Ho il piacere di invitarvi al seguente seminario che si terrà Mercoledì 15 ottobre, alle ore 16.00, nell'aula 2BC30. del Dipartimento di Matematica dell'Università degli Studi di Padova. Speaker: Prof. Jan Swart Affiliation: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic Title: Particle systems with cooperative branching Abstract: In a cooperative branching system, pairs of particles, rather than individuals, produce offspring. Interacting particle systems with this sort of interaction have been used to model the effect of sexual reproduction and in particular the effect that in many species, a low population density reduces the reproductive success of individuals due to the difficulty of finding a partner. In this talk, I will review some older work on this sort of models and also discuss recent joint work with Anja Sturm on a model with cooperative branching and coalesence. For such a model in one dimension, we show that for low cooperative branching rates, the process dies out at the same geometric rate as a pure coalescent. The proof uses ideas related to a general duality for monotone systems due to Lawrence Gray. -- Alessandra Bianchi Dip. di Matematica Pura e Applicata Università di Padova Via Trieste, 63 - 35121 Padova, Italy phone: +39 049 827 14 06 fax: +39 049 827 14 28 e-mail: bianchi@math.unipd.it http://www.math.unipd.it/~bianchi/