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9.30 -- 10.00 |
Breakfast |
|
10.00 -- 10.50 |
Benny Sudakov,
Princeton University and IAS Probabilistic method and the Ramsey-Turan-type problems Abstract: Ramsey and Turan-type questions are central in modern Combinatorics and received a considerable amount of attention over the last fifty years. In this talk we describe simple and yet surprisingly powerful probabilistic lemma and discuss its application to some old open problems in this subject. |
|
11.00 -- 11.50 |
Ira M. Gessel,
Brandeis University A survey of lattice path enumeration Abstract: The problem of counting lattice paths in a given region, with given steps, is one of the fundamental problems of enumerative combinatorics, and is closely related to counting problems involving trees, Lagrange inversion, Young tableaux, and polyominoes. In this talk I will describe some of the results and methods of this subject. |
|
12.00 -- 1.50 |
Lunch |
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1.50 -- 2.40 |
Peter Winkler,
Mathematical Sciences Research Center, Bell Labs Shuffling Abstract: Mixing in Markov chains is `big business' these days in combinatorics and the theory of computing, because of its importance in approximate sampling and estimation. We will take a look at how some modern techniques (joint work with Laci Lovasz) apply to an ancient mixing problem: how many times should you shuffle a deck of cards? Three different shuffling models lead to two gratifying answers and one stultifying open problem. (Sponsored by the Honors Program and Visiting Scholars Committee at URI.) |
|
2.40 -- 3.10 |
Coffee |
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3.10 -- 4.00 |
Michelle Wachs,
University of Miami Topology of Posets of Partitions, Trees and Graphs Abstract: Associated to every partially ordered set is a simplicial complex called the order complex. The order complex links combinatorics with topology and other areas of mathematics in a deep and fundamental way. In this talk I will present some new and old results on relationships between the order complexes of posets of partitions, trees and graphs that have arisen in various contexts in the literature. |
|
4.10 -- 5.00 |
Zoltan Furedi,
University of Illinois at Urbana-Champaign Triple systems not containing a Fano configuration and other Turan type problems Abstract: A Fano configuration is the hypergraph of 7 vertices and 7 triplets defined by the points and lines of the finite projective plane of order $2$. The largest triple system on $n$ vertices containing no Fano configuration is determined (for $n> n_1$). It is 2-chromatic with $\binom{n}{3}-\binom{\lfloor n/2 \rfloor}{3} -\binom{\lceil n/2 \rceil}{3}$ triples. This was a conjecture of Vera T. Sos. It is a joint work with M. Simonovits and independently proved by Keevesh ansd Sudakov. We also present a mindegree version: If a triple system has n vertices and contains no F_7 and every degree exceeds (3-c)/4 \binom{n}{2} then it is bipartite. |