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The University of Arizona: Adhesion-driven patterning in collective cell behaviour

The University of Arizona Mathematics Building 617 N. Santa Rita Ave., Tucson

Cellular adhesion is a fundamental mechanism underlying diverse collective cell behaviours, from tissue self-organisation in developmental biology to the formation of directional queues that guide cell migration. Modelling such interactions has also proven mathematically rich, motivating the use of continuum partial differential equation models that capture adhesion through nonlocal interaction kernels. These models can, for...

The University of Arizona: Some birational models of M_{g,n} and related algebras

The University of Arizona Mathematics Building 617 N. Santa Rita Ave., Tucson

The moduli space M_{g,n} of algebraic curves of genus g with n marked points is one of the central objects in geometry. I will discuss examples of birational models of M_{g,n} and their compactifications. I will be interested in such models that arise as GIT-quotients for torus actions (i.e., as spaces of certain torus orbits)...