# Dr Dale Roberts

## Research interests

My research interests are in high-dimensional probability theory and stochastic processes, algorithms, and their application to very large scale data science problems.

In 2017, 2018, and 2019, I taught a research-led course that looked at the application of random matrix theory in high-dimensional statistics and machine learning. Particular focus was on understanding how classic approaches break down when the dimensionality of the data becomes large and how these problems may be resolved using recent mathematical results.

From 2020 onwards, I will be teaching a postgraduate course on stochastic processes (Markov chains and mixing, random walks, Brownian motion, and applications).

I love programming, building my own research tools, and routinely release them on GitHub for others to use (see my profile). Many of my public projects are highly starred by the international community, my ranking is here.

## Biography

I graduated from the University of Technology, Sydney (UTS) with a first class Honours in Mathematics in 2006. After my honours I spent some time working in the finance industry. In 2012, I completed my Ph.D. in Mathematics at the University of New South Wales on the topic of Stochastic Partial Differential Equations (SPDE). On completing my PhD, I joined ANU as a Lecturer jointly appointed in RSFAS and the Mathematical Sciences Institute (MSI). At the start of 2014, I left the MSI and moved full-time to CBE/RSFAS. I was promoted to Senior Lecturer in 2014. From March 2017 to March 2018, I took a 12-month role as Director of External Research Engagement for the College of Business and Economics.

## Researcher's projects

For students seeking Honours or PhD supervision, some keywords to describe my mathematical interests are: stochastic differential equations, stochastic partial differential equations, partial differential equations, Lévy processes, Brownian motion, stochastic processes, random fields, random matrices, high-dimensional probability, random graphs, network theory, dynamics on graphs, high-dimensional statistics, multivariate statistics, statistical learning, machine learning, numerical analysis, numerical methods.

I also like taking these mathematical concepts and using them to solve real-world problems.

## Past student projects

- Emma Ai. PhD in Statistics
- Timothy McLennan-Smith. PhD in Statistics
- Wayne Wang. Honours in Statistics
- Rui Cheng. First class Honours in Statistics
- Michael Winjen. First class Honours in Statistics
- Remy Hamilton-Smith. Statistical Learning applied to Burnscar Classification and Natural Hazard Insurance. First class Honours in Actuarial Studies.
- Omar Al-Ghattas. Stochastic Portfolio Theory and Information-theoretical Portfolio Tracking. First class Honours in Statistics.
- Chaturi Bhaskaran. Overshoots of random walks and Lévy processes. First class Honours in Mathematics.
- Nam Ho. Batch and sequential learning with complexity measures. First class Honours in Mathematics.
- Emma Ai. Multiwindowed barrier options under stochastic volatility. M.Phil. in Mathematics.
- Yang Liu. Existence and uniqueness of solutions to ODEs and SDEs with irregular coefficients. First class Honours in Mathematics.
- Anjisht Gosain. Pricing of Himalaya options under the Heston stochastic volatility model. First class Honours in Finance.
- Lindon Roberts. Wavelet methods for variational inequalities. First class Honours in Mathematics & University medal.