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Photo - James Foster

James Foster

DPhil, MMath
Status
Postdoctoral Research Associate
Contact form
https://github.com/james-m-foster
+44 1865 280600
Research groups
  • Data Science
  • Stochastic Analysis

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Prizes, awards, and scholarships

G-Research PhD Prize (2020, first place)

STEM for Britain 2021 (finalist in the mathematical sciences category)

NeurIPS 2021 Outstanding Reviewer Award (given to the top 8% of reviewers)

Research interests

Stochastic analysis, differential equations, machine learning and rough path theory

I am particularly interested in numerical methods for stochastic differential equations (which was the topic of my DPhil thesis).

The main result of my DPhil thesis provides an interesting connection between Brownian motion and random polynomials.

A poster illustrating this idea can be found here.

Some of this work was also demonstrated in the Matlab example:

https://www.chebfun.org/examples/stats/RandomPolynomials.html

(courtesy of Prof. Nick Trefethen)

Teaching

Graduate lecturer at Worcester College, tutoring Linear Algebra and Analysis (2017-2018)

TT 2019, 2022: Tutor (Consultation Sessions) - B8.4 Information Theory

MT 2018, HT 2021, 2022: Tutor - B8.4 Information Theory

TT 2017, 2018: Tutor (Consultation Sessions) - B8.4 Communication Theory

MT 2016, 2017: Teaching Assistant - B8.4 Communication Theory

HT 2017: Teaching Assistant - B8.3 Mathematical Models of Financial Derivatives

Major / recent publications

Efficient and Accurate Gradients for Neural SDEs
Patrick Kidger, James Foster, Xuechen Li and Terry Lyons
Neural Information Processing Systems 2021

The Signature Kernel is the solution of a Goursat PDE
Cristopher Salvi, Thomas Cass, James Foster, Terry Lyons and Weixin Yang
SIAM Journal on Mathematics of Data Science (2021)

Neural SDEs as Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser and Terry Lyons
International Conference on Machine Learning 2021

Neural Rough Differential Equations for Long Time Series
James Morrill, Cristopher Salvi, Patrick Kidger, James Foster and Terry Lyons
International Conference on Machine Learning 2021

Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function
James Foster and Karen Habermann
arXiv:2102.10095

The shifted ODE method for underdamped Langevin MCMC
James Foster, Terry Lyons and Harald Oberhauser
arXiv:2101.03446

Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster and Terry Lyons
Neural Information Processing Systems 2020 (Spotlight)

An optimal polynomial approximation of Brownian motion
James Foster, Terry Lyons and Harald Oberhauser
SIAM Journal on Numerical Analysis (2020)

An asymptotic radius of convergence for the Loewner equation and simulation of SLE traces via splitting
James Foster, Terry Lyons and Vlad Margarint
arXiv:1912.06424

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