WEBPAGE/SYLL FOR RAMSEY THEORY COURSE FALL 2011

Meeting Times and Proposed Syllabus:

• Sunday Oct 30: 12-13 (Colloquim) and 13-13:30: Coloring Grids.
• Monday Oct 31: 11-13. Van Der Warden's Theorem and Poly VDW's theorem.
• Tuesday Nov 1: MultiDim VDW theorem and Rado's Theorem.
• Wed Nov 2: Ramsey's theorem and its variants.
• OTHER LECTURES IF WE HAVE TIME (see note below) Application of Multi Dim Ramsey Theory to Communication Complexity, Application of Ramsey's Theorem to Data Structures, Application of Ramsey's Theorem to Proving Programs Terminate, Lower bounds on logic resolution theorem proving with an eye towards proving lower bounds on Ramsey Theorems.

Note: If we can find time for a few more meetings then we may try to have some. If I need to give the same lecture twice, I can do that.

Requirements: I will give out some HWs but more important will be a PROJECT. Each student will do a different one (I may allow a pair of students to do one together) and it will be due DUE on JAN 9, 2012. I will then GRADE THEM, and I MAY ASK FOR CORRECTIONS AND/OR EXTENSIONS. The HW is worth 50% of your grade. The Project is worth 50% of your grade.

List of Project Ideas: projects.pdf

SOME TALKS ON SLIDES (THESE ARE NOT NECC GOING TO BE IN THE COURSE.)

1. Grid Colorings- Short Version for Colloquim.
2. Grid Colorings- Long Version to Read off line.
3. Lower Bounds on W(k,c),
4. 3AP's and Lower bounds on W(3,c)
5. Application to Multiparty Comm Comp)
6. Sane Bounds on Poly VDW Theorem)
7. 78 years of R(3,k). (Slides by Joel Spencer.)
8. Application of Ramsey's Theorem to Proving Programs Terminate (Long Version)
9. Application of Ramsey's Theorem to Proving Programs Terminate (Short Version)
10. Application of Ramsey's Theorem to Proving Programs Terminate (Shorter Version)
11. Lower Bounds on Resolution

SOME WEBSITES:

1. Applications of Ramsey Theory
2. VDW Papers

MISC:

1. VDW's Theorem: Variants and "Applications" by Gasarch, Kruskal, Parrish. (Unpublished and unpolished).
2. Lower Bounds on VDW Numbers:Randomized and Deterministic Constructive by Gasarch and Haeupler.
3. Application to Multiparty Comm Comp
4. Papers on 3-free sets:
   • Finding Large 3-free sets I: The Small $n$ Case, by Gasarch, Glenn, Kruskal.
   • Finding Large Sets without Arithmetic Progressions of Length Three: An Empirical View, by Gasarch, Glenn, Kruskal.
   • An Improved Construction of Progression-Free Sets by Micahel Elkin. (Best known construction of 3-free sets.)
   • On Sets of Integers not containing long arithmetic progressions by Laba and Lacey (best known results on $k$-free sets.)
5. Rectangle Free Colorings of Grids by Fenner, Gasarch, Glover.
6. Sane Bounds on some Poly VDW Numbers
7. A 2-coloring of 14x14 with no mono squares by Daniel Apon.
8. A Statement in Combinatorics that is Ind of ZFC by Fenner and Gasarch
9. Application of Ramsey's Theorem to Proving Programs Terminate
10. Ramsey's Theorem For Graphs
11. Ramsey's Theorem For 3-hypergraphs
12. Ramsey's Theorems in Hebrew