Лекции приглашенных математиков в МФТИ

В начале следующей недели в МФТИ (в Долгопрудном) проходят лекции по математике приглашенных математиков Нога Алона и Прасада Тетали.

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Noga Alon

Н. Алон прочитает две лекции:

  • 23 июня, Актовый зал ЛК, 17:05-18:30 — Coloring and girth.  The study of graphs with high girth and high chromatic number had a profound influence on the history of Combinatrics and Graph Theory, and led to the development of sophisticated methods involving tools from topology, number theory, algebra and combinatorics. I will discuss the topic focusing on a recent new explicit construction of graphs (and hypergraphs) of high girth and high chromatic number.

 

  • 24 июня, 239НК, 17:05-18:30 — Signrank and its applications in combinatorics and complexity.
    The sign-rank of a real matrix A with no 0 entries is the minimum rank of a matrix B so that A_{ij}B_{ij} > 0 for all i,j. The study of this notion combines combinatorial, algebraic, geometric and probabilistic techniques with tools from real algebraic geometry, and is related to questions in Communication Complexity, Computational Learning and Asymptotic Enumeration. I will discuss the topic and describe its background, several recent results from joint work with Morn and Yehudayoff, and some intriguing open problems.

tetali

Prasad Tetali

П. Тетали прочтет следующие лекции:

  • 22 июня, Актовый зал ЛК, 17:05-18:30 — Discrete Curvature and Applications.
    Inspired by exciting developments in optimal transport and Riemannian geometry, several independent groups have formulated notions of (Ricci) curvature in discrete spaces. I will mention briefly some of these approaches, results, examples and open problems.An interesting by-product is the result (obtained jointly with Klartag, Kozma, and Ralli) that the Cheeger inequality — relating the spectral gap to the edge-isoperimetric constant — is tight for the class of abelian Cayley graphs.

 

  • 23 июня, Актовый зал ЛК, 18:30-20:00 — Catalan Shuffles.
    Catalan numbers arise in many enumerative contexts as the counting sequence of combinatorial structures. In this work, we consider natural Markov chains on some of the realizations of the Catalan sequence, and derive estimates on the mixing time of the corresponding Markov chains.
    While our main result is an O(n^2 log n) bound on the mixing time for the random transposition chain on the so-called Dyck paths, we raise several open questions, including the optimality of the above bound.
    The novelty in our proof is in establishing a certain negative correlation property among random bases of the Catalan matroid, for which the Dyck paths form the bases.
    This is joint work with Damir Yeliussizov (Kazakhstan) and Emma Cohen (Georgia Tech).

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