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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...

A number is called a "period" if it can be expressed as the volume of a region in Euclidean space, defined by polynomial inequalities with rational coefficients. Many famous constants, such as π, log(2) and special values of the Riemann zeta function...

We will discuss a class of ideals in a polynomial ring studied by Mark Haiman in his work on the Hilbert scheme of points and discuss how they are related to homology of affine Springer fibers, Khovanov-Rozansky homology of links, and to the ORS...

Abstract TBA

Let $K$ be an algebraic number field. The Primitive Element Theorem implies that the number field $K$ can be generated over the field of rational numbers by a single element of $K$. We call such an element a generator of $K$. A simple and natural...

The Laplacian matrix L of a signed graph G may or may not be invertible. We present an entrywise combinatorial formula for the Moore-Penrose inverse of L, obtained by deriving a combinatorial expression for the Moore-Penrose inverse of an incidence...

I shall start with reminders on congruences and p-adic numbers, then give Hasse's contribution to the local-global principle. I shall then mention counterexamples to the "Hasse principle" and then describe various ways which have been devised to...