The conference

Nonlocal operators and partial differential equations

will begin on Sunday, June 27, 2010 (this is the day of arrivals). Lectures will start on Monday, morning.

Friday, July 2, 2010, is the last day of the conference. Lectures will finish by lunch or later. Saturday is the day of departures.

• Complete and updated program of the conference.
• PRESENTATIONS !!!

The conference place: Mathematical Research and Conference Center in Bedlewo, Poland.
We expect all participants to arrive to POZNAN. We shall help you in your trip from Poznan to the conference center in Bedlewo.

Please, send any question concerning the conference either to Grzegorz.Karch@math.uni.wroc.pl or to any member of the organizing committee.

There is a number of physical phenomena for which the Lévy processes and, in particular, a-stable processes can be used as a reasonable model. Examples of such non-Gaussian processes coming from fluid mechanics, solid state physics, fluid mechanics, polymer chemistry, biology, mathematical finance, etc. motivated several scientists to study linear and nonlinear initial-boundary value problems containing so-called Lévy operators. These integro-differential operators are the infinitesimal generators of a Lévy process (sometimes also called as an anomalous diffusion). Notice that the fractional Laplacian is a particular example of the Lévy operator.

The goal of the conference is to gather specialists working in two different fields — stochastic processes and nonlinear partial differential equations — in order to exchange experiences, ideas, and methods used in the study of models involving nonlocal operators motivated by Lévy processes and long range dependence phenomena. Moreover, recognized experts will be invited to give expository plenary talks accessible for PhD students and young researchers.

More detailed topics of the conference are given below:

• Boundary value problems for Lévy processes
• Spectral theory for nonlocal operators
• Fokker-Planck equations with anomalous diffusions
• Kinetic equations and anomalous diffusion limit
• Evolution equations with Lévy operators: fractal conservation laws (with the fractional Laplacian), nonlocal models for chemotaxis, the quasigeostrophic equation, ect.
• Nonlocal operators in dislocation dynamics
• Boltzmann equation versus the fractional diffusion equation

Scientific committee Piotr Biler Krzysztof Bogdan Tomasz Byczkowski Jean Dolbeault Cyril Imbert Grzegorz Karch Tadeusz Kulczycki Regis Monneau Wojbor A. Woyczynski

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Organizing committee Piotr Biler Krzysztof Bogdan Rafał Celiński Cyril Imbert Grzegorz Karch Tadeusz Kulczycki Regis Monneau Dominika Pilarczyk Andrzej Raczyński Robert Stańczy

(The list was updated: )

1. Franz Achleitner
   
   • On nonlinear conservation laws with a nonlocal diffusion term Abstract
2. Nathaël Alibaud
   • Recent results on large time asymptotic behavior for the fractal Burgers equation Abstract
3. Boris Andreianov
   
   • Renormalized solutions of fractional Laplace equation. Abstract
4. Rodrigo Bañuelos
   • Rearrangement inequalities for Lévy processes in domains; some results, some problems Abstract
5. Lucian Beznea
   • Nonlinear PDE and measure-valued branching processes. Abstract
6. Piotr Biler
   • A fractal porous medium equation Abstract
7. Adrien Blanchet
   • The critical mass Keller-Segel model Abstract
8. Krzysztof Bogdan
   • Nonlocal boundary value problems Abstract
9. Matthieu Brassart
10. Yana A. Butko
    • Hamiltonian and Lagrangian Feynman formulae for Feller semigroups Abstract
11. Tomasz Byczkowski
12. Rafał Celiński
13. Magdalena Czubak
    • Regularity of the critical and supercritical Burgers equation Abstract
14. Adina Giorgiana Ciomaga
    • On the Strong Maximum Principle for Second Order Nonlinear Integro-Differential Equations Abstract
15. Chi Hin Chan
    • Regularity theory for nonlinear integral operators Abstract
16. Bartłomiej Dyda
    • On fractional Hardy inequality Abstract
17. Jean Dolbeault
    
    • Mean-field attractive models: existence of stationary states and time-periodic solutions, orbital stability and symmetry issues. Abstract
18. Ivan Gentil
    
    • Hypercontractive bounds for no-diffusive operators Abstract
19. Jan Goncerzewicz
20. Cyril Imbert
    • Existence of solutions for a non-local higher order equation Abstract
21. Espen R. Jakobsen
    • Entropy solution theory for fractional degenerate convection-diffusion equations Abstract
22. Tomasz Jakubowski
    • Green function of fractional Laplacian perturbed by gradient operators Abstract
23. Aldéric Joulin
    • Commutation relations for birth-death processes Abstract
24. Kamil Kaleta
    • Intrinsic ultracontractivity for fractional Schroedinger operators Abstract
25. Grzegorz Karch
26. Moritz Kassmann
    • Regularity questions for nonlocal Dirichlet forms Abstract
27. Vasilis Kontis
28. Victoria P. Knopova
    • Transition density estimates for Lévy processes and some Lévy functionals Abstract
29. Tadeusz Kulczycki
    • Spectral theory for square root of Laplacian Abstract
30. Mateusz Kwaśnicki
    • Spectral theory for fractional Laplacian in half-line Abstract
31. Erik Lindgren
    • On a non-local and non-linear operator of infinite Laplacian-type Abstract
32. József Lörinczi
    • Fractional Schroedinger Operators for Kato-Class Potentials Abstract
33. Jacek Małecki
34. Mauro Mariani
    • Entropy and Einstein relation for fractional conservation laws. A variational approach. Abstract
35. Ante Mimica
    • Heat kernel estimates for a subordinate Brownian motion Abstract
36. Regis Monneau
    • Nonlocal dislocation dynamics: from microscopic models to macroscopic crystal plasticity. Abstract
37. María del Mar González Nogueras
    • Some geometrical problems for the conformal fractional Laplacian. Abstract
38. Łukasz Paszkowski
39. Dominika Pilarczyk
40. Andrzej Raczyński
41. Rémi Rhodes
    • Log-infinitely divisible random measures and related issues Abstract
42. Samira Rihani
43. Raphaël Roux
    
    • Convergence of an Euler scheme for a fractionnal scalar conservation law Abstract
44. Michał Ryznar
45. Hilde Sande
46. René Schilling
    • Transition probability densities of Lévy processes Abstract
47. Yannick Sire
    • Some topics involving fractional powers of elliptic operators Abstract
48. Luis Silvestre
    • Smooth solutions for the Hamilton-Jacobi equation with critical fractional diffusion Abstract
49. Russel Schwab
50. Bartłomiej Siudeja
    • Tight frames, Fourier multipliers and eigenvalue estimates. (joint work with Richard Laugesen) Abstract
51. Robert Stańczy
52. Kanako Suzuki
    • Spikes and diffusion waves in one-dimensional model of chemotaxis Abstract
53. Paweł Sztonyk
    • Asymptotics of transition densities of jump processes Abstract
54. Zoran Vondraček
    • Nonlocal operators and subordination Abstract
55. Bogusław Zegarliński
    • Ergodicity for nonlocal dissipative dynamics in infinite dimensions Abstract
56. Jacek Zienkiewicz

• Banach Center - Institute of Mathematics of the Polish Academy of Sciences
• Instytut Matematyczny, Uniwersytet Wrocławski
• Université Paris-Est