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Pierre Tarrago
Fri 12 Feb 2016, 1:00pm
Probability Seminar
MATH 126
Thermodynamic limit on the graph of Zigzag diagrams
MATH 126
Fri 12 Feb 2016, 1:00pm-2:00pm


 In this talk, I will first introduce the notions of Gibbs measures and thermodynamic limit on graded graphs, as they were defined by the Russian school (Vershik, Kerov, Olshanski,...). Then, I will present some results related to the thermodynamic limit on the graph of Zigzag diagrams: the latter is a graded graph whose set of vertices of degree n consists of words of length n-1 in two letters, and such that the edge structure is given by a simple combinatorial relation between words of consecutive lengths. This graph is related to the Young graph, and I will explain this relation by mapping paths on the graph of Zigzag diagrams to paths on the Young graph. "
Bob Hough
Institute for Advanced Study, Princeton
Fri 12 Feb 2016, 3:00pm
Department Colloquium
MATX 1100
Covering systems of congruences and the Lovasz Local Lemma
MATX 1100
Fri 12 Feb 2016, 3:00pm-4:00pm


The Lov\'{a}sz Local Lemma is a powerful technique from probabilistic combinatorics for treating many rare events with localized dependence structure.  I discuss the local lemma and its application in my negative solution to the following problem of Erd\H{o}s.

A distinct covering system of congruences is a collection of arithmetic progressions
a_i \bmod m_i, \qquad 1 < m_1 < m_2 < ... < m_k

whose union is the integers. Can m_1 be arbitrarily large?

Note for Attendees

Refreshments will be served in MATH 125 before the colloquium.