Fridays@2 - The Art of Mathematical Communication

No, you're not losing it, it really is 2pm. A special session:

Join bestselling author Simon Singh and Oxford Mathematician turned educator Junaid Mubeen for a session on maths communication. Learn how to present mathematics in a way that is both accessible and engaging, and how to apply these principles in a teaching context. 

Wed, 22 Oct 2025
11:00
L4

Two partition-function approaches to non-symmetric random tensor eigenvalues

Giacomo La Scala
(Oxford University)
Abstract
At large N, random matrices with Gaussian distributed entries follow the Wigner semicircular law for the distribution of their eigenvalues. Random tensors are of interest in contexts of d > 2 dimensional quantum theories but do not enjoy simple generalisations of eigenvalues. Work has recently been done by Gurau to extend Wigner’s law to totally symmetric random tensors, with an approach inspired by the partition function of a Gaussian p-spin model. Starting from Gurau’s approach, I will motivate and introduce two new attempts to define and study eigenvalues of non-symmetric random tensors through partition functions, at finite and large N. One approach, based on a definition of a characteristic function, will be related to Gurau’s distribution. The other, based on a permuted definition of eigenvalues, will hint at a universality with differently-computed distributions for symmetric and complex random tensors.

Oxford University Language Centre courses

Enrolment for Michaelmas term courses in Modern Languages and Academic English at the Language Centre is open until 12 noon on Wednesday of Week 1 (15 October). Classes take place weekly, online or in person, with many lunchtime and evening sessions on offer.

Oxford Mathematics merchandise!

Show your love for Oxford Maths with our exclusive range of branded merchandise! All of our merchandise can be bought online at the College Store.

Take advantage of a 10% discount on all our gear from t-shirts to fleeces to key rings. The discount code TCS-FRESH10 will run from 1 – 30 October. 

Tue, 21 Oct 2025

14:00 - 15:00
L3

Optimal control of the Dyson equation and large deviations for Hermitian random matrices

Prof Panagiotis E. Souganidis
(University of Chicago)
Abstract

Using novel arguments as well as techniques developed over the last  twenty years to study mean field games, in this paper (i) we investigate the optimal control of the Dyson equation, which is the mean field equation for the so-called Dyson Brownian motion, that is, the stochastic particle system satisfied by the eigenvalues of large random matrices, (ii) we establish the well-posedness of the resulting infinite dimensional Hamilton-Jacobi equation, 
(iii) we provide a complete and direct proof for the large deviations for the spectrum of large random matrices, and (iv) we study the asymptotic behavior of the transition probabilities of the Dyson Brownian motion.  Joint work with Charles Bertucci and Pierre-Louis Lions.

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Mon, 02 Feb 2026
15:30
L3

Mean field games without rational expectations

Benjamin MOLL
(LSE)
Abstract
Mean Field Game (MFG) models implicitly assume “rational expectations”, meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common noise, it becomes necessary to solve the “Master equation” (a.k.a. “Monster equation”), a Hamilton-JacobiBellman equation in which the infinite-dimensional density of agents is a state variable. The rational expectations assumption and the implication that agents solve Master equations is unrealistic in many applications. We show how to instead formulate MFGs with non-rational expectations. Departing from rational expectations is particularly relevant in “MFGs with a low-dimensional coupling”, i.e. MFGs in which agents’ running reward function depends on the density only through low-dimensional functionals of this density. This happens, for example, in most macroeconomics MFGs in which these lowdimensional functionals have the interpretation of “equilibrium prices.” In MFGs with a low-dimensional coupling, departing from rational expectations allows for completely sidestepping the Master equation and for instead solving much simpler finite-dimensional HJB equations. We introduce an adaptive learning model as a particular example of nonrational expectations and discuss its properties.
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