Spring 2007: MATH 8823 (Topics in Probabilistic Combinatorics)
Jeong Han Kim will deliver the lectures during January and February.
The class meets 1:05-2:55pm on Monday and Wednesday in Skiles 246.
LECTURE NOTES will be posted below as they become available:
Notes 1 (01/08/07)
Notes 2 (01/10/07)
Notes 3 (01/22-24/07)
Notes 4 (01/31-02/02/07) Lovasz local lemma
Notes 5 (02/03-05/07) The nibble and R(3,t)
Notes 6 (02/7-14/07) Branching process and G(n,c/n)
Presentation Poisson Cloning & Applications
Notes 7 (02/19-26/07) Poisson Cloning & Applications (contd.)
Notes 8 (02/26-28/07) Contiguity of RG and RRG?
Add to the reading list:
(0) D. Achlioptas, Y. Peres: The Threshold for the Random k-SAT is 2^k ln 2 - O(k);
Jour. of the AMS 17(2004), 947-973.
(1) M. Mezard, T. Mora, R. Zecchina: Clustering of Solutions in the Random SAT Problem;
Phys. Rev. Lett. 94(2005), 197-205. Also, cond-mat/0504070
(2) D. Achlioptas, F. Ricci-Tersenghi: On the Solution Space Geometry of Random CSPs;
Proc. of the ACM STOC (2006), 130-139.
Full version of the paper
(3) M. Mezard, T. Mora, R. Zecchina: Pairs of SAT assignments and Clustering in Random Boolean Formulae.
Available from arxiv or Mora's website:
http://ipnweb.in2p3.fr/~lptms/membres/mora/publi.en.html
(4) B. Cuckler and J. Kahn, Hamilton Cycles in Dirac graphs, to be posted.
(5) Jon Kleinberg : The Small World Phenomenon: An Algorithmic Perspective
http://www.cs.cornell.edu/home/kleinber/swn.ps
(6) Jon Kleinberg : Complex Networks and Decentralized Search Algorithms
http://www.cs.cornell.edu/home/kleinber/icm06-swn.pdf
PRESENTATIONS:
March 5th, 7th : Jeff Kahn (Rutgers)
March 12th : Tom Bohman (CMU)
March 14th : Prasad Tetali : Shearer's result on independence number of $K_r$-free graphs
April 2nd & 4th : Juan Vera : Preferrential attachment graphs
April 9th : David Howard/Alex Grigo (Papers 0,1,3)
April 11th : Prasad Tetali : Johansson's result on chromatic number of triangle free graphs.
April 16th : Josh Cooper (Univ. of South Carolina)
April 18th : Brad Green : Jon Kleinberg's work (Papers 5,6)/ Teena Carroll : Entropy & Enumeration
April 23rd : Mitch Keller/Armen Vagharshakyan
April 25th : Balinski/Young (Papers (4))