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Mathematics Institute

Applied Mathematics Seminars

Organisers: Clarice Poon and Ellen Luckins

The Applied Maths Seminars are held on Fridays 12:00-13.00. This year the seminar will be hybrid (at least for Term 1): you can choose to attend in person in room B3.02 or on MS Teams. The team for the seminar is the same as last year, but if you are not a member, you can send a membership request via MS Teams or email the organisers.

Please contact Clarice Poon or Ellen Luckins if you have any speaker suggestions for future terms.

Seminar Etiquette: Here is a set of basic rules for the seminar.

  • Please keep your microphone muted throughout the talk. If you want to ask a question, please raise your hand and the seminar organiser will (a) ask you to unmute if you are attending remotely or (b) get the speaker's attention and invite you to ask your question if you are in the room.
  • If you are in the room with us, the room microphones capture anything you say very easily, and this is worth keeping in mind ☺️.
  • You can choose to keep your camera on or not. Colleagues in the room will be able to see the online audience.
  • Please let us know if you would like to meet and/or have lunch with any of the speakers who are coming to visit us so that I can make sure you have a place in the room.

Term 1

Abstracts

Term 1

Week 1. Mohit Dalwadi (Oxford) -- Emergent phenomena from multiscale heterogeneity: losing symmetry and causing chaos
In this talk I use hybrid multiscale techniques to understand emergent phenomena arising in two fundamental problems in fluids and biology.
In the first part, I investigate an overarching question in developmental biology: how are cells able to decode spatio-temporally varying signals into functionally robust patterns in the presence of confounding effects caused by complex heterogeneous environments? This is linked to the general idea first explored by Alan Turing in the 1950s. I present a general theory of pattern formation in the presence of spatio-temporal input variations, and use multiscale mathematics to show how delayed bifurcations (via ‘R-tipping’) can allow biological systems to generate non-standard dynamic robustness for ‘free’ over physiologically relevant timescales. This work also has applications in pattern formation more generally.
In the second part, I investigate how the rapid motion of 3D microswimmers affects their emergent trajectories in viscous shear flow. This can be considered an active version of the classic fluid mechanics result of Jeffery’s orbits for inert spheroids, first explored in the 1920s. I show that the rapid short-scale motion exhibited by many microswimmers can have a significant effect on longer-scale trajectories, despite the common neglect of this motion in some mathematical models. I further demonstrate that fast-scale yawing can generate emergent asymmetry and subsequent chaos, in stark contrast to constant fast-scale rotation.
Week 2. Marcus Webb (Manchester) -- Low-rank approximation of analytic kernels
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. In this talk I will discuss a new framework for bounding the best low-rank approximation error of matrices arising from samples of a kernel that is analytically continuable in one of its variables to an open region of the complex plane. Elegantly, the low-rank approximations used in the proof are computable by rational interpolation using the roots and poles of Zolotarev rational functions, leading to a fast algorithm for their construction. A preprint can be found at https://arxiv.org/abs/2509.14017.
Week 3. Tristan Lawrie (Exeter) -- A Quantum Graph Model for Static and Time-Varying Metamaterials

Since the turn of the 21st century, metamaterials have garnered significant attention for their potential to exhibit highly nontrivial and exotic properties, such as cloaking or perfect lensing. This has driven substantial efforts to develop reliable mathematical models that accurately predict the required material compositions. In this work, we present a quantum graph approach to metamaterial design. Wave transport in the material is modelled as a network of vertices connected by one-dimensional edges governed by the wave equation. By varying the graph topology, edge lengths, and vertex boundary conditions, we demonstrate a range of nontrivial effects, including negative refraction, discrete angular filtering, and beam forming and steering. We compare the model's predictions with experimental results from both acoustic and electromagnetic networks, finding excellent agreement. These results establish quantum graph theory as an ideal mathematical framework for studying metamaterials.

Week 4. Audrey Repetti (Heriot Watt) -- Analysis and synthesis approximated denoisers for forward-backward plug-and-play algorithms

In this presentation we will study the behaviour of the forward-backward (FB) algorithm when the proximity operator is replaced by a sub-iterative procedure to approximate a Gaussian denoiser, in a Plug-and-Play (PnP) fashion. Specifically, we consider both analysis and synthesis Gaussian denoisers within a dictionary framework, obtained by unrolling dual-FB iterations or FB iterations, respectively. We analyse the associated global minimization problems as well as asymptotic behaviour of the resulting FB-PnP iterations. For each case, analysis and synthesis, we show that the FB-PnP algorithms solve the same problem whether we use only one or an infinite number of sub-iteration to solve the denoising problem at each iteration. We will illustrate our theoretical results on numerical simulations, considering an image restoration problem in a deep dictionary framework. Joint work with Matthieu Kowalski, Benoit Malezieux and Thomas Moreau.

Week 5. Albane Théry (Warwick) -- Single-cell models for bacterial motility in complex environments

Understanding and preventing bacterial infections requires insight into how microorganisms move and interact within realistic, structured environments such as biofilms or tissues. From a modelling perspective, these systems can be studied across multiple scales — from continuum PDEs approaches and agent-based models to single-cell descriptions. In this talk, we focus on this latter class of single-cell models, and study the coupling between individual motile bacteria and their environment.

We first examine how suspended particles influence the swimming of flagellated bacteria, combining analytical and semi-analytical results to explain the experimentally observed speed increase in suspensions. We then turn to microorganisms for which motility relies on elasto-hydrodynamic instabilities and such minimal models cannot capture key features of their motility. We present elasto-hydrodynamic simulations for the swimming of the oral pathogen Selenomonas sputigena and the gliding motion of filamentous cyanobacteria.
Week 6. Scott McCue (QUT) -- Complex-plane behaviour for nonlinear reaction diffusion models
This talk concerns solutions of nonlinear reaction diffusion models in the complex plane, which are a) interesting in their own right, and b) related to the crucial real-line behaviour. For example, a power series expansion in time will be divergent and break down at a complex singularity of the pde's initial condition, leading to an inner analysis that reveals information about time-dependent complex singularities. When one of these singularities hits the real axis, the real-valued solution undergoes finite-time blow-up. Thus, it is fruitful to track these singularities using analytical and numerical methods. In this talk, a family of semi-linear diffusion models will be discussed as prototype examples. Asymptotic limits of small time, small diffusion, near-blow-up and large time will be mentioned if time permits. This is work in progress done in collaboration with Prof John King from Nottingham and PhD student Daniel VandenHeuvel from Imperial College London.
Week 7. Maciej Buze (Lancaster) -- Barycenters in unbalanced optimal transport
A central challenge in many applications of optimal transport concerns finding a representative (probability) distribution of a given set of distributions. The basic optimal transport approach to this problem is to find the so-called barycenter, which is done by minimizing the sum of weighted two-marginal optimal transport costs between the barycenter and each input distributions. In a seminal contribution [1], it was subsequently shown that an equivalent and computationally favourable approach is to instead solve a single least-cost multi-marginal optimal transport problem.
If the input distributions do not all have equal mass, an unbalanced barycenter can be found via a recourse to the emerging theory of unbalanced optimal transportation. This, however, can be done in a number of ways, depending on how one penalises mass deviations, what cost function is employed and whether one wishes to consider the conic formulation --- see the detailed discussion in [2].
In this talk, following a gentle introduction to the topic, I will present several results on how to recover the celebrated least-cost multi-marginal formulation of Agueh and Carlier in the unbalanced setting [3] and discuss on-going work on generalising such results to unbalanced settings where such a reformulation is not possible.
Lastly, I will also touch upon applications of this and related results in the context of modelling of polycrystalline materials [4].
[1] Agueh, M., & Carlier, G. (2011). Barycenters in the Wasserstein space. SIAM Journal on Mathematical Analysis, 43(2), 904-924.
[2] Liero, M., Mielke, A., & Savaré, G. (2018). Optimal entropy-transport problems and a new Hellinger–Kantorovich distance between positive measures. Inventiones mathematicae, 211(3), 969-1117.
[3] Buze, M. (2025). Constrained Hellinger–Kantorovich barycenters: least-cost soft and conic multimarginal formulations. SIAM Journal on Mathematical Analysis, 57(1), 495-519.
[4] Buze, M., Feydy, J., Roper, S. M., Sedighiani, K., & Bourne, D. P. (2024). Anisotropic power diagrams for polycrystal modelling: Efficient generation of curved grains via optimal transport. Computational Materials Science, 245, 113317.
Week 8. James Griffin (Coventry) -- Automated Manufacturing and Control through Non-Destructive Testing (NDT) Methods: Pattern Recognition of Grinding Phenomena and In-situ Quality Monitoring of Laser Shock Peening
This titled work details the application of sensitive Acoustic Emission (AE) sensing and Machine Learning (ML) techniques for automated manufacturing and control using Non-Destructive Testing (NDT) methods. The focus encompasses pattern recognition within both grinding processes and Laser Shock Peening (LSP) quality control. For grinding, the research identifies and classifies micro and macro phenomena, including cutting, ploughing, and rubbing, alongside anomalies such as burn and chatter. Utilising Neural Networks (NN) and Genetic Algorithm (GA) optimised Fuzzy-clustering, the classification of grinding mechanics achieved accuracies between 82% and 96%. The work also examines the use of AE for in-situ quality monitoring during Laser Shock Peening (LSP), a surface strengthening technology. AE data is analysed to understand how process parameters, such as confinement layers (air, gel, water) and power densities (15% to 98%), influence the AE output, which correlates well with resulting surface modifications and residual stress detected by methods like Barkhausen noise. This generic strategy, leveraging signal extraction techniques like Short-time Fourier Transform (STFT), provides a foundation for developing intelligent, real-time ML models for automated process monitoring and quality control.
Week 9. Bernhard Schmitzer (Gottingen) -- The Riemannian geometry of Sinkhorn divergences
Optimal transport provides an intuitive and robust way to compare probability measures with applications in many areas of mathematics. This holds in particular for the Wasserstein-2 distance with its formal Riemannian structure.
While entropic regularization of optimal transport has several favourable effects, such as improved statistical sample complexity, it destroys this metric structure. The de-biased Sinkhorn divergence is a partial remedy, as it is positive, definite, and its sublevel sets induce the weak* topology. However, it does not satisfy the triangle inequality. We resolve this issue by considering the Hessian of the Sinkhorn divergence as a Riemannian tensor and study the induced distance. In this talk we outline the key steps of this construction, the corresponding induced notion of tangent space, some early results on the distance, and open directions for future work..

Aerial photograph of Maths Houses

See also:
Mathematics Research Centre
Mathematical Interdisciplinary Research at Warwick (MIR@W)
Past Events 
Past Symposia 

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Contact:
Mathematics Research Centre
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University of Warwick
Coventry CV4 7AL - UK
E-mail:
MRC@warwick.ac.uk

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