HT17 Distinguished Speaker Seminars
HILARY TERM 2017
Week 1: Friday 20th January, 3.30 p.m.
Speaker: Professor Wendelin Werner, ETH Zürich, Switzerland
Title: Random cracks in space.
Abstract: We will describe in non-technical terms some old and new ideas about what basic natural random objects and fields one can define in a given space with some geometric structure, and what one can do with them. This will probably include various joint recent and ongoing work with Jason Miller, Scott Sheffield, Qian Wei and Titus Lupu.
Week 2: Friday 27th January, 3.30 pm
Speaker: Professor Jean-Philippe Vert, Mines ParisTech, France
Title: Machine learning for patient stratification from genomic data
Abstract: As the cost and throughput of genomic technologies reach a point where DNA sequencing is close to becoming a routine exam at the clinics, there is a lot of hope that treatments of diseases like cancer can dramatically improve by a digital revolution in medicine, where smart algorithms analyze « big medical data » to help doctors take the best decisions for each patient. The application of machine learning-based techniques to genomic data raises however numerous computational and mathematical challenges that I will illustrate on a few examples of cancer patient stratification from gene expression or somatic mutation profiles.
Week 8: Friday 10th March, 3.30 p.m.
Speaker: Professor Martin Hairer, University of Warwick
Title: A BPHZ theorem for stochastic PDEs
Abstract: A classical result obtained in the 50's and 60's by Bogoliubov, Parasiuk, Hepp and Zimmerman provides a prescription on how to renormalise amplitudes of Feynman diagrams arising in perturbative quantum field theory in a consistent way. We will discuss an analogue of this theorem which has both an analytic and a probabilistic interpretation. In particular, we will see that it implies that the solutions to a large class of nonlinear stochastic PDEs depend on their driving noise in a surprisingly rigid way. This rigidity is a mathematical manifestation of the "universality" taken for granted when building our intuition on the large-scale behaviour of probabilistic models.