Simon Fraser University

In this talk I will discuss distribution results for traces of Frobenius for various families of elliptic curves with respect to the Lang--Trotter conjecture and extremal primes. These are related to the work of Sha--Shparlinski on the average Lang-...

It is well known that a line can intersect at most 2n-1 cells of the n x n chessboard. What happens in higher dimensions: how many cells of the d-dimensional [0,n]^d box can a hyperplane intersect? We also prove the integer analogue of the following...

The principle of ‘maximum entropy’ states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy with respect to a given prior (data) distribution. It was first formulated...

We present a kinetic version of the Watanabe-Strogatz (WS) transform for vector models in this paper. From the generalized WS-transform, we can reduce the kinetic vector model into an ODE system. We also obtain the cross-ratio type constant of motion...

A basic example of a family of curves with level structure is the Hesse pencil of elliptic curves: $$x^3+y^3+z^3+ \lambda xyz = 0,$$ which gives a family of elliptic curves with labelled 3-torsion points. The parameter $\lambda$ is a parameter on the...

Clemens–Griffiths introduced the classical intermediate Jacobian obstruction to rationality for complex threefolds, and used it to show irrationality of the cubic threefold. Recently, over non-closed fields, Hassett–Tschinkel and Benoist–Wittenberg...

Data-driven modeling refers to the use of measurement data to infer the parameters and structure of a mathematical model. Motivated by problems in collective cell biology, this talk will explore algorithms which automate the map from experimental...

Kinetic equations describe the nonequilibrium dynamics of a complex system using a probability density function. Despite of their important role in multiscale modeling to bridge microscopic and macroscopic scales, numerically solving kinetic...

Abstract: Metasurfaces are surfaces with microscopic objects on top, which can yield unexpected physical properties like, bending of light, relocating sound peaks, flat lenses, color printing, holograms and cloaking devices. In this talk we consider...

Abstract: Given a family G of graphs on a common vertex set X, we say that G is rainbow connected if for every vertex pair u, v ∈ X, there exists a path from u to v that uses at most one edge from each graph of G. We consider the case that G contains...