Simon Fraser University

Abstract We will survey results on, and techniques for, the generalized Fermat equation x^p + y^q = z^r, where p, q, and r satisfy 1/p + 1/q + 1/r 1. This is joint work with Imin Chen, Sander Dahmen, and Soroosh Yazdani.

AbstractPart of the Langlands Program is to find a meaningful correspondence between representations of Galois groups and representations of reductive algebraic groups. I will attempt to motivate this through an example and then concentrate on what...

Abstract: The classical Martin boundary is concerned with harmonic functions: the non-negative solutions of Laplace's equation 1/2\Delta u=0 in a given domain D of R^n. Harmonic functions are extensively studied and well understood. A culminating...

The purpose of this seminar is to serve as a venue where students can get an opportunity to show their work to their fellow students and acquire or practice the necessary presentation skills that will be required in their tie1d of work, as well as...

Abstract: When solving convection dominated partial differential equations, such as the incompressible and compressible Euler equations in fluid dynamics, it is a challenge to design numerical schemes which are both strongly stable and high order...

Abstract: Self assembly is the idea of creating a system whose component parts spontaneously assemble into a structure of interest. In biological systems, there are striking examples where complicated structures (ie the bacterial ribosome) can...

There is a marked difference in the weather patterns and climate between the Earth's equatorial and midlatitude regions. Much of this difference is due to the active role of moisture and convection in the tropics. However, the even the dry fluid...

AbstractIn modern language, Fermat's Descent Infini establishes that an elliptic curve has a Mordell-Weil group of rank 0. Since then, the method has been generalized to provide an upper bound on the rank of any elliptic curve and further work also...

Abstract. In recent past we were interested to study some special composition of polynomial equation f(g(x)) = f(x)hm(x) where f, g and h are unknown polynomials with coefficients in arbitrary field K, f is non-constant and separable, deg g ! 2, g! "...

AbstractMany arithmetic geometric results have an arithmetic dynamic analogue. For instance, Siegel's theorem that an elliptic curve has only finitely many integer points is analogous to the fact that any orbit under a rational function whose second...