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.

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 Cyril Imbert Grzegorz Karch Tadeusz Kulczycki Regis Monneau

(The list was updated: )

1. Nathaël Alibaud
2. Boris Andreianov
   
   • Renormalized solutions of fractional Laplace equation. Abstract
3. Rodrigo Bañuelos
4. Lucian Beznea
5. Piotr Biler
6. Adrien Blanchet
7. Krzysztof Bogdan
8. Tomasz Byczkowski
9. Simone Cifani
10. Adina Giorgiana Ciomaga
11. Chi Hin Chan
12. Ewa Damek
13. Bartłomiej Dyda
14. Jean Dolbeault
    
    • Mean-field attractive models: existence of stationary states and time-periodic solutions, orbital stability and symmetry issues. Abstract
15. Jérôme Droniou
16. Adriana Garroni
17. Ivan Gentil
    
    • Hypercontractive bounds for no-diffusive operators Abstract
18. Jan Goncerzewicz
19. Cyril Imbert
20. Niels Jacob
21. Espen R. Jakobsen
    • Monotone numerical schemes for nonlocal HJB equations arising in control of Levy-diffusions. Abstract
22. Tomasz Jakubowski
23. Aldéric Joulin
24. Benjamin Jourdain
25. Kamil Kaleta
26. Grzegorz Karch
27. Moritz Kassmann
28. Vassili Kolokoltsov
29. Tomasz Komorowski
30. Victoria P. Knopova
31. Tadeusz Kulczycki
32. Mateusz Kwaśnicki
33. József Lörinczi
34. Mauro Mariani
35. Ante Mimica
36. Regis Monneau
    • Nonlocal dislocation dynamics: from microscopic models to macroscopic crystal plasticity. Abstract
37. María del Mar González Nogueras
38. Rémi Rhodes
39. Jean-Michel Roquejoffre
40. Michał Ryznar
41. Hilde Sande
42. René Schilling
43. Yannick Sire
    • Some topics involving fractional powers of elliptic operators Abstract
44. Luis Silvestre
45. Russel Schwab
46. Bartłomiej Siudeja
47. Paweł Sztonyk
48. Raphaël Roux
    
    • Convergence of an Euler scheme for a fractionnal scalar conservation law Abstract
49. Milton David Jara Valenzuela
    • Scaling limits of particle systems with long jumps
50. Juan Luis Vázquez Suárez
51. Zoran Vondraček
52. Bogusław Zegarliński

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