# Seminars & Events for PACM/Applied Mathematics Colloquium

##### Lipschitz extension from finite subsets

Suppose that X is a metric space and that x_1,...,x_n are n points in X. Every 1-Lipschitz function from {x_1,...,x_n} to a normed space Z can be extended to a Z-valued function that is defined on all of X and has Lipschitz constant that is bounded from above by a quantity that depends only on n. It is a longstanding question to determine the best possible asymptotic dependence on n here. This talk will start by explaining the long line of works on this question starting from the early 1980s, involving a variety of analytic, probabilistic, combinatorial and geometric techniques, followed by a description of recent progress.

##### Tensors and their Eigenvectors

Eigenvectors of square matrices are central to linear algebra. Eigenvectors of tensors are a natural generalisation. The spectral theory of tensors was pioneered by Lim and Qi around 2005. It has numerous applications, and ties in closely with optimization and dynamical systems. We present an introduction that emphasises algebraic and geometric aspects.