Martin Geller

PhD, Mathematics at Oxford (in progress),
MSc, Financial Computing and Analytics Group at UCL,
MSc, Department of Economics at LSE
Oxford Mathematics
UCL Financial Computing
London School of Economics

Email: martin.geller(at)maths.ox.ac.uk

Correspondence Address:
Mailbox 344,
254 Pentonville Road
London N1 9FQ,
UK

CV: Available here

Office :
Mathematical Institute,
Andrew Wiles Building,
Woodstock Road,
Oxford
OX2 6GG,
UK

Mobile: +44 (0) 7446 847 469
Office Tel: +44 (0) 1865 615 303

Works

My research is focused on analytically-rigorous probability theory under the supervision of Prof. Terry Lyons.
Recently, I have been focused on developing a notion of sum of rough paths, with the objective of developing
a calculus on rough path space. My pre-print can be found here.

Some of my earlier works in my PhD include:
Approximating diffusion reflections at elastic boundaries and its application to an optimal control problem
Comparing two proofs of Doob's theorem, the original one and a novel one using coupling
What is AlphaFold?, partly non-technical and partly technical overview of AlphaFold

During my graduate studies in mathematical finance, I also produced a number of research pieces:
Optimisation and machine learning applied to forecast euro-dollar using Twitter sentiment
PCA and unsupervised learning of stock returns
Information theory applied to analyse cryptocurrencies
Supervised learning applied to forecast financial crises
Regularisation for the computation of Markowitz' mean-variance efficient portfolio
I also produced one short paper in abstract moral philosophy

Research interests

Currently, I am interested in topics at the interface of mathematical analysis and probability. Specifically, my research interests include:
(These headers link to key publications on each subject)
Stochastic Partial Differential Equations (SPDEs) (in particular, the application of Malliavin calculus to SPDEs)
Markov Processes
Ergodic Theory
Large Deviations
Differential Geometry Approaches to Stochastic Analysis

Teaching

Currently, I act as TA for two sets of the course Stochastic Analysis and PDEs at Oxford. In addition, I have tutored approximately 50 students
privately in subjects (mostly at BSc level) including mathematics, probability, mathematical finance, econometrics, and computer science.

Courses Taken

In my current PhD, I have taken a variety of courses in advanced analysis and probability:

Foundations of Data Science,
Foundations of Stochastic Analysis ,
Function Spaces and Distribution Theory,
Theories of Deep Learning,
Advanced Topics in Stochastic Analysis (Imperial),
Advanced Topics in Stochastic Processes (Imperial),
Simulation Methods and Stochastic Algorithms,
Limit Theorems and Large Deviations in Probability,
Malliavin Calculus (Imperial),
Optimal Transport & Partial Differential Equations.

In the academic years 2018-19, I studied a Master's degree in mathematical finance at UCL's Financial Computing and Analytics Group. The courses I took were:
Dissertation (top 3%),
Applied Machine Learning (1st class),
Machine Learning with Applications in Finance (1st class),
Numerical Methods for Finance (top 3%),
Financial Data and Statistics (top 5%),
Financial Engineering (upper 2nd class),
Financial Market Modelling and Analysis (top of the class),
Market Microstructure (1st class),
Algorithmic Trading (1st class).

In 2017-18, I was an MSc student at LSE's Department of Economics, where I focussed on econometrics and mathematical economics. Here, I took the following courses:
Mathematics for Econometrics (1st class for EC400),
Mathematics for Macroeconomics,
Mathematics for Microeconomics,
Econometrics (upper 2nd class),
Macroeconomics (upper 2nd class),
Dissertation in Abstract Moral Philosophy (1st class),
Philosophy of Economics (1st class),

In the academic years 2014-17, I took a total of 29 semester-long modules in my BSc in mathematical economics. The ones I enjoyed the most were:
Real Analysis (top 4%),
Algebra (top 4%),
Calculus (top 2%),
Linear Algebra (top 2%),
Econometrics I (1st class),
Econometrics II (1st class),
Probability and Statistics I (top 4%),
Probability and Statistics II (top 4%).

Personal Interests

Language learning is an activity that I take seriously. I actively maintain my near-native fluency in French, Spanish, Portuguese, and conversational Japanese.

My other interests are piano and chess. I have 15 years of experience playing tango pieces, including Nazareth's Odeon (of which one of the best interpretations is here). In chess, my favourite opening is the Caro-Kann Defence.

Last change: 17 January 2021