Typical REU topics and suggested background reading

We do not expect students to read these prior to the REU.
Not all of these topics are represented in the REU each summer-- this is only to give you an idea of what we might work on.
Glancing at REU reports from previous summers will help round out this picture.
  1. Cluster algebras - see this survey by Lauren Williams.
  2. Crystal bases- see this survey talk by Anne Schilling
  3. Cyclic sieving phenomena - see this survey by Bruce Sagan
  4. Dynamical algebraic combinatorics - see this survey by Jessica Striker
  5. Free resolutions and syzygies- see this survey by Gunnar Fløystad, Jason McCullough and Irena Peeva
  6. Friezes and cluster algbras - see this survey by Sophie Morier-Genoud
  7. Gröbner bases- see this survey by Bernd Sturmfels
  8. Integrable systems - see this survey by Paul Zinn-Justin
  9. Invariant theory of finite groups - see this survey by Richard Stanley
  10. Kazhdan-Lusztig Combinatorics - see this survey by Francesco Brenti
  11. Lattice models and puzzles - see this paper by Paul Zinn-Justin
  12. Lattice models and Yang-Baxter equations - see this paper by Ben Brubaker, Dan Bump and Sol Friedberg
  13. Matroids - see these notes by Vic Reiner
  14. Networks on surfaces - see this survey by Rick Kenyon
  15. Numerical semigroups - see these intros to numerical semigroups and Kunz polyhedra by Chris O'Neill.
  16. Quasisymmetric and Chromatic symmetric functions - see these notes by Franco Saliola
  17. Quivers - see these chapters by Ralf Schiffler
  18. Reflection groups, Weyl groups, and Hecke algebras - see this survey by Raphael Rouquier
  19. Representations of finite groups - see this book by Ben Steinberg
  20. Sandpile groups - see Chapters 3,4 of this book by Carly Klivans.
  21. Stanley-Reisner rings - see this survey by Chris Francisco, Jeffrey Mermin, and Jay Schweig.
  22. Superalgebras and clusters - see this paper by Musiker, Ovenhouse and Zhang
  23. Symmetric functions - see Chapter 9 of these notes by Jeremy Martin.
  24. Total positivity - see this survey by Sergey Fomin.
  25. Webs - see this paper by Fraser, Lam and Le .

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