Past Events

A hybrid asymptotic-numerical approach is developed to study hotspot patterns for a three-component 1-D reaction-diffusion (RD) system that models urban crime with police intervention. Our analysis is focused on a scaling regime where there are two...

We discuss some recent work on the pinned distance problem in the plane using "effective dimension", a tool from algorithmic information theory. This work improves lower bounds on the dimension of pinned distance sets depending on the Hausdorff and...

The Hardy and Littlewood k-tuple prime conjecture is one of the most enduring unsolved problems in mathematics. In 1999, Gadiyar and Padma presented a heuristic derivation of the 2-tuples conjecture by employing the orthogonality principle of...

Particles with diameters of nanometres to micrometres form the building blocks of many of the materials around us, and can be designed in a multitude of ways to form new ones. Such particles commonly live in fluids, where they jiggle about randomly...

A basic question about an algebraic variety X is how similar it is to projective space. One measure of similarity is the minimum degree of a rational map from X to projective space, the "degree of irrationality". This number, not to mention the...

Let M=SL2(ℤ[i])∖ℍ(3) be the Bianchi orbifold, and let {fn}∞n=1⊂L2(M) be a sequence of Hecke--Maass forms on it. We should that the probability measures on M with densities |fn(x)|2 with respect to the Riemannian volume become equidistributed on M...

A Latin square is an n by n grid filled with n symbols so that each symbol appears exactly once in every row and column. A transversal in a Latin square is a selection of entries with no row, column, or symbol repetition. The study of transversals in...

We will discuss the link between Hochschild cohomology and deformations of an algebra A. We will see that the Hochschild cochains of A can be endowed with a differential graded (DG) Lie algebra structure. The Maurer-Cartan equation describes the...

Complex systems theory has taught us that simple, higher-level laws with few effective parameters can emerge from the interaction of small-scale components. As biology is becoming more and more quantitative, one can use a combination of first...

Let ℤ be the ring of integers, and let 𝔽p[t] be the ring of polynomials in one variable defined over the finite field 𝔽p of p elements. Since the characteristic of ℤ is 0, while that of 𝔽p[t] is the positive prime number p, it is a striking theme in...