Jan Olucha Fuentes

Hi, I'm Jan. I'm a second year PhD student under the supervision of Alex Cox at the University of Bath, working as a part of the MaThRad research programme through the SAMBa Center for Doctoral Training. I did my Master's at the University of Cambridge and my Bachelor's at King's College London.

Mathematical Interests

My mathematical interests are mainly in Probability. Some keywords of my interests: Monte Carlo simulation, variance reduction algorithms, rare-event simulation, Feynman–Kac measures, etc.

Currently, I am interested in understanding the theory behind algorithms for computing expectations of the form \[ \mathbf{E}\left[ f(X_t)\prod_{s=1}^{t} G_s(X_s) \right], \] where \((X_t)_{t\geq 0}\) is a discrete-time Markov chain on a measurable state space \((E,\mathcal{E})\), \(f:E\to\mathbf{R}\) is a test function, and \((G_t)_{t\geq 0}\) is a collection of functions on \(E\), called potential functions.

Academic CV

• Bachelor's degree in Mathematics (2023): King's College London. I received the IMA (Institute of Mathematics and Applications) Prize for achieving the best results (95%) in the final year of my degree.
• Master's degree in Pure Mathematics (2024): University of Cambridge.
• Doctor in Philosophy (2030): University of Bath

Outreach and teaching

Outside my research, I am very involved in mathematical outreach and teaching. My primary goal as a mathematician is to make mathematics a subject for everyone through thoughtful pedagogy and communication:

• In 2021, I started a YouTube channel, where I talk about topics of mathematical nature for a Spanish-speaking audience.
• Since 2023 I work with the charity We Solve Problems to bring high quality mathematical enrichment activities to kids. At We Solve Problems we run "Maths Circles", a kind of social club for maths-loving bright young students. Since the summer of 2025, I serve as the Head of Curriculum of this organisation.
• During my time at King's College London I worked as a tutor on the King's Factor programme, an extra-curricular programme where high school students can get mentoring to prepare for university entrance exams.
• During my PhD I worked as a Teaching Assistant for the following courses: Probability 2 (winter term 2026)

Contact

To contact me please email me via jof36@bath.ac.uk

Cheers!