Mini-courses:

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Daniel Ahlberg​​

Title: Competing growth with reinforcement​

Abstract: In this series of lectures we will study competition between growing entities with a reinforcement effect. More precisely, we shall consider competing growth on an underlying discrete structure that can be described in terms of interacting Polya urns, or as a multi-type branching random walk (BRW) where particles of different type annihilate upon contact. A continuous space version of this process can be described as annihilating branching Brownian motion (ABBM). We shall foremost be concerned with the possible coexistence between two or more types, and investigate how this depends on the underlying graph on which they evolve. Along the way we shall describe some key techniques involving martingales and couplings, as well as several open problems and conjectures.

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Igor Kortchemski: 

Title: Limits of random trees

Abstract: We will sketch a landscape of scaling limits and local limits of random Bienaymé-Galton-Watson trees.

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Cécile Mailler

Title: Pólya urns

Abstract:  In the first part of the course, we will review classical results on Pólya urns, from Markov’s results on the standard urn (1906), to Janson’s results on “irreducible” urns (2004). In the second part, we will focus on more recent developments of the theory, and in particular the generalisation to infinitely-many colours.

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Contributed talks:

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Gabriel Hernán Berzunza Ojeda​: TBA

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Sam Olesker-Taylor: TBA

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Gesine Reinert: TBA

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Minmin Wang: TBA

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