Il Prof. Yuri Kondratiev [Fakultät für Mathematik Universität Bielefeld ]
sarà ospite del Dipartimento di Informatica dell’Università di Verona [
Strada le Grazie, 15 - Vr ] nei giorni dal 27 al 31 Ottobre 2014 e terrà il
seguente mini corso [8 ore]
Statistical dynamics for interaction particle systems
articolato in tre lezioni, che si terranno nell'edificio Ca' Vignal 2 -
Aula M, nei giorni
- Lunedì 27 Ottobre [ 13:30-16:30 ]
- Mercoledì 29 Ottobre [ 15:30-18:30 ]
- Giovedì 30 Ottobre [ 13:30-15:30 ]
con il seguente programma
*Abstract*
We will discuss an approach to modeling of real world phenomena by
interacting particle systems in the continuum. In many cases, evolutions of
considered systems may be described as Markov stochastic processes. Related
statistical dynamics are evolutions of macroscopic states associated with
the forward Kolmogorov (or Fokker-Planck) equations for these Markov
processes. We will study statistical dynamics in terms of corresponding
hierarchical chains of evolution equations for correlation functions. These
chains admit mesoscopic scalings that leads to kinetic evolution equations
for densities of considered systems. Particular examples which will be
discussed include *models from mathematical physics, ecology, cell biology
and socio-economic models*. Between other aspects these examples illustrate
such notions as dynamical phase transitions, non-local evolution equations,
front propagation, self-aggregation, effects of environment fluctuations
etc.
*Tentative program*
1. Configuration spaces
2.
Harmonic analysis on configuration spaces
3.
Statistical Markov evolutions and hierarchical chains
4.
Birth-and-death Markov processes on configuration spaces
5.
Conservative stochastic dynamics
6.
Mesoscopic scalings and kinetic equations
7.
Multicomponent systems
8.
Applications
(a) Mathematical physics
(b) Ecological models
(c) Cancer modeling
(d) Social models
Per informazioni contattare: luca.dipersio(a)univr.it
__
Luca Di Persio - PhD
assistant professor of
Probability and Mathematical Finance
Dept. Informatics University of Verona
strada le Grazie 15 - 37134 Verona - Italy
Tel : +39 045 802 7968
Dept. Math University of Trento
V. Sommarive, 14 - 38123 Povo - Italy
Tel : +39 0461 281686