Jan Olucha Fuentes

Hi, I'm Jan. I did my undergraduate degree in Mathematics between 2021 and 2024 at King's College London (KCL), where I was the President of the Mathematics Student Society during my last year. I am currently studying Part III of the Mathematical Tripos at Cambridge, and I will (hopefully) be starting a PhD at the University of Bath under the supervision of Alex Cox in September 2025. This is my CV in the form of a website, where you can find my academic trajectory and some of the stuff I've written.

Education

• BSc Mathematics: King's College London, final grade 93%
• Notable grades: Rings and Modules (100%), Statistical Mechanics (100%), Applied Differential Equations (100%), Real Analysis (99%), Probability Theory (98%)
• MASt Mathematics: Cambridge (2025)

Awards

When I was at King's College London I was awarded the IMA (Institute of Mathematics and Applications) Prize for achieving the best results (95%) in the final year of my degree.

Mathematical Interests

My mathematical interests are mainly in probability. I enjoy thinking about probabilistic models with physical relevance: interacting particle systems, statistical mechanics, random walks, etc.

Mathematical Work

• Undergraduate Thesis: Attractors of Iterated Function Systems (IFS): where do they live and how to see them, supervised by Jean Lagacé.
• Part III Essay (draft): Random Walks on Dynamical Percolation, supervised by Perla Sousi.

Outreach work

In 2021 I started a YouTube channel, where I talk about topics of mathematical nature for a Spanish-speaking audience.

Teaching experience

• King's College London: King's Factor Tutor (2022-2024)
• We Solve Problems: Head Tutor (2023-2024)
• FunTech: Summer Tutor in Python and Cybersecurity (2024)

Lecture Notes

Throughout my education, I have typed up notes for several of the courses I took. Some people found them useful, so I am sharing them here. The strength of these notes lies not just in the mathematical content but in the extensive list of examples and questions they contain. That said, be warned—these notes may have typos, errors, and the occasional colorful language. Some are quite rough and lack structure, but I am gradually refining those I find most worthwhile.

Notes from King’s College London

The following notes were written during my time at King’s College London. They vary in quality, and while some are fairly structured, others are more of a raw compilation of ideas and exercises.

Notes from Cambridge (Work in Progress)

I am currently writing a new set of lecture notes based on my studies at Cambridge. These are still in progress, but I hope they will be of significantly higher quality than those written previously. The topics I plan to cover include:

Contact

To contact me please email me via jo504@cam.ac.uk

Cheers!