North Meets South

Continuous and discrete (finite element) de Rham complexes have inspired key progress in the mathematical and numerical analysis of the Maxwell equations. In this talk, we derive new differential complexes from the de Rham complexes. These complexes have applications in, e.g., general relativity and continuum mechanics. Examples include the elasticity (Kröner or Calabi) complex, which encodes fundamental structures in Riemannian geometry and elasticity. This homological algebraic construction is inspired by the Bernstein-​Gelfand-Gelfand (BGG) machinery from representation theory. Analytic results, e.g., various generalisations of the Korn inequality, follow from the algebraic structures. We briefly discuss applications in numerical PDEs and other fields.

Davide Spriano

Title: Growth of groups.

Abstract:
Given a transitive graph, it is natural to consider how many vertices are contained in a ball of radius n, and to study how this quantity changes as n increases. We call such a function the growth of the graph.

In this talk, we will see some examples of growth of Cayley graph of groups, and survey some classical results. Then we will see a dichotomy in the growth behaviour of groups acting on CAT(0) cube complexes.