Instructor

Will Perkins

* willp@uic.edu*

Office: SEO 626

Office Hours: Mondays and Wednesdays 11:00am-12:00pm, or by appointment

Course Information
#### Main Topics of the Course:

- Fundamentals of statistical physics: Gibbs measures, partition functions, correlations, phase transitions
- Algorithms for approximatate counting and sampling
- Phase coexistence and absence of phase transition
- Cluster expansion
- Polymer models
- Entropy methods
- Pirogov-Sinai theory
- Applications to extremal and enumerative combinatorics
- Algorthms at low temperatures
- Spin models on random graphs
- Sphere packings and the hard sphere model

References

- Friedli and Velenik, Statistical Mechanics of Lattice Systems
- Alon and Spencer, The Probabilistic Method
- Mezard and Montanari, Information, Physics, and Computation
- Levin and Peres, Markov Chains and Mixing Times

Schedule

- Jan 11What is statistical physics? How is it related to combinatorics and algorithms?
- Jan 13Gibbs measures and partition functions
- Jan 15Correlations and correlation decay
- Jan 18NO CLASS - MLK Day
- Jan 20Phase transitions and absence of phase transition
- Jan 22Peierls' Argument
- Jan 25Markov chains
- Jan 27Counting and sampling
- Jan 29Open problems in approximate counting
- Feb 1Extremal problems for regular graphs
- Fev 3Independent sets in triangle-free graphs
- Feb 5Matchings in regular graphs
- Feb 8tba
- Feb 10tba
- Feb 12tba
- Feb 15tba
- Feb 17tba
- Feb 19tba
- Feb 22tba
- Feb 24tba
- Feb 26tba
- Mar 1tba
- Mar 3tba
- Mar 5tba
- Mar 8tba
- Mar 10tba
- Mar 12tba
- Mar 15tba
- Mar 17tba
- Mar 19tba
- Mar 22no class - spring break
- Mar 24no class - spring break
- Mar 26no class - spring break
- Mar 29tba
- Mar 31tba
- Apr 2tba
- Apr 5tba
- Apr 7tba
- Apr 9tba
- Apr 12tba
- Apr 14tba
- Apr 16tba
- Apr 19tba
- Apr 21tba
- Apr 23tba
- Apr 26tba
- Apr 28tba
- Apr 30tba