Department of Mathematics colloquium - Sibe Mardešić presents a sequence of lectures given by leading experts in the fields of theoretical and applied mathematics. The lectures take place at the Department of Mathematics, Faculty of Science, Bijenička cesta 30, Zagreb.

### Lecture announcement

**Time:**October 2, 2024 at 12:15PM

**Lecture room:**A101

**About the lecturer**: Jean Bertoin is a leading expert in several branches of probability theory. His books Lévy processes (1996) and Random fragmentation and coagulation processes (2006) have been used worldwide as standard references and graduate textbooks. Professor Bertoin obtained doctorate from Université Pierre et Marie Curie (Paris VI) in 1987 under the supervision of Marc Yor. He received numerous awards for his work, including the Rollo Davidson Prize (awarded to early career probabilists) in 1996, an invited talk at the International Congress of Mathematicians in Beijing in 2002, and an invited address at the European Congress of Mathematics in Kraków in 2012. He is currently a professor at the University of Zurich, where he assumed the position about ten years ago. Professor Bertoin’s work has a major impact on both theoretical and applied probability. Math genealogy webpage currently lists 29 of his graduate students and 57 descendants.

**Lecture abstract**: After a brief introduction to the notion of reinforcement for stochastic processes, we will focus on branching processes, viewed as basic population models. In a classical Galton-Watson process individuals reproduce independently one from the others and according to a fixed reproduction law ν. The reinforced version depends on a memory parameter q∈(0,1). The number of children of a typical individual is then either, with probability q, the same as that of one of its forebears picked at random, or with complementary probability 1-q, given by an independent sample from ν. We estimate the average size of the population at a large generation. Our approach uses a remarkable non-linear differential equation and the analysis of singularities; it owes much to works by Flajolet and co-authors. The lecture is based on joint works with Bastien Mallein (Université Toulouse).