CNRS-PAN Mathematics Summer Institute, Cracow 2 - 9 July, 2017



In collaboration with the Institute of Mathematics, Jagiellonian University, Institute of Mathematics, Polish Academy of Sciences, CNRS, Imperial College London, IMP Universite Paul Sabatier Toulouse, and ANR project STAB.

Supported by Warsaw Center of Mathematics and Computer Sciences.

Organizers: Dominique Bakry (Toulouse), Szymon Peszat (Cracow), and Bogusław Zegarliński (London).

The meeting will review recent results in the area of analysis/stochastics. Besides a number of presentation by international participants, the meeting will include two mini-courses (suitable for PhD students and young researchers). It is probable that we will be able to cover the accommodation of some number of participants (with the strong emphasis of young people and researchers without financial support of their organizations). In order to register, send an e-mail to: Szymon Peszat on e.mail adress napeszat@cyf-kr.edu.pl

The venue of the workshop is the main building of the Faculty of Mathematics and Computer Sciences, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków. Previous and related activities: Minicourses:
  • Sergey Bobkov (Minneapolis): A second order concentration of measure on the sphere, and its application to randomized central limit theorems.
  • Abstract: There will be discussed deviation inequalities for smooth functions on the sphere with improved rates relying upon the second partial derivatives (Hessians). Such results are illustrated in the problem of rates of normal approximation for weighted sums of dependent random variables under proper second order correlation-type conditions.
  • Persi Diaconis (Stanford): THE MATHEMATICS OF SHUFFLING CARDS.
    • Lecture 1 Introduction. These lectures will prove theorems about real world methods of shuffling cards (e.g., it takes about 7 riffle shuffles to mix up 52 cards). The first lecture sets up the problem and proves the 7 shuffles theorem.
    • Lecture 2 Adding numbers. When numbers are added in the usual way, carries occur along the way. It turns out that the carries form a Markov chain with an "amazing" transition matrix. Strange to say, these problems are closely related to the mathematics of riffle shuffling.
    • Lecture 3 Hyperplane walks. There is an elegant family of random walks on the chambers of a hyperplane arrangement. This includes various shuffling schemes. All these walks are explicitly diagonalizable and have "closed form" stationary distributions.
    • Lecture 4 shuffling cards and Hopf algebras. Hopf algebras are algebraic "gadgets" used by topologists. In many examples, the "Hopf square map" has a simple probabilistic interpretation. The free associative algebra leads to riffle shuffles, symmetric functions leads to a rock breaking model of Kolmogorov. The hard work done by combinatorialists and others gives explicit forms of the eigenvectors.
    • Lecture 5 Overhand shuffling. This commonly used method of mixing needs different sets of tools for analysis, coupling, and comparison theory will be introduced and do a pretty good job.
    • Lecture 6 Smooshing. The "wash of smoosh" shuffle is widely used in poker tournaments and in Monte Carlo. It involves sliding the cards around on the table to mix them. I will introduce a fluid mechanics model to study this and a novel coupling technique to get quantitative results.


Participants: Dominique Bakry (Toulouse), Sergey Bobkov (Minneapolis), Dariusz Buraczewski (Wroclaw), Persi Diaconis (Stanford), Jose Carillo (London), Jose A. Canizo (Granada), Klaudiusz Czudek (Gdansk), Xu Lihu (Macau), Piotr Markowski (Gdansk), Laurent Miclo (Toulouse), Miroslav Strupl (Prague), Tomasz Szarek (Gdansk), Robert Wolstenholme (Prague), Frantisek Zak (Prague).