Monday 18th November, 8:30PM
High-dimensional data and the Lasso
Dr Rajen Shah (DPMMS) 

How would you try to solve a linear system of equations with more unknowns than equations? Of course, there are infinitely many solutions, and yet this is the sort of the problem statisticians face with many modern datasets, arising in genetics, imaging, finance and many other fields. What’s worse, our equations are often corrupted by noisy measurements! In this talk I will introduce a statistical method called the Lasso that has been at the centre of the huge amount of research that has gone into solving these problems.

We have been asked to share opportunities offered by Jump Trading, one of the TMS’ sponsors. Please find information attached in the pdf here. Jump Trading Quant Research Opportunities

Our final talk – yes, final talk! – of this year is given by Professor Eric Lauga. Details below, hope to see lots of you there!

Monday 4 March, 8:30PM
Elliptical billiards and Poncelet trajectories
Professor Pelham Wilson (DPMMS)
Given an elliptical billiard table, to any ball trajectory which doesn’t cross the line segment joining the two foci, there is an associated smaller confocal ellipse inscribed in the trajectory. A Poncelet trajectory is one which is closed after a finite number of bounces. We’ll see that if there is one such closed trajectory with n segments, then starting from every point on the outer ellipse, there is a similar closed trajectory with n segments and the same inscribed ellipse, and indeed all these trajectories have the same length
Analogous geometric properties hold more generally for any pair of conics in the plane, and in modern terminology the existence of analogous Poncelet polygons is related to the torsion points on an associated elliptic curve.