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 email@example.com
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:
CNRS-PAN Mathematics Summer Institute, Cracow 27 June - 2 July, 2016
CNRS-PAN Mathematics Summer Institute, Cracow 28 June - 4 July, 2015
CNRS-PAN Mathematics Summer Institute, Cracow 26 June - 4 July, 2014
CNRS-PAN Mathematics Summer Institute, Cracow 1 - 7 July, 2013
Workshop on Analysis and Stochastic Analysis, Cracow 11 - 15 July,
Workshop on Stochastic Analysis and Related Fields, Cracow 20 - 22 July,
Noncommutative Workshop, Cracow 9-12 September 2013
Noncommutative Workshop, Cracow 20-25 September 2015
- Sergey Bobkov (Minneapolis):
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), Persi Diaconis (Stanford), Jose Carillo (London),
Jose A. Canizo (Granada)