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We have all been treated to the excitement of a good science story. Think Discovery Channel or National Geographic. The stories are really engaging! Well, the very same tools and techniques that make great science stories can be used to strengthen...

Phylogenetic trees are mathematical objects that encode information about ancestry relationships and are often used in the interpretation of genomic data. They have proved especially useful for advancing our understanding of pathogen populations that...

Bounded harmonic functions on groups (and their alter ego, the Poisson boundary)—bounded functions such that f(x) is the average of f(xa), where a is chosen from some probability measure—are objects of key importance in random walks, dynamics, and...

An F-decomposition of a graph G is a set of subgraphs of G, each isomorphic to F, whose edge sets partition the edge set of G. I will speak about a result showing that, for each odd k ≥ 5, any graph G of sufficiently large order n with minimum degree...

Isogenies between elliptic curves have attracted a lot of attention, and over finite fields the structures that they generate are fascinating. For supersingular primes, isogeny graphs are very connected. For ordinary primes, isogeny graphs have a lot...

Secure online communications and financial transactions depend on public key cryptography—but the methods we use today are susceptible to attack by quantum computers. When that will happen is uncertain, though estimates range from 5 to 25 years. This...

In this talk, we start by recalling the well-known problem of multivariate approximation by polynomials of total degree, concerning finding good points for interpolation. This allowed the discovery of the Padua Points, the first set of unisolvent and...

TBA

In this talk we see how representation theory can be used in numerical methods for partial differential equations (PDEs) and how numerics can give more efficient methods for computational problems in representation theory. In particular, we will see...

A deformation quantization of a manifold is a noncommutative deformation of its algebra of functions; the idea originated in physics, as a way of relating the classical and quantum descriptions of mechanical systems. At leading order in the...