Photo of me, taken September 2019

Josh Fogg

they/them · Contact · JCMB 6311

I'm a PhD student and tutor in the University of Edinburgh's School of Mathematics. My research is supervised by Julian Hall, interested in Numerical Linear Algebra and Optimization.

When not furiously coding I can often be found reading trashy fiction, running long distances, or playing slightly more ridiculous sports. My personal (hodgepodge) blog can be found here.


My current work is on improving the efficiency and applicability of Markowitz' Critical Line Algorithm, a tool for exploring the pareto frontier of dual-objective portfolio optimization. Practically that means spending a lot of time coding, improving the numerical linear algebra, and searching for application specific shortcuts.

More broadly my research interest could be labelled as 'algorithms'. While at the University of Manchester I did my undergraduate thesis with Françoise Tisseur on Google's PageRank algorithm and then my masters thesis with Chris Johnson was on Veach's algorithm for Monte Carlo Light Transport Simulation.


The Life and Work of Harry M Markowitz
2024-09, 33rd ECOR, Copenhagen 📅

Portfolio Optimization for Genetic Selection
2023-09, PiFORUM23, Birmingham 🥈

Portfolio Optimization for Genetic Selection
2023-08, EUROpt Workshop, Budapest

Portfolio Optimization for Genetic Selection
2023-07, APDIO Optimization, Aveiro

Portfolio Optimization in Genetics
2023-06, SIAM UKIE National SCC, Oxford 🥈

Portfolio Optimization Techniques in a New Context
2023-04, SIAM UKIE Annual Meeting, Dublin

High Performance Portfolio Optimization
2022-06, SIAM UKIE National SCC, Edinburgh

High Performance Portfolio Optimization
2021-11, fORum, Edinburgh-Trier

Circumference of an ellipse? Can't do it mate
2021-11, PG Colloquium, EdinburghBlog Version

From Finance to Genetics: Improving CLA
2021-06, YRM Conference, Bristol

5 Things I've Learned From Research
2020-11, SIAM UG Outreach Event, EdinburghBlog Version

Improving Algorithms; Why Bother?
2020-10, PG Colloquium, Edinburgh

Genetics Portfolio Optimization
2020-09, MIGS PhD Conference, Edinburgh


If you're one of my students drop me an email with any questions. Tutors from workshops aren't the ones marking your work but if you've a query about why you got the mark you did let me know; I might be able to have a guess.

2023/24 Semester 2

Sutton Trust

In the summers of 2020 and 2021 I delivered a mini-course as part of the Sutton Trust summer school on machine learning alongside Isabella Deutsch. My primary contributions were an R/Shiny app (code, app) for exploring an application of decision trees and a series of mini research projects on that and applied maths more broadly.

Past Teaching

2023/24 Semester 1

2022/23 Semester 2

2022/23 Semester 1

2021/22 Semester 2

2021/22 Semester 1

2020/21 Semester 2

2020/21 Semester 1

2019/20 Semester 2

Other Bits

I'm a member of the UCU and occasional contributor to the school's outreach team. In 2019/20 and 2020/21 I was a PhD rep within the school. In 2019/20 I also provided tech support for SMSTC.