
Fri 12 Feb 2016, 1:00pm
Probability Seminar
MATH 126

Thermodynamic limit on the graph of Zigzag diagrams

MATH 126
Fri 12 Feb 2016, 1:00pm2:00pm
Abstract
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 n1 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. "
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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, 3:00pm4:00pm
Abstract
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?
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Seminar Information Pages

Note for Attendees
Refreshments will be served in MATH 125 before the colloquium.