CNRS-PAN Mathematics Summer Institute, Cracow 26 June
- 4 July, 2014
In collaboration with the Faculty of Applied Mathematics,
AGH University of Science and Technology, Institute of
Mathematics, Jagiellonian University, Institute of
Mathematics, Polish Academy of Sciences, CNRS, Imperial College
London, IMP Université Paul Sabatier Toulouse, and
ANR project STAB.
Organized by: Dominique Bakry (Toulouse), Szymon Peszat
(Cracow), and Bogusław Zegarliński (London).
The meeting will review recent results in the area of discrete and
continuous probability/stochastics intertwined with related
problems and methods of mathematical analysis. Besides a number of
presentation by international participants, the meeting will
include one 6 hrs mini-course (suitable for PhD students and
young researchers).
The venue is the Institute of Mathematics, Polish Academy of Sciences,
Św. Tomasza 30/7.
Previous and related
activities:
Minicourse:
- Thierry Lévy
(Paris) Connections in physics: an introduction to the
stochastic quantisation
of gauge theories
Abstract:
The best available physical models of the world at the subatomic scale
are gauge theories : theories in which part of the physical substance
(the electromagnetic potential, for instance) is modelled by a
connection on a principal bundle. On the mathematical side, gauge
theories provide deep insights into low-dimensional geometry and
topology, and are a rich source of intuition (for a handful of
privileged people, at least) and of fascinating hard problems (for the
rest of us).
The goal of these lectures is to outline a path which connects classical
nineteenth century physics to something of the formidable edifice of
quantum field theory, and more specifically of the formulation in terms
of functional integrals of gauge theories. We will try to understand how
physicists, who once were solving the Maxwell equations, ended up
integrating functionals of geometric nature over the infinite
dimensional space of connections over space-time. We will then discuss
some of the mathematical issues and perspectives which arise from the
consideration of these functional integrals.
List of participants:
- D. Bakry (Toulouse)
- D. Chafaï (Paris)
- C. Delan (Toulouse)
- T. Lévy (Paris)
- S. Li (Toulouse)
- E. Marciniak (Cracow)
- M. Ottobre (London)
- S. Peszat (Cracow)
- M. Pitera (Cracow)
- P. Przybyłowicz (Cracow)
- M. Riedle (London)
- P. Rola (Cracow)
- D. Stroock (Cambridge, USA)
- A. Sulima (Cracow)
- D. Tarłowski (Cracow)
- J. Trybuła (Cracow)
- D. Zawisza (Cracow)
- B. Zegarliński (London)
For more information contact S. Peszat, e-mail
napeszat[AT]cyf-kr.edu.pl
Tentative Program:
Wednesday 25 June Arrival day
Thursday 26 June
- 10.00 - 11.30 Registration
- 11.30 - 11.50 T&C
- 11.50 - 12.30 D. Zawisza:
Monotone mean-variance preferences in continuous time stochastic factor
model
- 14.30 - 16.30 T. Lévy:
(Mini-course)
- 16.30 - 16.50 T&C
- 16.50 - 18.00 B. Zegarliński:
Analysis of reaction diffusion systems via log-Sobolev inequalities
Friday 27 June
- 10.00 - 11.30 S. Peszat:
Smoothening effects of transition semigroups
- 11.30 - 11.50 T&C
- 11.50 - 12.50 D. Stroock:
Gauss applied to Banach
Saturday 28 June
Sunday 29 June
Monaday 30 June
- 10.00 - 11.30 D. Bakry:
About hypergroup property
- 11.30 - 11.50 T&C
- 11.50 - 12.20 P. Rolla:
Arbitrage in markets with bid-ask spreads
- 14.30 - 16.30 T. Lévy:
(Mini-course)
- 16.30 - 16.50 T&C
- 16.50 - 17.20 D. Tarłowski:
Nonautonomous dynamical systems in stochastic global
optimization
Tuesday 1 July
- 10.00 - 11.30 D. Chafaï:
Random walks on regular graphs and the semicircle law
- 11.30 - 11.50 T&C
- 11.50 - 12.30 M. Pitera:
On time consistency for dynamic utility measures
- 15.00 - 16.30 M. Ottobre:
Diffusion limits for Random Walk Metropolis algorithm
- 16.30 - 16.50 T&C
- 16.50 - 17.20 E. Marciniak:
On optimal dividend problem for an
insurance risk models with surplus-dependent premiums
- 18.30 - 20.30
History of Science Evening, Aula Jagiellońska, Collegium Maius,
D. Stroock: "Mark Kac, a Simple Pole in Ithaca New York".
Wednesday 2 July
- 10.00 - 12.00 T. Lévy:
(Mini-course)
- 14.30 - 16.00 M. Riedle:
Cylindrical Lévy processes
- 19.00 - Conference Dinner
Thursday 3 July
- 10.00 - 11.00: Discussion groups
- 11.00 - 11.30 T&C
- 11.30 - 12.30: Discussion groups
- 15.00 - 17.30 Discussion Groups
- 17.30 - 18.00 T&C
Friday 4 July
- 10.00 - 11.00 Discussion groups
- 11.00 - 11.50 T&C
- 11.50 - 12.30 Discussion groups
- 14.30 - 16.30 Discussion Groups
- 16.30 - 16.50 T&C
