Colloquium Mathematics, Prof. Roberto Fernandez
Join us for coffee and tea at 15.45 p.m.
Date: Tuesday, March 13th 2012
Speaker: Prof. Roberto Fernandez
Room: 5161.0267 (Bernoulliborg)
Time: 16.15
Title: Improvement of the Lov\'{a}sz Local Lemma via
Cluster Expansion
Abstract:
Shearer observed that the Lov\'asz Local Lemma is related with the independent set polynomial on graphs. Scott and Sokal showed that the latter, coincide with the partition function of the hard core lattice gas on graphs. The logarithm of this partition function is the natural object for the application of cluster expansion techniques. Through this chain of arguments, better convergence conditions for cluster expansions translate into an improved version of the Lov\'asz Local Lemma. I will discuss the latest version of the lemma obtained from the strongest results available for cluster expansions. As applications I will present bounds on conditions for the existence of independent sets for partitions of vertices, $k$-SAT families of clauses and latin transversal matrices.
Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and
Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl )
Laatst gewijzigd: | 10 februari 2021 14:29 |
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