Math 194: Combinatorial Game Theory

Math 194: Combinatorial Game Theory Math 194: Combinatorial Game Theory

Time and place: MWF 1:00-2:00pm, Sever 110 (CLASS HAS MOVED!!!)

Course Head: Jacob Lurie
Office: 235 Science Center
Office hours: Wednesday 3-4.
Phone: (617) 495-1651

Course Assistant: Elena Udovina
Office hours: Sunday, 9:30 - ?, Lowell Dining Hall.
Section Meetings: Wednesdays, 6PM, Location: Science Center 101B

Prerequisites: Familiarity with abelian groups, equivalence relations, ordered sets, etcetera (Math 122 or equivalent).

Textbook: "On Numbers and Games" by John Conway. Not required; we will not follow the book closely, but it is the best available reference on this material.

Course Description: An introduction to the theory of combinatorial games (games of no chance and perfect information). Topics: the arithmetic of games, structure theory for impartial games, surreal numbers, temperature theory for finite games, and Norton's analysis of "all small" games via the atomic weight calculus. The course syllabus.

Some Related Links:

Software for performing calculations in combinatorial game theory. Worth a look if you'd like to do some experiments on your own.

Homework Assignments:

Problem Set 1. (Corrected.) Solutions.

Problem Set 2. Solutions.

Problem Set 3. Solutions.

Problem Set 4. (Corrected.) Solutions.

Problem Set 5. (Corrected.) Solutions.

Problem Set 6.

Problem Set 7. (Corrected.) Solutions.

Problem Set 8. Solutions.

Problem Set 9. Solutions.

Problem Set 10. Solutions.

Final exam. (Take home, due Monday, May 22 at noon.)

Course Notes

Lecture 1. (Notes courtesy of Elena Udovina.)
Lecture 2. (Notes courtesy of Elena Udovina.)
Lecture 3. (Notes courtesy of Elena Udovina.)
Lecture 4. (Notes courtesy of Elena Udovina.)
Lecture 5. (Notes courtesy of Elena Udovina.)
Lecture 6. (Notes courtesy of Elena Udovina.)
Lecture 7. (Notes courtesy of Elena Udovina.)
Lecture 8. (Notes courtesy of Elena Udovina.)
Lecture 9. (Notes courtesy of Elena Udovina.)
Lecture 10. (Notes courtesy of Elena Udovina.)
Lecture 11. (Notes courtesy of Elena Udovina.)
Lecture 12. (Notes courtesy of Elena Udovina.)
Lecture 13. (Notes courtesy of Elena Udovina.)
Lecture 14. (Notes courtesy of Elena Udovina.)
Lecture 15. (Notes courtesy of Elena Udovina.)
Lecture 16. (Notes courtesy of Elena Udovina.)
Lecture 17. (Notes courtesy of Elena Udovina.)
Lecture 18. (Notes courtesy of Elena Udovina.)
Lecture 19. (Notes courtesy of Elena Udovina.)
Lecture 20. (Notes courtesy of Elena Udovina.)
Lecture 21. (Notes courtesy of Elena Udovina.)
Lecture 22. (Notes courtesy of Elena Udovina.)
Lecture 23. (Notes courtesy of Elena Udovina.)
Lecture 24. (Notes courtesy of Elena Udovina.)
Lecture 25. (Notes courtesy of Elena Udovina.)
Lecture 26. (Notes courtesy of Elena Udovina.)
Lecture 27. (Notes courtesy of Elena Udovina.)
Lecture 28. (Notes courtesy of Elena Udovina.)
Lecture 29. (Notes courtesy of Elena Udovina.)
Lecture 30. (Notes courtesy of Elena Udovina.)
Lecture 31. (Notes courtesy of Elena Udovina.)
Lecture 32. (Notes courtesy of Elena Udovina.)
Lecture 33. (Notes courtesy of Elena Udovina.)
Lecture 34. (Notes courtesy of Elena Udovina.)

Back to Jacob Lurie's home page. ****** Syllabus for my topics class: Lecture 1: Introduction/Inspiration Lecture 2: Construction of the Operations Lecture 3: Proof of the Adem Relations Lecture 4: Admissible monomials, free unstable modules Lecture 5: Unstable Algebras/Enveloping Construction Lecture 6: Proof that we get all unstable operations Lecture 7: Description in terms of automorphisms of the forgetful functor Lecture 8: The Steenrod algebra, basic facts and consequences of Adem - admissible basis - steenrod algebra generated by operations corresponding to powers of 2 - unstable modules/algebras Lecture 9: Serre-Cartan theorem on cohomology of Eilenberg-Maclane spaces Lecture 10: Milnor's presentation + relationship with formal groups Lecture 11: Local Noetherianness for unstable modules Lecture 12?: Koszulness Lecture 13: Loop and Suspension constructions, reduced modules, the Phi functor, nilpotent modules Lecture 14: Some Injective Modules: J(n) and Carlsson's modules Lecture 15: Operation rings and relationship with dual Steenrod algebra Lecture 16: Tensor product injectivity theorem Lecture 17: Lannes's T-functor + very basic properties (commutativity with Phi?) Lecture 18: Commutativity of T with suspensions Lecture 19: Exactness of T/ injectivity result for H^* BV Lecture 20: Compatibility with tensor products Lecture 21: T functor on unstable algebras Lecture 22: Compute T on Eilenberg-MacLane Spaces Lecture 23: Eilenberg-Moore Spectral sequence and T Lecture 24: p-profinite homotopy category Lecture 25: main theorem in p-profinite language Lecture 26: Corollary: atomicity of BV in p-profinite category. Extend to finite p-groups, deduce one version of Sullivan conjecture Lecture 27: p-nilpotent homotopy theory. Atomicity of BV there. Lecture 28: Arithmetic square. Lecture 29: Haynes's proof in simply connected case, using reduction to p-groups. Lecture 30: Haynes's reduction to simply connected case. Corollary: homotopy invariance of construction of coarse moduli spaces. Extension: no maps from K( pi, 2) into finite complexes, etcetera. Lecture 31: p-adic homotopy theory and E-infty rings. Lecture 32: Gabriel's thesis Lecture 33: Classification of Injectives Lecture 34: The nilpotent filtration Lecture 35: Relationship with analytic functors Lecture 36: The polynomial/Krull filtrations Lecture 37: Compatibility of the filtrations/ convergence questions/ successive quotients and representations of the symmetric groups