiainen, "Non-Gaussian fixed points of the block spin transformation. Hierarchical model approximation". Comm. Math. Phys. 89 (1983), no. 2, 191--220.
Project 6: Cluster expansions and nonequilibrium models. Read: W. I. Skrypnik, "On polymer expansion for Gibbsian states of nonequilibrium systems of interacting Brownian oscillators". Ukrain. Mat. Zh. 55 (2003), no. 10, 1356--1377; translation in Ukrainian Math. J. 55 (2003), no. 10, 1639--1661.
Project 7: Cluster expansions and stochastic lattice fields. Read: J. Dimock, "A cluster expansion for stochastic lattice fields". J. Statist. Phys. 58 (1990), no. 5-6, 1181--1207.
Project 8: Renormalization. Read: Sections II.1, II.2 and II.3 of the book by V. Rivasseau "From perturbative to constructive renormalization".
Project 9: Cluster expansions. Read: T. Kuna, Y. Kondratiev and J. Da Silva, "Marked Gibbs measures via cluster expansion". Methods Funct. Anal. Topology 4 (1998), no. 4, 50--81. Arxiv preprint.
Project 10: Fermions. Read: M. Salmhofer, "Clustering of fermionic truncated expectation values via functional integration", Arxiv preprint.
Project 11: Supersymmetry and cluster expansions. Read: M. Disertori, H. Pinson and T. Spencer, "Density of states for random band matrices". Comm. Math. Phys. 232 (2002), no. 1, 83--124.
Project 12: Cluster expansions. Read: S. Poghosyan and H. Zessin, "Asymptotic expansion of the log-partition function for a gas of interacting Brownian loops" J. Math. Phys. 48 (2007), no. 9, 093301, 13 pp.
Project 13: Lattice field models and scaling limits. Read: S. Albeverio, M. S. Bernabei and X. Y. Zhou, "Lattice approximations and continuum limits of phi 4_2 quantum fields". J. Math. Phys. 45 (2004), no. 1, 149--178.
Project 14: Cluster expansions and renormalization group. Read: L. Bertini, E. Cirillo and E. Olivieri, "Renormalization group in the uniqueness region: weak Gibbsianity and convergence". Comm. Math. Phys. 261 (2006), no. 2, 323--378.
Project 15: SDEs and constructive field theory. Read: G. Jona-Lasinio and R. Seneor, "Study of stochastic differential equations by constructive methods. I". J. Statist. Phys. 83 (1996), no. 5-6, 1109--1148.