Past Events

We use properties of modular forms to extend the Ramanujan-Mordell formula. Our result yields to formulas for representation numbers by the quadratic form ∑2ai=1x2i+∑2bi=1py2i, for all non-negative integers a,b and for all odd prime p. We obtain this...

Suppose two populations with different genetic types live close to each other and can interbreed, but hybrid offspring have a lower evolutionary fitness. The interface between such populations is known as a hybrid zone. We can model this situation...

We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled via an interaction potential. We set up the model...

ABSTRACT: Optimization and optimal dynamical control are used to investigate the accuracy of analytical estimates for solutions of some basic nonlinear partial differential equations of mathematical hydrodynamics. Even though many mathematical...

When you send your credit card number over the Internet, cryptography helps to ensure that no one can steal the number in transit. Julius Caesar and Mary Queen of Scots used cryptography to send secret messages, in the latter case with ill-fated...

The Wasserstein space, which is the space of probability measures endowed with the so-called (quadratic) Wasserstein distance coming from optimal transport, can formally be seen as a Riemannian manifold of infinite dimension. We propose, through a...

Consider a system of N particles moving according to Brownian motions and branching at rate one. Each time a particle branches, the particle in the system furthest from the origin is killed. It turns out that we can use results about a related...

A coupled PDE-ODE model used to describe communication between dynamically active signaling compartments (biological cells) is analyzed using strong localized perturbation theory. In the limit D >> 1, the coupled model is reduced into a nonlinear...

Take n objects and put them in a container. What is the configuration space of all the ways they can fit in the container without intersecting? How does the topology of that configuration space change depending on the size of the objects and the size...

In 1993, Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank 1 boolean intervals whose minimal faces together form a subcomplex. Stanley further conjectured that complexes...