MCS 591: Statistical Physics and Applications

MCS 591

Spring 2021

Monday, Wednesday, Friday 10:00 - 10:50 am online

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:

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

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  • Mar 22no class - spring break

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