In this talk, I will discuss a model mixture of active (self-propelled) and passive (diffusive) particles with non-reciprocal effective interactions (or forces that violate Newton’s third law). We derive the hydrodynamic PDE limit for the particle densities, which is not a Wasserstein gradient flow of any free energy, consistent with the microscopic model having non-equilibrium steady states. We study the emergence of collective behaviour, which includes phase separation and dynamical (travelling) steady states.

In this talk, I will describe a family of observables for 3D quantum Yang-Mills theory based on regularising connections with the YM heat flow. I will describe how these observables can be used to show that there is a unique renormalisation of the stochastic quantisation equation of YM in 3D that preserves gauge symmetries. This complements a recent result on the existence of such a renormalisation. Based on joint work with Hao Shen.

Property (T) is a rigidity property for group representations. It is generally very difficult to determine whether an infinite group has property (T) or not. It has long been known that a discrete group with a finite symmetric generating set has property (T) if and only if the group Laplacian is a positive element in the maximal group C*-algebra. However, this characterization has not been useful in addressing the question for automorphism groups of (non-abelian) free groups. In his 2016 paper, Ozawa proved that the phenomenon of 'positivity' of the group Laplacian is observed in the real group algebra, meaning that the Laplacian can be decomposed into a 'sum of squares'. This result transformed checking property (T) into a finite-dimensional condition that can be performed with the assistance of computers. In this talk, we will introduce property (T) and discuss Ozawa's result in detail.

I will talk about preliminaries in Arakelov geometry. Also, a historical overview will be provided. This talk will be the basis of a later talk about the theory of globally valued fields.

Multicomponent fluids are mixtures of distinct chemical species (i.e. components) that interact through complex physical processes such as cross-diffusion and chemical reactions. Additional physical phenomena often must be accounted for when modelling these fluids; examples include momentum transport, thermality and (for charged species) electrical effects. Despite the ubiquity of chemical mixtures in nature and engineering, multicomponent fluids have received almost no attention from the finite element community, with many important applications remaining out of reach from numerical methods currently available in the literature. This is in spite of the fact that, in engineering applications, these fluids often reside in complicated spatial regions -- a situation where finite elements are extremely useful! In this talk, we present a novel class of high-order finite element methods for simulating cross-diffusion and momentum transport (i.e. convection) in multicomponent fluids. Our model can also incorporate local electroneutrality when the species carry electrical charge, making the numerical methods particularly desirable for simulating liquid electrolytes in electrochemical applications. We discuss challenges that arise when discretising the partial differential equations of multicomponent flow, as well as some salient theoretical properties of our numerical schemes. Finally, we present numerical simulations involving (i) the microfluidic non-ideal mixing of hydrocarbons and (ii) the transient evolution of a lithium-ion battery electrolyte in a Hull cell electrode.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

Many matrices that arise in scientific computing and in data science have internal structure that can be exploited to accelerate computations. The focus in this talk will be on matrices that are either of low rank, or can be tessellated into a collection of subblocks that are either of low rank or are of small size. We will describe how matrices of this nature arise in the context of fast algorithms for solving PDEs and integral equations, and also in handling "kernel matrices" from computational statistics. A particular focus will be on randomized algorithms for obtaining data sparse representations of such matrices.

At the end of the talk, we will explore an unorthodox technique for discretizing elliptic PDEs that was designed specifically to play well with fast algorithms for dense structured matrices.

The study of periods of automorphic forms is a key theme in the Langlands program and has become an important tool to tackle various problems in Number Theory and Arithmetic Geometry.  For instance, Waldspurger formula and its generalisations have created a fertile ground for numerous arithmetic applications. In recent years, the conjectures of Sakellaridis and Venkatesh (and then Ben-Zvi, Sakellaridis, and Venkatesh) in the context of spherical varieties has led to a deeper understanding of automorphic periods and their relation to special values of $L$-functions. In this talk, I present work in progress aimed at looking at certain non-spherical cases. Precisely, I will describe a new integral representation of the degree 12 "exterior square x standard" $L$-function on generic cusp forms on $\mathrm{GU}(2,2) \times \mathrm{GL}(2)$ (or $\mathrm{GL}(4) \times \mathrm{GL}(2)$) and how it can be used to relate the non-vanishing of its central value to a certain cohomological period.  If time permits, I will describe how the same strategy applies to the case of $\mathrm{GSp}(6) \times \mathrm{GL}(2)$. This is joint work with Armando Gutierrez Terradillos.

I will sketch a proof of the statement in the title and outline how it is related to Ehrenfeucht–Fraïssé games on C*-algebras. I will provide the relevant background on C*-algebras (and descriptive set theory) and explain how to construct a standard Borel category X that can play a role of their `moduli'. The theorem from the title is an application of the compactness theorem, for a suitable first-order theory whose models correspond to functors from X. If time permits, I will mention some related problems and connections with conceptual completeness for infinitary logic. This talk is based on several discussions with Ehud Hrushovski, Jennifer Pi, Mira Tartarotti, and Stuart White after a reading group on the paper "Games on AF-algebras" by Ben De Bondt, Andrea Vaccaro, Boban Velickovic and Alessandro Vignati.

The question can be formulated as a statistical hypothesis asserting that the distribution of the shapes of closed curves representing outlines of cell nuclei in a spatial domain is independent of the distribution of their locations. The key challenge in developing a procedure to test the hypothesis from a sample of spatially indexed curves (e.g. from an image) lies in how symmetries in the data are accounted for: shape of a curve is a property that is invariant to similarity transformations and reparameterization, and the shape space is thus an infinite-dimensional quotient space. Starting with a convenient geometry for the shape space developed over the last few years, I will discuss dependence measures and their estimates for spatial point processes with shape-valued marks, and demonstrate their use in testing for spatial independence of marks in a breast cancer application.  

The Morse-Conley complex is a central object in information compression in topological data analysis, as well as the application of homological algebra to analysing dynamical systems. Given a poset-graded chain complex, its Morse-Conley complex is the optimal chain-homotopic reduction of the initial complex that respects the poset grading.  In this work, we give a purely algebraic derivation of the Morse-Conley complex using homological perturbation theory. Unlike Forman’s discrete Morse theory for cellular complexes, our algebraic formulation does not require the computation of acyclic partial matchings of cells.  We show how this algebraic perspective also yields efficient algorithms for computing the Conley complex.  This talk features joint work with Álvaro Torras Casas and Ulrich Pennig in "Computing Connection Matrices of Conley Complexes via Algebraic Morse Theory" (arXiv:2503.09301). 
 

This session, led by the Counselling Service,  will guide you through a CBT informed understanding of anxiety, which may arise about exams. The session includes:

• Psychoeducation - what is happening in the brain and body when we worry about exams
• Paradox of worry – how more pressure, makes studying less likely
• Experiential exercises – management strategies to maintain focus and engagement
• Takeaway tools – a collection of managing stress skills for self-guided practice
• Practical tips – enhance your exam preparation

We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with Itô noise, for particle systems exhibiting mean-field interactions both in the drift and the noise terms. Global existence and uniqueness of solutions to the corresponding SPDEs are established via the variational approach to SPDEs. To estimate the weak error, we employ the Kolmogorov equation technique on the space of probability measures. This work generalizes previous results for independent Brownian particles — where Laplace duality was used. In particular, we recover the same weak error rate as in that setting. This paper builds on joint work with X. Ji., H. Kremp and  N.  Perkowski.

I will present some contributions to the quasiisometry classification of solvable Lie groups of exponential growth that we obtain using sublinear bilipschitz equivalences, which are generalized quasiisometries. This is joint work with Ido Grayevsky.

Given a Hamiltonian circle action on a symplectic manifold, Fukaya and Teleman tell us that we can relate the equivariant Fukaya category to the Fukaya category of a symplectic reduction.  Yanki Lekili and I have some conjectures that extend this story - in certain special examples - to singular values of the moment map. I'll also explain the mirror symmetry picture that we use to support our conjectures, and how we interpret our claims in Teleman's framework of `topological group actions' on categories.

The landmark completion of the Elliott classification program for unital separable simple nuclear C*-algebras saw three regularity properties rise to prominence: Z-stability, a C*-algebraic analogue of von Neumann algebras' McDuffness; finite nuclear dimension, an operator algebraic version of having finite Lebesgue dimension; and strict comparison, a generalization of tracial comparison in II_1 factors. Given their relevance to classification, most of the investigations into their interplay have focused on the simple nuclear case.

 The purpose of this talk is to advertise the general study of these properties and discuss their applications both within and outside operator algebras. Concretely, I will explain how characterizing when certain twisted group C*-algebras are Z-stable can provide new partial solutions to a well-known problem in generalized time-frequency analysis; this is joint work with U. Enstad. If time allows, I will also briefly discuss how a different incarnation of tracial comparison (finite radius of comparison) for non-commutative tori relates to the existence of smooth Gabor frames; this last part is joint work with U. Enstad and also H. Thiel.

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A fundamental question in neuroscience is to understand how information is represented in the activity of  tens of thousands of neurons in the brain. Towards this end, low-rank matrix and tensor decompositions are commonly used to identify correlates of behavior in high-dimensional neural data. In this talk I will first present a novel tensor decomposition based on the slice rank which is able to disentangle mixed modes of covarying patterns in data tensors. Second, to compliment this statistical approach, I will present our recent dynamical systems modelling of neural activity over learning. Rather than factorizing data tensors themselves, we instead fit a dynamical system to the data, while constraining the tensor of parameters to be low rank. Together these projects highlight how applications in neural data can inspire new classes of low-rank models.

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Sard’s theorem asserts that the set of critical values of a smooth map from one Euclidean space to another one has measure zero. A version of this result for infinite-dimensional Banach manifolds was proven by Smale for maps with Fredholm differential. However, when the domain is infinite dimensional and the range is finite dimensional, the result is not true – even under the assumption that the map is “polynomial” – and a general theory is still lacking. In this seminar, I will provide sharp quantitative criteria for the validity of Sard’s theorem in this setting, obtained combining a functional analysis approach with new tools in semialgebraic geometry. As an application, I will present new results on the Sard conjecture in sub-Riemannian geometry. Based on a joint work with A. Lerario and L. Rizzi.

Parameters in mathematical models are often impossible to determine fully or accurately, and are hence subject to uncertainty. By modelling the input parameters as stochastic processes, it is possible to quantify the uncertainty in the model outputs. 

In this talk, we employ the multilevel Monte Carlo (MLMC) method to compute expected values of quantities of interest related to partial differential equations with random coefficients. We make use of the circulant embedding method for sampling from the coefficient, and to further improve the computational complexity of the MLMC estimator, we devise and implement the smoothing technique integrated into the circulant embedding method. This allows to choose the coarsest mesh on the  first level of MLMC independently of the correlation length of the covariance function of the random  field, leading to considerable savings in computational cost.

 

Please note; this talk is hosted by Rutherford Appleton Laboratory, Harwell Campus, Didcot, OX11 0QX

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