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. Cyclic sieving phenomena - see this survey by Bruce Sagan
  3. Free resolutions and syzygies- see this survey by Gunnar Fløystad, Jason McCullough and Irena Peeva
  4. Friezes and cluster algbras - see this survey by Sophie Morier-Genoud
  5. Gröbner bases- see this survey by Bernd Sturmfels
  6. Lattice models and puzzles - see this paper by Paul Zinn-Justin
  7. Lattice models and Yang-Baxter equations - see this paper by Ben Brubaker, Dan Bump and Sol Friedberg
  8. Matroids - see these notes by Vic Reiner
  9. Networks on surfaces - see this survey by Rick Kenyon
  10. Numerical semigroups - see these intros to numerical semigroups and Kunz polyhedra by Chris O'Neill.
  11. Quasisymmetric and Chromatic symmetric functions - see these notes by Franco Saliola
  12. Quivers - see these chapters by Ralf Schiffler
  13. Reflection groups, Weyl groups, and Hecke algebras - see this survey by Raphael Rouquier
  14. Representations of finite groups - see this book by Ben Steinberg
  15. Sandpile groups - see Chapters 3,4 of this book by Carly Klivans.
  16. Stanley-Reisner rings - see this survey by Chris Francisco, Jeffrey Mermin, and Jay Schweig.
  17. Symmetric functions - see Chapter 9 of these notes by Jeremy Martin.
  18. Total positivity - see this survey by Sergey Fomin.

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