L2

Gauss invented Gaussian quadrature following an approach entirely different from the one we now find in textbooks. I will describe leisurely the contents of Gauss's original memoir on quadrature, an impressive piece of mathematics, based on continued fractions, Padé approximation, generating functions, the hypergeometric series and more.

Given a Calabi-Yau threefold X, one can count curves on X using various approaches, for example using stable maps or ideal sheaves; for any curve class on X, this produces an infinite sequence of invariants, indexed by extra discrete data (e.g. by the domain genus of a stable map).  Conjecturally, however, this sequence is determined by only a finite number of integer invariants, known as Gopakumar-Vafa invariants.  In this talk, I will propose a direct definition of these invariants via sheaves of vanishing cycles, building on earlier approaches of Kiem-Li and Hosono-Saito-Takahashi.  Conjecturally, these should agree with the invariants as defined by stable maps.  I will also explain how to prove the conjectural correspondence for irreducible curves on local surfaces.  This is joint work with Yukinobu Toda.

This document reviews the so called least square methodology (LSM) and its application for the valuation and risk of callable exotics and regulatory value adjustments (xVA). We derive valuation algorithms for xVA, both with or without collateral, that are particularly accurate, efficient and practical. These algorithms are based on a reformulation of xVA, designed by Jesper Andreasen and implemented in Danske Bank's award winning systems, that hasn't been previously published in full. We then investigate the matter of risk sensitivities, in the context of Algorithmic Automated Differentiation (AAD). A rather recent addition to the financial mathematics toolbox, AAD is presently generally acknowledged as a vastly superior alternative to the classical estimation of risk sensitivities through finite differences, and the only practical means for the calculation of the large number of sensitivities in the context of xVA. The theory and implementation of AAD, the related check-pointing techniques, and their application to Monte-Carlo simulations are explained in numerous textbooks and articles, including Giles and Glasserman's pioneering Smoking Adjoints. We expose an extension to LSM, and, in particular, we derive an original algorithm that resolves the matters of memory consumption and efficiency in differentiating simulations together with the LSM step.

We report on recent developments in the study of nonlocal operators. The central object of the talk are quadratic forms similar to those that define Sobolev spaces of fractional order. These objects are naturally linked to Markov processes via the theory of Dirichlet forms. We provide regularity results for solutions to corresponding integrodifferential equations. Our emphasis is on forms with singularand anisotropic measures. Some of the objects under consideration are related to the Boltzmann equation, which leads to an interesting question of comparability of quadrativ forms. The talk is based on recent results joint with B. Dyda and with K.-U. Bux and T. Schulze.

Data science: The secret to unlocking operational performance within the UK’s largest retail supply chain

Chris Reddick was instrumental in setting up the InFoMM CDT. After helping secure the EPSRC funding he chaired the Industrial Engagement Committee and supported the CDT in all its Industrial relations. The success of the CDT, as evidenced by the current size of the industrial partnership and the vibrant programme we have developed, is in no small part due to Chris' charm, vision, and tenacity.

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There are many opportunities within Oxford to communicate your excitement about mathematics and your own research to a wider audience, whether adults or school students.  In this session we'll hear about some of those opportunities, and have some training on how to write a press release, so that you are well placed to share your next research paper with the public.

Featuring 
Rebecca Cotton-Barratt, Schools Liaison Officer and Admissions Coordinator in the Mathematical Institute
Mareli Grady, Schools Liaison Officer in the Statistics Department and Mathemagicians Coordinator in the Mathematical Institute
Stuart Gillespie, Media Relations Officer for the University of Oxford

As part of a suite of products that provide a drive thorough vehicle tyre inspection system the assessment of wheel alignment would be useful to drivers in maintaining their vehicles and reducing tyre wear.  The current method of assessing wheel alignment involves fitting equipment to the tyre and assessment within a garage environment. 

The challenge is to develop a technique that can be used in the roadway with no equipment fitted to the vehicle.  The WheelRight equipment is already capturing images of tyres from both  front and side views.  Pressure sensors in the roadway also allow a tyre pressure footprint to be created.  Using the existing data to interpret the alignment of the wheels on each axle is a preferred way forward.