Colloquium: Dr. Jim Carlson

FOCUS on Math: Dr. Michael Dorff

FOCUS on Math: Dr. John Friedlander

Dr. John Friedlander, University of Toronto

 

"A Brief History of Primes"

 

Problems about prime numbers have long fascinated mathematicians, both professional and amateur. We will discuss some of the problems, old and new, that have been posed about these numbers, some of the methods that have been used to attack them, and some of the successes and failures along the way. We also touch on primality and the factorization of integers and their use in internet and banking security. The lecture is intended to be accessible to all students taking some undergraduate mathematics.

Colloquium: Dr. Vianey Villamizar

Date: Tuesday, October 5.

 

Title: Multiple Acoustic Scattering from Complexly Shaped Objects

 

Abstract: The classical exterior boundary value problem (BVP) for multiple acoustic scattering is reformulated as an equivalent interface problem. The interface B of the new problem is formed by separate artificial boundaries Bm enclosing the different obstacles. A rigorous proof of the equivalence between these two problems is given for smooth interfaces Bm of arbitrary shape. This equivalent BVP is numerically solved by coupling a Dirichlet-to-Neumann boundary condition on the interface B with a second order finite difference technique, which is supported by novel elliptic grids. This leads to a drastic reduction of storage and computational cost and greatly simplifies the grid generation process.

 

As a validation of the technique, a second order convergence of the approximate far-field pattern to the exact one for two circular cylindrical obstacles is easily obtained. Since inverse scattering problems are typically solved using iterative methods that require solution of direct problems, our results may have an impact on current techniques employed in identification of medical conditions in the human brain, in the detection of cancerous cells, and in radar imaging among many others.

Number Theory Seminar




We consider a variant of the Bombieri-Vinogradov theorem. Rather than  average over all moduli q in an interval, we average over q = f(k), where  f is a polynomial with integer coefficients.

Colloquium: Dr. Shaun Fallat

Dr. Shaun Fallat of the University of Regina will be the speaker at this fall’s second colloquium September 21.

 

A matrix is called totally positive (resp. totally nonnegative) if all of its minors are positive (resp. nonnegative). This important class of matrices grew out of three separate applications: Vibrating systems, interpolation and statistics.

Colloquium: Dr. Vadim Kaloshin

To Be or Not To Be a Math Major/Minor?