Come take a break and get to know other Mathematrix members over some crafts! All supplies and sweet treats provided.

Prof Ian Griffiths (a mental health first aider in the department) will lead a discussion about how to protect your mental health when studying an intense graduate degree and outline the support and resources available within the Mathematical Institute. 

The dynamics of spatially-structured networks of N interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does synaptic weight scaling suffice, by itself, to guarantee the convergence of network dynamics to a deterministic population equation, even when networks are not assumed to be homogeneous or spatially structured? In this work, we consider networks of stochastic integrate-and-fire neurons with arbitrary synaptic weights satisfying a O(1/N) scaling condition. Borrowing results from the theory of dense graph limits, or graphons, we prove that, as N tends to infinity, and up to the extraction of a subsequence, the empirical measure of the neurons' membrane potentials converges to the solution of a spatially-extended mean-field partial differential equation (PDE). Our proof requires analytical techniques that go beyond standard propagation of chaos methods. In particular, we introduce a weak metric that depends on the dense graph limit kernel and we show how the weak convergence of the initial data can be obtained by propagating the regularity of the limit kernel along the dual-backward equation associated with the spatially-extended mean-field PDE. Overall, this result invites us to reinterpret spatially-extended population equations as universal mean-field limits of networks of neurons with O(1/N) synaptic weight scaling. This work was done in collaboration with Pierre-Emmanuel Jabin (Penn State) and Datong Zhou (Sorbonne Université).

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Join us for the inaugural session of Mathematrix book club! Have you heard that office workplaces often have the thermostat set at a temperature that is too cold for women to work comfortably? This month we will be discussing the academic articles behind concepts that often come up in conversations about gender inequality in the workplace. The goal of book club is to develop an evidence-based understanding of diversity in mathematics and academia. 

Join us for an initial welcome pizza lunch to start the academic year to learn about what's happening in Mathematrix in 2025/26! Meet other students who are from underrepresented groups in mathematics and allies :) 

Please RSVP here to confirm your spot: https://forms.gle/3bacFBQzXFrFB4Ux7

TBA