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TBA. 

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

We apply techniques of exponential asymptotics to the KdV equation to derive the small-time behaviour for dispersive waves that propagate in one direction.  The results demonstrate how the amplitude, wavelength and speed of these waves depend on the strength and location of complex-plane singularities of the initial condition.  Using matched asymptotic expansions, we show how the small-time dynamics of complex singularities of the time-dependent solution are dictated by a Painlevé II problem with decreasing tritronquée solutions.  We relate these dynamics to the solution on the real line.

Over the last decade, adversarial attack algorithms have revealed instabilities in artificial intelligence (AI) tools. These algorithms raise issues regarding safety, reliability and interpretability; especially in high risk settings. Mathematics is at the heart of this landscape, with ideas from  numerical analysis, optimization, and high dimensional stochastic analysis playing key roles. From a practical perspective, there has been a war of escalation between those developing attack and defence strategies. At a more theoretical level, researchers have also studied bigger picture questions concerning the existence and computability of successful attacks. I will present examples of attack algorithms for neural networks in image classification, for transformer models in optical character recognition and for large language models. I will also show how recent generative diffusion models can be used adversarially. From a more theoretical perspective, I will outline recent results on the overarching question of whether, under reasonable assumptions, it is inevitable that AI tools will be vulnerable to attack.

How do you efficiently look for jobs?

How can you make the most of careers fairs?

What makes a CV or cover letter stand out?

Get practical advice and bring your questions!

In this talk, we use type theory to construct a family of depth $\frac{1}{N}$ minimax supercuspidal representations of $p$-adic $\text{GL}(2N, F)$ which we call \textit{middle supercuspidal representations}. These supercuspidals may be viewed as a natural generalization of simple supercuspidal representations, i.e. those supercuspidals of minimal positive depth. Via explicit computations of twisted gamma factors, we show that middle supercuspidal representations may be uniquely determined through twisting by quasi-characters of $F^{\times}$ and simple supercuspidal representations of $\text{GL}(N, F)$. Furthermore, we pose a conjecture which refines the local converse theorem for general supercuspidal representations of $\text{GL}(n, F)$.

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TBA

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This session will look at how you can get the most out of your lectures and tutorials. We’ll talk about how to prepare effectively, make lectures more productive, and understand what tutors expect from you during tutorials. You’ll leave with practical tips to help you study more confidently and make your learning time count.

This session is likely to be most relevant for first-year undergraduates, but all are welcome.

Cell and tissue movement during development, immune response, and cancer invasion depends on chemical or mechanical guidance cues. In many systems, this guidance arises not from long-range, pre-patterned cues but from self-generated gradients locally shaped by cells. However, how heterogeneous cell mixtures coordinate their migration by self-generated gradients remains largely unexplored. In this talk, I will first summarize our recent discovery that immune cells steer their long-range migration using self-generated chemotactic cues (Alanko et al., 2023). I will then introduce a multi-component Keller-Segel model that describes migration and patterning strategies of heterogeneous cell populations (Ucar et al., 2025). Our model predicts that the relative chemotactic sensitivities of different cell populations determine the shape and speed of traveling density waves, while boundary conditions such as external cell and attractant reservoirs substantially influence the migration dynamics. We quantitatively corroborate these predictions with in vitro experiments on co-migrating immune cell mixtures. Interestingly, immune cell co-migration occurs near the optimal parameter regime predicted by theory for coupled and colocalized migration. Finally, I will discuss the role of mechanical interactions, revealing a non-trivial interplay between chemotactic and mechanical non-reciprocity in driving collective migration.
 

Mathematicians often like to think of maths as objective. Science communicator Hana Ayoob joins us to discuss how the fact that humans do maths means that the ways maths is developed, used, and communicated are not neutral.

Modern deep learning methods provide the state-of-the-art in image reconstruction in most areas of computational imaging. However, such techniques are very data hungry and in a number of key imaging problems access to ground truth data is challenging if not impossible. This has led to the emergence of a range of self-supervised learning algorithms for imaging that attempt to learn to image without ground truth data. 

In this talk I will review some of the existing techniques and look at what is and might be possible in self-supervised imaging.

Equations of fluctuating hydrodynamics, also called Dean-Kawasaki type equations, are stochastic PDEs describing the evolution of finitely many interacting particles which obey a Langevin equation. First, we give a mathematical derivation for such equations. The focus is on systems of interacting particles described by second order Langevin equations. For such systems,  the equations of fluctuating hydrodynamics are a stochastic variant of Vlasov-Fokker-Planck equations, where the noise is white in space and time, conservative and multiplicative. We show a dichotomy previously known for purely diffusive systems holds here as well: Solutions exist only for suitable atomic initial data, but provably not for any other initial data. The class of systems covered includes several models of active matter. We will also discuss regularisations, where existence results hold under weaker assumptions. 

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What do the roots of random polynomials look like? Classical works of Erdős-Turán and others show that most roots are near the unit circle and they are approximately rotationally equidistributed. We will begin with an understanding of why this happens and see how ideas from extremal combinatorics can mix with analytic and probabilistic arguments to show this. Another main feature of random polynomials is that their roots tend to "repel" each other. We will see various quantitative statements that make this rigorous. In particular, we will study the smallest separation $m_n$ between pairs of roots and show that typically $m_n$ is on the order of $n^{-5/4}$. We will see why this reflects repulsion between roots and discuss where this repulsion comes from. This is based on joint work with Oren Yakir.

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A discussion on how race and ethnicity interact with the concept of merit in academia, based on sections from the book 'Misconceiving Merit' by Blair-Loy and Cech.