Thu, 12 Jun 2025

12:00 - 13:00
L3

Microfluidic model of haemodynamics in complex media

Anne Juel
(University of Manchester)
Further Information

Short Bio
Anna Juel is a physicist whose research explores the complex dynamics of material systems, particularly in two-phase flows and wetting phenomena. Her group focuses on microfluidics, fluid-structure interactions, and complex fluid flows, with applications ranging from chocolate moulding to airway reopening and flexible displays. Based at the Manchester Centre for Nonlinear Dynamics, her experimental work often uncovers surprising behaviour, driving new insights through combined experimentation and modelling.

Abstract
The flow of red blood cells (RBCs) in heterogeneous biological porous tissues such as the human placenta, remains poorly understood despite the essential role the microvasculature plays in maintaining overall health and functionality of tissues, blood flow and transport mechanisms. This is in great part because the usual description of blood as a simple fluid breaks down when the size of RBCs is similar to that of the vessel. In this study, we use a bespoke suspension of ultra-soft microcapsules with a poroelastic membrane, which have been previously shown to mimic the motion and large deformations of RBCs in simple conduits [1], in order to explore soft suspension flows in planar porous media. Our planar porous devices are Hele-Shaw channels, where the capsules are slightly confined within the channel depth, and in which we increase confinement by adding regular or disordered arrays of pillars. We perform experiments that relate the global resistance of the suspension flow through the porous media to the local distributions of capsule concentration and velocity as a function of volume fraction, capillary number Ca, the ratio of viscous to elastic forces, and geometry. We find that the flow patterns in Hele-Shaw channels and ordered porous media differ significantly from those in disordered porous media, where the presence of capsules promotes preferential paths and supports anomalous capsule dispersion. In contrast, the flows in ordered geometries develop intriguing shear-banding patterns as the volume fraction increases. Despite the complex microscopic dynamics of the suspension flow, we observe the emergence of similar scaling laws for the global flow resistance in both regular and disordered porous media as a function of Ca. We find that the scaling exponent decreases with increasing volume fraction because of cooperative capsule mechanisms, which yield relative stiffening of the system for increasing Ca.
 
[1] Chen et al. Soft Matter 19, 5249- 5261.
 
Thu, 06 Feb 2025
17:00
L3

Asymptotic theories: from finite structures to infinite fields

Philip Dittmann
(University of Manchester)
Abstract

I will discuss several interesting examples of classes of structures for which there is a sensible first-order theory of "almost all" structures in the class, for certain notions of "almost all". These examples include the classical theory of almost all finite graphs due to Glebskij-Kogan-Liogon'kij-Talanov and Fagin (and many more examples from finite model theory), as well as more recent examples from the model theory of infinite fields: the theory of almost all algebraic extensions and the universal/existential theory of almost all completions of a global field (both joint work with Arno Fehm). Interestingly, such asymptotic theories are sometimes quite well-behaved even when the base theories are not.

Fri, 28 Feb 2025

12:00 - 13:00
Quillen Room

Why Condensed Abelian Groups are Better Than Topological Abelian Groups

Jiacheng Tang
(University of Manchester)
Abstract

The category PAb of profinite abelian groups is an abelian category with many nice properties, which allows us to do most of standard homological algebra. The category PAb naturally embeds into the category TAb of topological abelian groups, but TAb is not abelian, nor does it have a satisfactory theory of tensor products. On the other hand, PAb also naturally embeds into the category CondAb of "condensed abelian groups", which is an abelian category with nice properties. We will show that the embedding of profinite modules into condensed modules (actually, into "solid modules") preserves usual homological notions such Ext and Tor, so that the condensed world might be a better place to study profinite modules than the topological world.

Thu, 21 Nov 2024
17:00

Generic differential automorphisms in positive characteristic

Omar León Sánchez
(University of Manchester)
Abstract

It is well known that the theory of differential-difference fields in characteristic zero has a model companion. Here by a differential-difference field I mean a field with a differential and a difference structure where the operators commute (in other words the difference structure is a differential-endomorphism). The theory DCFA_0 was studied in a series of papers by Bustamante. In this talk I will address the case of positive characteristic.

Thu, 06 Feb 2025

14:00 - 15:00
Lecture Room 3

Deflation Techniques for Finding Multiple Local Minima of a Nonlinear Least Squares Problem

Marcus Webb
(University of Manchester)
Abstract

Deflation is a technique to remove a solution to a problem so that other solutions to this problem can subsequently be found. The most prominent instance is deflation we see in eigenvalue solvers, but recent interest has been in deflation of rootfinding problems from nonlinear PDEs with many isolated solutions (spearheaded by Farrell and collaborators). 

 

In this talk I’ll show you recent results on deflation techniques for optimisation algorithms with many local minima, focusing on the Gauss—Newton algorithm for nonlinear least squares problems.  I will demonstrate advantages of these techniques instead of the more obvious approach of applying deflated Newton’s method to the first order optimality conditions and present some proofs that these algorithms will avoid the deflated solutions. Along the way we will see an interesting generalisation of Woodbury’s formula to least squares problems, something that should be more well known in Numerical Linear Algebra (joint work with Güttel, Nakatsukasa and Bloor Riley).

 

Main preprint: https://arxiv.org/abs/2409.14438

WoodburyLS preprint: https://arxiv.org/abs/2406.15120

Thu, 31 Oct 2024
16:00
L4

Re(Visiting) Large Language Models in Finance

Eghbal Rahimikia
(University of Manchester)
Abstract

This study introduces a novel suite of historical large language models (LLMs) pre-trained specifically for accounting and finance, utilising a diverse set of major textual resources. The models are unique in that they are year-specific, spanning from 2007 to 2023, effectively eliminating look-ahead bias, a limitation present in other LLMs. Empirical analysis reveals that, in trading, these specialised models outperform much larger models, including the state-of-the-art LLaMA 1, 2, and 3, which are approximately 50 times their size. The findings are further validated through a range of robustness checks, confirming the superior performance of these LLMs.

Thu, 09 May 2024

17:00 - 18:00
L3

Existentially closed valued difference fields

Jan Dobrowolski
(University of Manchester)
Abstract
I will report on a joint work in progress with F. Gallinaro and R. Mennuni in which we aim to understand the (non-elementary) class of existentially closed valued difference fields (of equicharacteristic zero). As our approach relies on our earlier results with Mennuni about automorphisms of ordered abelian groups, I will start by briefly overviewing those.
Thu, 18 Jan 2024

12:00 - 13:00
L3

Coupling rheology and segregation in granular flows

Nico Gray
(University of Manchester)
Further Information

Professor Nico Gray is based in the Department of Mathematics at the University of Manchester. 

This is from his personal website:

My research interests lie in understanding and modelling the flow of granular materials, in small scale experiments, industrial processes and geophysical flows.

[Mixing in a rotating drum][Flow past a rearward facing pyramid]

Current research is aimed at understanding fundamental processes such as the flow past obstacles, shock waves, dead-zones, fluid-solid phase transitions, particle size segregation and pattern formation. A novel and important feature of all my work is the close interplay of theory, numerical computation and experiment to investigate these nonlinear systems. I currently have three active experiments which are housed in two laboratories at the Manchester Centre for Nonlinear Dynamics. You can click on the videos and pictures as well as the adjacent toolbar to find out more about specific problems that I am interested in.

Abstract

During the last fifteen years, there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the μ(I)-rheology (where μ is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This talk details theoretical and numerical frameworks (based on OpenFOAM®) which unify these disconnected endeavours. Coupling the segregation with the flow, and vice versa, is not only vital for a complete theory of granular materials, but is also beneficial for developing numerical methods to handle evolving free surfaces. This general approach is based on the partially regularized incompressible μ(I)-rheology, which is coupled to a theory for gravity/shear-driven segregation (Gray & Ancey, J. Fluid Mech., vol. 678, 2011, pp. 353–588). These advection–diffusion–segregation equations describe the evolving concentrations of the constituents, which then couple back to the variable viscosity in the incompressible Navier–Stokes equations. A novel feature of this approach is that any number of differently sized phases may be included, which may have disparate frictional properties. The model is used to simulate the complex particle-size segregation patterns that form in a partially filled triangular rotating drum. There are many other applications of the theory to industrial granular flows, which are the second most common material used after fluids. The same processes also occur in geophysical flows, such as snow avalanches, debris flows and dense pyroclastic flows. Depth-averaged models, that go beyond the μ(I)-rheology, will also be derived to capture spontaneous self-channelization and levee formation, as well as complex segregation-induced flow fingering effects, which enhance the run-out distance of these hazardous flows.

 

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Tue, 27 Feb 2024

14:00 - 15:00
L5

Modular Reduction of Nilpotent Orbits

Jay Taylor
(University of Manchester)
Abstract

Suppose 𝐺𝕜 is a connected reductive algebraic 𝕜-group where 𝕜 is an algebraically closed field. If 𝑉𝕜 is a 𝐺𝕜-module then, using geometric invariant theory, Kempf has defined the nullcone 𝒩(𝑉𝕜) of 𝑉𝕜. For the Lie algebra 𝔤𝕜 = Lie(𝐺𝕜), viewed as a 𝐺𝕜-module via the adjoint action, we have 𝒩(𝔤𝕜) is precisely the set of nilpotent elements.

We may assume that our group 𝐺𝕜 = 𝐺 × 𝕜 is obtained by base-change from a suitable ℤ-form 𝐺. Suppose 𝑉 is 𝔤 = Lie(G) or its dual 𝔤* = Hom(𝔤, ℤ) which are both modules for 𝐺, that are free of finite rank as ℤ-modules. Then 𝑉 ⨂ 𝕜, as a module for 𝐺𝕜, is 𝔤𝕜 or 𝔤𝕜* respectively.

It is known that each 𝐺 -orbit 𝒪 ⊆ 𝒩(𝑉) contains a representative ξ ∈ 𝑉 in the ℤ-form. Reducing ξ one gets an element ξ𝕜 ∈ 𝑉𝕜 for any algebraically closed 𝕜. In this talk, we will explain two ways in which we might want ξ to have “good reduction” and how one can find elements with these properties. We will also discuss the relationship to Lusztig’s special orbits.

This is on-going joint work with Adam Thomas (Warwick).

Thu, 01 Jun 2023
17:00
L4

Cancelled: An effective mixed André-Oort result

Gareth Jones
(University of Manchester)
Abstract

Habegger showed that a subvariety of a fibre power of the Legendre family of elliptic curves is special if and only if it contains a Zariski-dense set of special points. I'll discuss joint work with Gal Binyamini, Harry Schmidt, and Margaret Thomas in which we use pfaffian methods to obtain an effective uniform version of Manin-Mumford for products of CM elliptic curves. Using this we then prove an effective version of Habegger's result.

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