Past Events

We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation Δu+b(α)⋅∇u=f in a bounded domain Ω⊂ℝ2containing the origin, where f∈W−1q(Ω) with q>2 and b(α):=b−αx|x|2 , b is a divergence...

Adinkras are decorated graphs that encapsulate information about conjectural relationships between fundamental particles in physics. If we color the edges of an Adinkra with a rainbow of shades in a specific order, we obtain a special curve that we...

Let B be a normed space and let A be a subspace. When does a continuous linear functional on A admit a unique norm-preserving extension to B? If A and B are C*-algebras and the functional is a so-called pure state, this question was at the heart of a...

Arithmetic Statistics is an emerging subbranch of Number Theory where we count arithmetic objects when bounded by some quantitative invariant, like height. One example is counting polynomials with integer coefficients having a fixed Galois group...

Eternal domination is a graph game where mobile guards are placed on vertices and then moved in order to defend against sequences of attacks. If only one guard is allowed to move in response to an attack, then it has been shown that there is no...

A symplectic Hamiltonian manifold consists of a Lie group action on a symplectic manifold, together with the additional structure of a moment map, which encodes the group action in terms of the assignment of Hamiltonian vector fields. In special...

We give conditions on a real-valued function F on ℤd, for d>2, which ensure that the solution G to the convolution equation (F∗G)(x)=δ0,x has Gaussian decay |x|−(d−2) for large |x|. Precursors of our results were obtained by Hara in the 2000s, using...

So far, we learned that a deformation problem is controlled by a DG Lie algebra, and that solutions to the deformation problem correspond to Maurer-Cartan (MC) elements. However, different MC elements may yield equivalent deformations! The DG Lie...

The questions of how healthy colonic crypts maintain their size under the rapid cell turnover in intestinal epithelium, and how homeostasis is disrupted by driver mutations, are central to understanding colorectal tumorigenesis. We propose a three...

Michael Drazin introduced the idea of a “pseudoinverse” for rings and semigroups in 1961. These inverses categorically are rather special as (like ordinary inverses) they are preserved by all functors when they exist. A category is Drazin when all...