Tue, 09 Jun 2026

14:00 - 15:00
L5

Permutations with an invariant set of size k

Ben Green
((Mathematical Institute University of Oxford))
Abstract

Denote by p(k) the limit, as n tends to infinity, of the probability that a random permutation on n letters has some invariant set of size k. For example, p(1) = 1 - 1/e. I will discuss the asymptotic behaviour of p(k). Joint work with Mehtaab Sawhney.

Mon, 18 May 2026

15:30 - 16:30
L3

Rough Stochastic Differential Equations (RSDEs) and Applications

Prof. Peter Friz
(Technical University of Berlin)
Abstract

Recent advances at the interface of stochastic analysis, rough path theory, stochastic filtering, stochastic control, and mean-field systems have led to a rapidly developing framework for analyzing stochastic dynamics conditioned on common/observation noice. This talk will survey how rough stochastic differential equations, introduced in 2021 by A. Hocquet, K. Lê and the speaker, lead to a unifying perspective across several areas of applied probability.

(Additional coauthors include F. Bugini, J. Dause, W. Stannat, H. Zhang and P.Zorin-Kranich.)

Tue, 21 Jul 2026

16:00 - 17:00
L5

How hypoxic memory shapes tumor invasion under cyclic hypoxia

Dr Gopinath Sadhu
(Department of Bioengineering, Indian Institute of Science)
Abstract

Tumor growth and angiogenesis drive complex spatiotemporal variation in micro-environmental oxygen levels. Previous experimental studies have observed that cancer cells exposed to chronic hypoxia retained a phenotype characterized by enhanced migration and reduced proliferation, even after being shifted to normoxic conditions, a phenomenon which we refer to as hypoxic memory. However, because dynamic hypoxia and related hypoxic memory effects are challenging to measure experimentally, our understanding of their implications in tumor invasion is quite limited. Here, we propose a novel phenotype-structured partial differential equation modeling framework to elucidate the effects of hypoxic memory on tumor invasion along one spatial dimension in a cyclically varying hypoxic environment. We incorporated hypoxic memory by including time-dependent changes in hypoxic-to-normoxic phenotype transition rate upon continued exposure to hypoxic conditions. Our model simulations demonstrate that hypoxic memory significantly enhances tumor invasion without necessarily reducing tumor volume. This enhanced invasion was sensitive to the induction rate of hypoxic memory, but not the dilution rate. Further, shorter periods of cyclic hypoxia contributed to a more heterogeneous profile of hypoxic memory in the population, with the tumor front dominated by hypoxic cells that exhibited stronger memory. Overall, our model highlighted the complex interplay between hypoxic memory and cyclic hypoxia in shaping heterogeneous tumor invasion patterns.

Keywords: Tumor invasion, cyclic hypoxia, hypoxic memory, phenotype-structured model

Our HouseWelcome to the House of Fun! The Madness jukebox musical, Our House, by student production company Cross Keys Productions, showing at the Oxford Playhouse, 20th-23rd May,
Demographic changes and behavioural responses shape vulnerability to infectious disease outbreaks
Evans, A Hart, W Jung, E Nah, K Bonic-Babic, K Jung, S Thompson, R (14 May 2026)
Variational inference via Gaussian interacting particles in the Bures--Wasserstein geometry
Borghi, G Carrillo de la Plata, J Proceedings of machine learning research

Green Templeton College are offering discounted tickets for mathematicians at their ball on July 3rd.

The discount is £40 off the usual price. More information (SSO).

Image: Thomas Cantrell Dugdale - The Arrival of the Jarrow Marchers

Thu, 11 Jun 2026
15:00
L4

TBC

Daniel Drimbe
(University of Iowa)
Abstract

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