The mathematics and mechanics of bodies described by implicit constitutive equations Abstract. After first discussing the need for implicit constitutive relations to describe the response of both solids and fluids, I will then discuss applications wherein such implicit constitutive relations … Read more
N-spherical functors and categorification of Euler’s continuants Abstract. Euler’s continuants are universal polynomials expressing the numerator and denominator of a finite continued fraction in terms of its entries. Remarkably, they make an appearance in the very foundations of category theory: … Read more
Harmonic coordinates and asymptotic decay conditions Abstract. In General Relativity, an "isolated system at a given instant of time "is modeled as an asymptotically Euclidean (AE) initial data set (M,g,K) where (M,g) is a Riemannian manifold, K is a symmetric … Read more
Limited space available so sign up now! https://forms.gle/r2WrLTYZTszRQfLZ8 Given the success of the faculty lightning talks in January, the faculty will repeat this, but we are also creating an event for you the graduate students to develop and practice your “elevator pitch” … Read more
Integrable lattice models and symmetric functions, part 1 Abstract: I will talk about how integrable lattice models from statistical mechanics unexpectedly became about the most powerful tool to study symmetric functions from representation theory and combinatorics of affine flag varieties. The talk … Read more
One-dimensional hydrogenic ions with screened nuclear Coulomb field Abstract. We study the spectrum of the Dirac Hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus … Read more
Scientific Machine Learning for Computational Wave Imaging Problems: from Carbon Zero Emissions to Breast Cancer Detection Abstract. AI for Science (aka “AI4Science”) is currently one of the most prominent topics in the machine learning community. In this talk, I will focus … Read more
Physically Inspired Mathematics Seminar Website
Higher codimension area-minimizers: structure of singularities and uniqueness of tangent cones Abstract. The problem of determining the size and structure of the interior singular set of area-minimizing surfaces has been studied thoroughly in a number of different frameworks, with many … Read more
Asymptotic Preserving Numerical Methods for Multiscale Problems Abstract. Many phenomena in nature exhibit multiscale behaviors, which can be rather different in character. These phenomena can be categorized into two groups. On the one hand, there are problems featuring localized singularities, … Read more
Integrable lattice models and symmetric functions: Part 2 Physically Inspired Mathematics Seminar Website
Homogenization of the Einstein equations under symmetry Abstract. Due to their nonlinear nature, the Einstein's equations are not closed under weak convergence. Compactness singulaties associated to highly oscillatory solutions may be identified with additional, non-trivial matter. In 1989, Burnett conjectured … Read more
