Mon, 07 Nov 2016

14:15 - 15:15
L1

Probabilistic Numerical Computation: A New Concept?

MARK GIROLAMI
(University of Warwick)
Abstract

Ambitious mathematical models of highly complex natural phenomena are challenging to analyse, and more and more computationally expensive to evaluate. This is a particularly acute problem for many tasks of interest and numerical methods will tend to be slow, due to the complexity of the models, and potentially lead to sub-optimal solutions with high levels of uncertainty which needs to be accounted for and subsequently propagated in the statistical reasoning process. This talk will introduce our contributions to an emerging area of research defining a nexus of applied mathematics, statistical science and computer science, called "probabilistic numerics". The aim is to consider numerical problems from a statistical viewpoint, and as such provide numerical methods for which numerical error can be quantified and controlled in a probabilistic manner. This philosophy will be illustrated on problems ranging from predictive policing via crime modelling to computer vision, where probabilistic numerical methods provide a rich and essential quantification of the uncertainty associated with such models and their computation. 

Fri, 09 Jun 2017

16:00 - 17:00
L1

The cover of the December AMS Notices

Caroline Series
(University of Warwick)
Abstract

The cover of the December 2016 AMS Notices shows an eye-like region picked out by blue and red dots and surrounded by green rays. The picture, drawn by Yasushi Yamashita, illustrates Gaven Martin’s search for the smallest volume 3-dimensional hyperbolic orbifold. It represents a family of two generator groups of isometries of hyperbolic 3-space which was recently studied, for quite different reasons, by myself, Yamashita and Ser Peow Tan.

After explaining the coloured dots and their role in Martin’s search, we concentrate on the green rays. These are Keen-Series pleating rays which are used to locate spaces of discrete groups. The theory also suggests why groups represented by the red dots on the rays in the inner part of the eye display some interesting geometry.
 

Thu, 15 Dec 2016

17:00 - 18:00
L1

Oxford Mathematics Christmas Public Lecture: The Mathematics of Visual Illusions - Ian Stewart SOLD OUT

Ian Stewart
(University of Warwick)
Abstract

Puzzling things happen in human perception when ambiguous or incomplete information is presented to the eyes. Rivalry occurs when two different images, presented one to each eye, lead to alternating percepts, possibly of neither image separately. Illusions, or multistable figures, occur when a single image can be perceived in several ways. The Necker cube is the most famous example. Impossible objects arise when a single image has locally consistent but globally inconsistent geometry. Famous examples are the Penrose triangle and etchings by Maurits Escher.

In this lecture Ian Stewart will demonstrate how these phenomena provide clues about the workings of the visual system, with reference to recent research in the field which has modelled simplified, systematic methods by which the brain can make decisions. In these models a neural network is designed to interpret incoming sensory data in terms of previously learned patterns. Rivalry occurs when different interpretations are confused, and illusions arise when the same data have several interpretations.

The lecture will be non-technical and highly illustrated, with plenty of examples.

Please email @email to register

Mon, 01 Feb 2016

14:15 - 15:15
L5

Hölder regularity for a non-linear parabolic equation driven by space-time white noise

Hendrik Weber
(University of Warwick)
Abstract

We consider the non-linear equation $T^{-1} u+\partial_tu-\partial_x^2\pi(u)=\xi$

driven by space-time white noise $\xi$, which is uniformly parabolic because we assume that $\pi'$ is bounded away from zero and infinity. Under the further assumption of Lipschitz continuity of $\pi'$ we show that the stationary solution is - as for the linear case - almost surely Hölder continuous with exponent $\alpha$ for any $\alpha<\frac{1}{2}$ w. r. t. the parabolic metric. More precisely, we show that the corresponding local Hölder norm has stretched exponential moments.

On the stochastic side, we use a combination of martingale arguments to get second moment estimates with concentration of measure arguments to upgrade to Gaussian moments. On the deterministic side, we first perform a Campanato iteration based on the De Giorgi-Nash Theorem as well as finite and infinitesimal versions of the $H^{-1}$-contraction principle, which yields Gaussian moments for a weaker Hölder norm. In a second step this estimate is improved to the optimal

Hölder exponent at the expense of weakening the integrability to stretched exponential.

 

This is joint work with Felix Otto.

 

Mon, 18 Jan 2016

15:45 - 16:45
L5

"On the splitting phenomenon in the Sathe-Selberg theorem: universality of the Gamma factor

Yacine Barhoumi
(University of Warwick)
Abstract

We consider several classes of sequences of random variables whose Laplace transform presents the same type of \textit{splitting phenomenon} when suitably rescaled. Answering a question of Kowalski-Nikeghbali, we explain the apparition of a universal term, the \textit{Gamma factor}, by a common feature of each model, the existence of an auxiliary randomisation that reveals an independence structure.
The class of examples that belong to this framework includes random uniform permutations, random polynomials or random matrices with values in a finite field and the classical Sathe-Selberg theorems in probabilistic number theory. We moreover speculate on potential similarities in the Gaussian setting of the celebrated Keating and Snaith's moments conjecture. (Joint work with R. Chhaibi)
 

Thu, 28 Jan 2016

16:00 - 17:00
L5

Iwasawa theory for the symmetric square of a modular form

David Loeffler
(University of Warwick)
Abstract

Iwasawa theory is a powerful technique for relating the behaviour of arithmetic objects to the special values of L-functions. Iwasawa originally developed this theory in order to study the class groups of number fields, but it has since been generalised to many other settings. In this talk, I will discuss some new results in the Iwasawa theory of the symmetric square of a modular form. This is a joint project with Sarah Zerbes, and the main tool in this work is the Euler system of Beilinson-Flach elements, constructed in our earlier works with Kings and Lei.

Mon, 09 Nov 2015

15:45 - 16:45
Oxford-Man Institute

: Gradient estimates for Brownian bridges to submanifolds

JAMES THOMPSON
(University of Warwick)
Abstract

Abstract: A diffusion process on a Riemannian manifold whose generator is one half of the Laplacian is called a Brownian motion. The mean local time of Brownian motion on a hypersurface will be considered, as will the situation in which a Brownian motion is conditioned to arrive in a fixed submanifold at a fixed positive time. Doing so provides motivation for the remainder of the talk, in which a probabilistic formula for the integral of the heat kernel over a submanifold is proved and used to deduce lower bounds, an asymptotic relation and derivative estimates applicable to the conditioned process.

 

Mon, 02 Nov 2015

15:45 - 16:45
Oxford-Man Institute

: Pfaffians, 1-d particle systems and random matrices.

ROGER TRIBE
(University of Warwick)
Abstract

Abstract: Joint work with Oleg Zaboronsky (Warwick).

Some one dimensional nearest neighbour particle systems are examples of Pfaffian point processes - where all intensities are determined by a single kernel.In some cases these kernels have appeared in the random matrix literature (where the points are the positions of eigenvalues). We are attempting to use random matrix tools on the particle sytems, and particle tools on the random matrices.

 

 

Thu, 22 Oct 2015

12:00 - 13:00
L6

A two-speed model for rate-independent elasto-plasticity

Filip Rindler
(University of Warwick)
Abstract
In the first part of this talk I will develop a model for (phenomenological) large-strain evolutionary elasto-plasticity that aims to find a balance between physical accuracy and mathematical tractability. Starting from a viscous dissipation model I will show how a time rescaling leads to the new concept of "two-speed" solutions, which combine a rate-independent "slow" evolution with rate-dependent "fast" transients during jumps. An existence theorem for two-speed solutions to fully nonlinear elasto-plasticity models is the long-term goal and as a first step I will present an existence result for the small-strain situation in this new framework. This theorem combines physically realistic behaviour on jumps with minimisation in the "elastic" variables. The proof hinges on a time-stepping scheme that alternates between elastic minimisation and elasto-plastic relaxation. The key technical ingredient the "propagation of (higher) regularity" from one step to the next.
Thu, 15 Oct 2015

16:00 - 17:00
L5

Sums of seven cubes

Samir Siksek
(University of Warwick)
Abstract

In 1851, Carl Jacobi made the experimental observation that all integers are sums of seven non-negative cubes, with precisely 17 exceptions, the largest of which is 454. Building on previous work by Maillet, Landau, Dickson, Linnik, Watson, Bombieri, Ramaré, Elkies and many others, we complete the proof of Jacobi's observation.

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