Department of Applied Mathematics and Theoretical Physics, Cambridge University

Tue 14 Apr 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Fast computation of the semiclassical Schrodinger equation

ESB 4133 (PIMS Lounge)
Tue 14 Apr 2015, 12:30pm2:00pm
Abstract
The computation of the semiclassical Schrödinger equation presents a number of difficult challenges because of the presence of high oscillation and the need to respect unitarity. Typical strategy involves a spectral method in space and Strang's splitting in time, but it is of low accuracy and sensitive to high oscillation. In this talk we sketch an alternative strategy, based on highorder symmetric Zassenhaus splittings, combined with spectral collocation, which preserve unitarity and whose accuracy is immune to high oscillation. These splittings, whose analysis requires Liealgebraic techniques, can be implemented with large time steps and allow for an exceedingly affordable computation of underlying exponentials. The talk will be illustrated by the computation of different quantum phenomena.
hide

UBC

Tue 14 Apr 2015, 1:00pm
Graduate Student Seminar
MATH 126

What is...Machine Learning?

MATH 126
Tue 14 Apr 2015, 1:00pm2:00pm
Abstract
In this gentle introduction to machine learning I will give an overview of the most popular algorithms for supervised and unsupervised learning. You will see that machine learning can be surprisingly simple, yet powerful, while always being mathematically appealing. I will finish by walking us through two example applications using Python's scikitlearn library.
hide

University of Toronto

Fri 17 Apr 2015, 3:00pm
Department Colloquium
MATX 1100

Rational Points on Elliptic Curves

MATX 1100
Fri 17 Apr 2015, 3:00pm4:30pm
Abstract
The classical problem of Diophantine equations is to solve polynomial equations over the rationals. More generally, we may consider solutions over an extension of the rationals. If the equations define an elliptic curve (or more generally, an Abelian variety), there is more structure. In particular, the set of rational points forms a group which is finitely generated. What happens if we consider the same problem over an infinite extension (or equivalently, over an infinite tower of extensions)? The problem becomes very subtle and is the subject of current research. We shall describe some of the recent results in this area.
hide

Seminar Information Pages

Note for Attendees
Lunch will be provided.