Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Wed, 28 Sep 2022 09:00 -
Sun, 30 Jun 2024 17:00
Mathematical Institute

Cascading Principles - a major mathematically inspired exhibition by Conrad Shawcross - extended until June 2024

Further Information

Oxford Mathematics is delighted to be hosting one of the largest exhibitions by the artist Conrad Shawcross in the UK. The exhibition, Cascading Principles: Expansions within Geometry, Philosophy, and Interference, brings together over 40 of Conrad's mathematically inspired works from the past seventeen years. Rather than in a gallery, they are placed in the working environment of the practitioners of the subject that inspired them, namely mathematics.

Conrad Shawcross models scientific thought and reasoning within his practice. Drawn to mathematics, physics, and philosophy from the early stages of his artistic career, Shawcross combines these disciplines in his work. He places a strong emphasis on the nature of matter, and on the relativity of gravity, entropy, and the nature of time itself. Like a scientist working in a laboratory, he conceives each work as an experiment. Modularity is key to his process and many works are built from a single essential unit or building block. If an atom or electron is a basic unit for physicists, his unit is the tetrahedron.

Unlike other shapes, a tetrahedron cannot tessellate with itself. It cannot cover or form a surface through its repetition - one tetrahedron is unable to fit together with others of its kind. Whilst other shapes can sit alongside one another without creating gaps or overlapping, tetrahedrons cannot resolve in this way. Shawcross’ Schisms are a perfect demonstration of this failure to tessellate. They bring twenty tetrahedrons together to form a sphere, which results in a deep crack and ruptures that permeate its surface. This failure of its geometry means that it cannot succeed as a scientific model, but it is this very failure that allows it to succeed as an art work, the cracks full of broad and potent implications.

The show includes all Conrad's manifold geometric and philosophical investigations into this curious, four-surfaced, triangular prism to date. These include the Paradigms, the Lattice Cubes, the Fractures, the Schisms, and The Dappled Light of the Sun. The latter was first shown in the courtyard of the Royal Academy and subsequently travelled all across the world, from east to west, China to America.

The show also contains the four Beacons. Activated like a stained-glass window by the light of the sun, they are composed of two coloured, perforated disks moving in counter rotation to one another, patterning the light through the non-repeating pattern of holes, and conveying a message using semaphoric language. These works are studies for the Ramsgate Beacons commission in Kent, as part of Pioneering Places East Kent.

The exhibition Cascading Principles: Expansions within Geometry, Philosophy, and Interference is curated by Fatoş Üstek, and is organised in collaboration with Oxford Mathematics. 

The exhibition is open 9am-5pm, Monday to Friday. Some of the works are in the private part of the building and we shall be arranging regular tours of that area. If you wish to join a tour please email @email.

The exhibition runs until 30 June 2024. You can see and find out more here.

Watch the four public talks centred around the exhibition (featuring Conrad himself).

The exhibition is generously supported by our longstanding partner XTX Markets.

Images clockwise from top left of Schism, Fracture, Paradigm and Axiom

Schism Fracture

Axiom Paradigm

Wed, 24 Apr 2024
16:00
L6

Harmonic maps and virtual properties of mapping class groups

Ognjen Tošić
(University of Oxford)
Abstract

It is a standard result that mapping class groups of high genus do not surject the integers. This is easily shown by computing the abelianization of the mapping class group using a presentation. Once we pass to finite index subgroups, this becomes a conjecture of Ivanov. More generally, we can ask which groups admit epimorphisms from finite index subgroups of the mapping class group. In this talk, I will present a geometric approach to this question, using harmonic maps, and explain some recent results.

Thu, 25 Apr 2024

12:00 - 13:00
L3

Static friction models, buckling and lift-off for a rod deforming on a cylinder

Rehan Shah
(Queen Mary, University of London)

The join button will be published 30 minutes before the seminar starts (login required).

Further Information

Dr. Rehan Shah, Lecturer (Assistant Professor) in Mathematics and Engineering Education, Queen Mary University of London

Abstract

We develop a comprehensive geometrically-exact theory for an end-loaded elastic rod constrained to deform on a cylindrical surface. By viewing the rod-cylinder system as a special case of an elastic braid, we are able to obtain all forces and moments imparted by the deforming rod to the cylinder as well as all contact reactions. This framework allows us to give a complete treatment of static friction consistent with force and moment balance. In addition to the commonly considered model of hard frictionless contact, we analyse two friction models in which the rod, possibly with intrinsic curvature, experiences either lateral or tangential friction. As applications of the theory we study buckling of the constrained rod under compressive and torsional loads, finding critical loads to depend on Coulomb-like friction parameters, as well as the tendency of the rod to lift off the cylinder under further loading. The cylinder can also have arbitrary orientation relative to the direction of gravity. The cases of a horizontal and vertical cylinder, with gravity having only a lateral or axial component, are amenable to exact analysis, while numerical results map out the transition in buckling mechanism between the two extremes. Weight has a stabilising effect for near-horizontal cylinders, while for near-vertical cylinders it introduces the possibility of buckling purely due to self-weight. Our results are relevant for many engineering and medical applications in which a slender structure winds inside or outside a cylindrical boundary.


 

Thu, 25 Apr 2024

14:00 - 15:00
Lecture Room 3

ESPIRA: Estimation of Signal Parameters via Iterative Rational Approximation

Nadiia Derevianko
(University of Göttingen)
Abstract

We introduce a new method - ESPIRA (Estimation of Signal Parameters via Iterative Rational Approximation) \cite{DP22,  DPP21} - for the recovery of complex exponential  sums
$$
f(t)=\sum_{j=1}^{M} \gamma_j \mathrm{e}^{\lambda_j t},
$$
that are determined by a finite number of parameters: the order $M$, weights $\gamma_j \in \mathbb{C} \setminus \{0\}$ and nodes  $\mathrm{e}^{\lambda_j} \in \mathbb{C}$ for $j=1,...,M$.  Our new recovery procedure is based on the observation that Fourier coefficients (or DFT coefficients) of exponential sums have a special rational structure.  To  reconstruct this structure in a stable way we use the AAA algorithm  proposed by Nakatsukasa et al.   We show that ESPIRA can be interpreted as a matrix pencil method applied to Loewner matrices. 

During the talk we will demonstrate that ESPIRA outperforms Prony-like methods such as ESPRIT and MPM for noisy data and for signal approximation by short exponential sums.  

 

Bibliography
N. Derevianko,  G.  Plonka, 
Exact reconstruction of extended exponential sums using rational approximation of their Fourier coefficients, Anal.  Appl.,  20(3),  2022,  543-577.


N. Derevianko,  G. Plonka,  M. Petz, 
From ESPRIT to ESPIRA: Estimation of signal parameters by iterative rational approximation,   IMA J. Numer. Anal.,  43(2),  2023, 789--827.  


Y. Nakatsukasa, O. Sète,   L.N. Trefethen,  The AAA algorithm for rational approximation.
SIAM J. Sci. Comput., 40(3),   2018,  A1494–A1522.  

Thu, 25 Apr 2024
16:00
Lecture Room 4, Mathematical Institute

The leading constant in Malle's conjecture

Dan Loughran
(University of Bath)
Abstract

A conjecture of Malle predicts an asymptotic formula for the number of number fields with given Galois group and bounded discriminant. Malle conjectured the shape of the formula but not the leading constant. We present a new conjecture on the leading constant motivated by a version for algebraic stacks of Peyre's constant from Manin's conjecture. This is joint work with Tim Santens.

Thu, 25 Apr 2024
16:00
L4

Reinforcement Learning in near-continuous time for continuous state-action spaces

Dr Lorenzo Croissant
(CEREMADE, Université Paris-Dauphine)
Further Information

Please join us for reshments outside the lecture room from 1530.

Abstract

We consider the reinforcement learning problem of controlling an unknown dynamical system to maximise the long-term average reward along a single trajectory. Most of the literature considers system interactions that occur in discrete time and discrete state-action spaces. Although this standpoint is suitable for games, it is often inadequate for systems in which interactions occur at a high frequency, if not in continuous time, or those whose state spaces are large if not inherently continuous. Perhaps the only exception is the linear quadratic framework for which results exist both in discrete and continuous time. However, its ability to handle continuous states comes with the drawback of a rigid dynamic and reward structure.

        This work aims to overcome these shortcomings by modelling interaction times with a Poisson clock of frequency $\varepsilon^{-1}$ which captures arbitrary time scales from discrete ($\varepsilon=1$) to continuous time ($\varepsilon\downarrow0$). In addition, we consider a generic reward function and model the state dynamics according to a jump process with an arbitrary transition kernel on $\mathbb{R}^d$. We show that the celebrated optimism protocol applies when the sub-tasks (learning and planning) can be performed effectively. We tackle learning by extending the eluder dimension framework and propose an approximate planning method based on a diffusive limit ($\varepsilon\downarrow0$) approximation of the jump process.

        Overall, our algorithm enjoys a regret of order $\tilde{\mathcal{O}}(\sqrt{T})$ or $\tilde{\mathcal{O}}(\varepsilon^{1/2} T+\sqrt{T})$ with the approximate planning. As the frequency of interactions blows up, the approximation error $\varepsilon^{1/2} T$ vanishes, showing that $\tilde{\mathcal{O}}(\sqrt{T})$ is attainable in near-continuous time.

Thu, 25 Apr 2024
17:00
Lecture Theatre 1

The Ubiquity of Braids - Tara Brendle

Tara Brendle
(University of Glasgow)
Further Information

What do maypole dancing, grocery delivery, and the quadratic formula all have in common? The answer is: braids! In this talk Tara will explore how the ancient art of weaving strands together manifests itself in a variety of modern settings, both within mathematics and in our wider culture.    

Tara Brendle is a Professor of Mathematics in the School of Mathematics & Statistics at the University of Glasgow. Her research lies in the area of geometric group theory, at the interface between algebra and topology. She is co-author of 'Braids: A Survey', appearing in 'The Handbook of Knot Theory'.

Please email @email to register to attend in person.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Thursday 16 May at 5-6pm and any time after (no need to register for the online version).

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Banner for event with details against backdrop of braids
Thu, 25 Apr 2024

17:00 - 18:00
L3

Bi-interpretability and elementary definability of Chevalley groups

Elena Bunina
(Bar-Ilan University)
Abstract

We prove that any adjoint Chevalley group over an arbitrary commutative ring is regularly bi-interpretable with this ring. The same results hold for central quotients of arbitrary Chevalley groups and for Chevalley groups with bounded generation.
Also, we show that the corresponding classes of Chevalley groups (or their central quotients) are elementarily definable and even finitely axiomatizable.

Fri, 26 Apr 2024

12:00 - 13:00
L3

On Spectral Data for (2,2) Berry Connections, Difference Equations, and Equivariant Quantum Cohomology

Daniel Zhang
(St John's College)
Abstract

We study supersymmetric Berry connections of 2d N = (2,2) gauged linear sigma models (GLSMs) quantized on a circle, which are periodic monopoles, with the aim to provide a fruitful physical arena for recent mathematical constructions related to the latter. These are difference modules encoding monopole solutions via a Hitchin-Kobayashi correspondence established by Mochizuki. We demonstrate how the difference modules arises naturally by studying the ground states as the cohomology of a one-parameter family of supercharges. In particular, we show how they are related to one kind of monopole spectral data, a deformation of the Cherkis–Kapustin spectral curve, and relate them to the physics of the GLSM. By considering states generated by D-branes and leveraging the difference modules, we derive novel difference equations for brane amplitudes. We then show that in the conformal limit, these degenerate into novel difference equations for hemisphere partition functions, which are exactly calculable. When the GLSM flows to a nonlinear sigma model with Kähler target X, we show that the difference modules are related to deformations of the equivariant quantum cohomology of X.

Fri, 26 Apr 2024

14:00 - 15:00
L3

Polynomial dynamical systems and reaction networks: persistence and global attractors

Professor Gheorghe Craciun
(Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison)
Abstract
The mathematical analysis of global properties of polynomial dynamical systems can be very challenging (for example: the second part of Hilbert’s 16th problem about polynomial dynamical systems in 2D, or the analysis of chaotic dynamics in the Lorenz system).
On the other hand, any dynamical system with polynomial right-hand side can essentially be regarded as a model of a reaction network. Key properties of reaction systems are closely related to fundamental results about global stability in classical thermodynamics. For example, the Global Attractor Conjecture can be regarded as a finite dimensional version of Boltzmann’s H-theorem. We will discuss some of these connections, as well as the introduction of toric differential inclusions as a tool for proving the Global Attractor Conjecture.
We will also discuss some implications for the more general Persistence Conjecture (which says that solutions of weakly reversible systems cannot "go extinct"), as well as some applications to biochemical mechanisms that implement cellular homeostasis. 
 


 

Fri, 26 Apr 2024

15:00 - 16:00
L5

Lagrangian Hofer metric and barcodes

Patricia Dietzsch
(ETH Zurich)

The join button will be published 30 minutes before the seminar starts (login required).

Further Information

Patricia is a Postdoc in Mathematics at ETH Zürich, having recently graduated under the supervision of Prof. Paul Biran.

Patricia is working in the field of symplectic topology. Some key words in her current research project are: Dehn twist, Seidel triangle, real Lefschetz fibrations and Fukaya categories. Besides this, she is a big fan of Hofer's metric, expecially of the Lagrangian Hofer metric and the many interesting open questions related to it. 

Abstract

 

This talk discusses an application of Persistence Homology in the field of Symplectic Topology. A major tool in Symplectic Topology are Floer homology groups. These are algebraic invariants that can be associated to pairs of Lagrangian submanifolds. A richer algebraic invariant can be obtained using 
filtered Lagrangian Floer theory. This gives rise to a persistence module and a barcode. Its bar lengths are invariants for the pair of Lagrangians. 
 
We explain how these numbers can be used to estimate the Lagrangian Hofer distance between the two Lagrangians: It is a well-known stability result  that the bar lengths are lower bounds of the distance. We show how to get an upper bound of the distance in terms of the bar lengths in the special case of equators in a cylinder.
Fri, 26 Apr 2024
15:30
Large Lecture Theatre, Department of Statistics, University of Oxford

Inaugural Green Lecture: Tackling the hidden costs of computational science: GREENER principles for environmentally sustainable research

Dr Loïc Lannelongue, Heart and Lung Research Institute, University of Cambridge and the Cambridge-Baker Systems Genomics Initiative
(Department of Statistics, University of Oxford)
Further Information

PLEASE REGISTER FOR THE EVENT HERE: https://www.stats.ox.ac.uk/events/inaugural-green-lecture-dr-loic-lanne…

Dr Loïc Lannelongue is a Research Associate in Biomedical Data Science in the Heart and Lung Research Institute at the University of Cambridge, UK, and the Cambridge-Baker Systems Genomics Initiative. He leads the Green Algorithms project, an initiative promoting more environmentally sustainable computational science. His research interests also include radiogenomics, i.e. combining medical imaging and genetic information with machine learning to better understand and treat cardiovascular diseases. He obtained an MSc from ENSAE, the French National School of Statistics, and an MSc in Statistical Science from the University of Oxford, before doing his PhD in Health Data Science at the University of Cambridge. He is a Software Sustainability Institute Fellow, a Post-doctoral Associate at Jesus College, Cambridge, and an Associate Fellow of the Higher Education Academy.

Abstract

From genetic studies and astrophysics simulations to statistical modelling and AI, scientific computing has enabled amazing discoveries and there is no doubt it will continue to do so. However, the corresponding environmental impact is a growing concern in light of the urgency of the climate crisis, so what can we all do about it? Tackling this issue and making it easier for scientists to engage with sustainable computing is what motivated the Green Algorithms project. Through the prism of the GREENER principles for environmentally sustainable science, we will discuss what we learned along the way, how to estimate the impact of our work and what levers scientists and institutions have to make their research more sustainable. We will also debate what hurdles exist and what is still needed moving forward.

 

Fri, 26 Apr 2024

18:00 - 21:00
Christ Church College

Moriarty Lecture & OCIAM Dinner

Professor Paul C Bressloff
(University of Utah)
Further Information
6.00pm Moriarty Lecture 
               Given by Professor Paul Bresslof (University of Utah & Imperial College)
               Michael Dummett Lecture Theatre.
7.00pm Drinks reception
7.45pm OCIAM Annual Dinner
Mon, 29 Apr 2024

11:00 - 12:00
Lecture Room 3

Deep Gaussian processes: theory and applications

Aretha Teckentrup
(University of Edinburgh)
Further Information

Please note that this seminar starts at 11am and finishes at 12pm. 

Abstract

Deep Gaussian processes have proved remarkably successful as a tool for various statistical inference tasks. This success relates in part to the flexibility of these processes and their ability to capture complex, non-stationary behaviours. 

In this talk, we will introduce the general framework of deep Gaussian processes, in which many examples can be constructed, and demonstrate their superiority in inverse problems including computational imaging and regression.

 We will discuss recent algorithmic developments for efficient sampling, as well as recent theoretical results which give crucial insight into the behaviour of the methodology.

 

Mon, 29 Apr 2024
15:30
Lecture Room 3

Sharp interface limit of 1D stochastic Allen-Cahn equation in full small noise regime

Prof. Weijun Xu
(Beijing International Center for Mathematical Research)
Abstract

We consider the sharp interface limit problem for 1D stochastic Allen-Cahn equation, and extend a classic result by Funaki to the full small noise regime. One interesting point is that the notion of "small noise" turns out to depend on the topology one uses. The main new idea in the proof is the construction of a series of functional correctors, which are designed to recursively cancel out potential divergences. At a technical level, in order to show these correctors are well behaved, we also develop a systematic decomposition of functional derivatives of the deterministic Allen-Cahn flow of all orders, which might have its own interest.
Based on a joint work with Wenhao Zhao (EPFL) and Shuhan Zhou (PKU).

Mon, 29 Apr 2024
16:00
L2

TBC

Fred Tyrrell
(University of Bristol)
Abstract

TBC

Tue, 30 Apr 2024
11:00
L5

A priori bounds for subcritical fractional $\phi^4$ on $T^3$

Salvador Cesar Esquivel Calzada
(Universitat Munster)
Abstract

We study the stochastic quantisation for the fractional $\varphi^4$ theory. The model has been studied by Brydges, Mitter and Scopola in 2003 as a natural extension of $\phi^4$ theories to fractional sub-critical dimensions. The stochastic quantisation equation is given by the (formal) SPDE 

\[

(\partial_t + (-\Delta)^{s}) \varphi = - \lambda \varphi^3 + \xi

\]

where $\xi$ is a space-time white noise over the three dimensional torus. The equation is sub-critical for $s > \frac{3}{4}$.

 

We derive a priori estimates in the full sub-critical regime $s>\frac{3}{4}$. These estimates rule out explosion in finite time and they imply the existence of an invariant measure with a standard Krylov-Bogoliubov argument. 

Our proof is based on the strategy developed for the parabolic case $s=1$ in [Chandra, Moinat, Weber, ARMA 2023]. In order to implement this strategy here, a new Schauder estimate for the fractional heat operator is developed. Additionally, several algebraic arguments from [Chandra, Moinat, Weber, ARMA 2023] are streamlined significantly. 

 

This is joint work with Hendrik Weber (Münster). 

Tue, 30 Apr 2024

14:00 - 15:00
tbc

Unipotent Representations and Mixed Hodge Modules

Lucas Mason-Brown
((Oxford University))
Abstract

One of the oldest open problems in representation theory is to classify the irreducible unitary representations of a semisimple Lie group G_R. Such representations play a fundamental role in harmonic analysis and the Langlands program and arise in physics as the state space of quantum mechanical systems in the presence of G_R-symmetry. Most unitary representations of G_R are realized, via some kind of induction, from unitary representations of proper Levi subgroups. Thus, the major obstacle to understanding the unitary dual of G_R is identifying the "non-induced" unitary representations of G_R. In previous joint work with Losev and Matvieievskyi, we have proposed a general construction of these non-induced representations, which we call "unipotent" representations of G_R. Unfortunately, the methods we employ do not provide a proof that these representations are unitary. In this talk, I will explain how one can apply Saito's theory of mixed Hodge modules to overcome this difficulty, giving a uniform proof of the unitarity of all unipotent representations. This is joint work in progress with Dougal Davis

Tue, 30 Apr 2024

14:00 - 15:00
L4

The rainbow saturation number

Natalie Behague
(University of Warwick)
Abstract

The saturation number of a graph is a famous and well-studied counterpoint to the Turán number, and the rainbow saturation number is a generalisation of the saturation number to the setting of coloured graphs. Specifically, for a given graph $F$, an edge-coloured graph is $F$-rainbow saturated if it does not contain a rainbow copy of $F$, but the addition of any non-edge in any colour creates a rainbow copy of $F$. The rainbow saturation number of $F$ is the minimum number of edges in an $F$-rainbow saturated graph on $n$ vertices. Girão, Lewis, and Popielarz conjectured that, like the saturation number, for all $F$ the rainbow saturation number is linear in $n$. I will present our attractive and elementary proof of this conjecture, and finish with a discussion of related results and open questions.

Tue, 30 Apr 2024
15:00
L6

Graph products and measure equivalence

Camille Horbez
Abstract

Measure equivalence was introduced by Gromov as a measure-theoretic analogue to quasi-isometry between finitely generated groups. In this talk I will present measure equivalence classification results for right-angled Artin groups, and more generally graph products. This is based on joint works with Jingyin Huang and with Amandine Escalier. 

Tue, 30 Apr 2024
15:30
C6

Stability of strong Cayley fibrations

Gilles Englebert
(Oxford)
Abstract

Please note unusual day and room. 

Motivated by the SYZ conjecture, it is expected that $G_2$ and Spin(7)-manifolds also admit calibrated fibrations. One potential way to construct examples is via gluing of complex fibrations, as in the program of Kovalev. For this to succeed we need that the fibration property is stable under deformation of the ambient Spin(7)-structure. Here the main difficulty lies in the analysis of the singular fibres. In this talk I will present a stability result for fibrations with conically singular Cayleys modeled on the complex cone $\{x^2 + y^2 + z^2 = 0\}$ in ${\mathbb C}^3$.

Tue, 30 Apr 2024
16:00
L6

TBA

Brad Rodgers (Queen's University, Kingston)
Abstract

TBA

Tue, 30 Apr 2024

16:00 - 17:00
C2

Equivariantly O2-stable actions: classification and range of the invariant

Matteo Pagliero
(KU Leuven)
Abstract

One possible version of the Kirchberg—Phillips theorem states that simple, separable, nuclear, purely infinite C*-algebras are classified by KK-theory. In order to generalize this result to non-simple C*-algebras, Kirchberg first restricted his attention to those that absorb the Cuntz algebra O2 tensorially. C*-algebras in this class carry no KK-theoretical information in a strong sense, and they are classified by their ideal structure alone. It should be mentioned that, although this result is in Kirchberg’s work, its full proof was first published by Gabe. In joint work with Gábor Szabó, we showed a generalization of Kirchberg's O2-stable theorem that classifies G-C*-algebras up to cocycle conjugacy, where G is any second-countable, locally compact group. In our main result, we assume that actions are amenable, sufficiently outer, and absorb the trivial action on O2 up to cocycle conjugacy. In very recent work, I moreover show that the range of the classification invariant, consisting of a topological dynamical system over primitive ideals, is exhausted for any second-countable, locally compact group.

In this talk, I will recall the classification of O2-stable C*-algebras, and describe their classification invariant. Subsequently, I will give a short introduction to the C*-dynamical working framework and present the classification result for equivariant O2-stable actions. Time permitting, I will give an idea of how one can build a C*-dynamical system in the scope of our classification with a prescribed invariant. 

Thu, 02 May 2024

11:00 - 12:00
C3

TBA

Stefan Ludwig
(Ecole Normale Superieure)
Abstract

TBA

Thu, 02 May 2024

12:00 - 13:00
L3

Path integral formulation of stochastic processes

Steve Fitzgerald
(University of Leeds)

The join button will be published 30 minutes before the seminar starts (login required).

Abstract

Traditionally, stochastic processes are modelled one of two ways: a continuum Fokker-Planck approach, where a PDE is solved to determine the time evolution of the probability density, or a Langevin approach, where the SDE describing the system is sampled, and multiple simulations are used to collect statistics. There is also a third way: the functional or path integral. Originally developed by Wiener in the 1920s to model Brownian motion, path integrals were famously applied to quantum mechanics by Feynman in the 1950s. However, they also have much to offer classical stochastic processes (and statistical physics).  

In this talk I will introduce the formalism at a physicist’s level of rigour, and focus on determining the dominant contribution to the path integral when the noise is weak. There exists a remarkable correspondence between the most-probable stochastic paths and Hamiltonian dynamics in an effective potential [1,2,3]. I will then discuss some applications, including reaction pathways conditioned on finite time [2]. We demonstrate that the most probable pathway at a finite time may be very different from the usual minimum energy path used to calculate the average reaction rate. If time permits, I will also discuss the extremely nonlinear crystal dislocation response to applied stress [4].  

[1] Ge, Hao, and Hong Qian. Int. J. Mod. Phys. B 26.24 1230012 (2012)     

[2] Fitzgerald, Steve, et al. J. Chem. Phys. 158.12 (2023).

[3] Honour, Tom and Fitzgerald, Steve. in press J. Phys. A (2024)

[4] Fitzgerald, Steve. Sci. Rep. 6 (1) 39708 (2016)

 

Thu, 02 May 2024

14:00 - 15:00
Lecture Room 3

Mathematics: key enabling technology for scientific machine learning

Wil Schilders
(TU Eindhoven)
Abstract

Artificial Intelligence (AI) will strongly determine our future prosperity and well-being. Due to its generic nature, AI will have an impact on all sciences and business sectors, our private lives and society as a whole. AI is pre-eminently a multidisciplinary technology that connects scientists from a wide variety of research areas, from behavioural science and ethics to mathematics and computer science.

Without downplaying the importance of that variety, it is apparent that mathematics can and should play an active role. All the more so as, alongside the successes of AI, also critical voices are increasingly heard. As Robert Dijkgraaf (former director of the Princeton Institute of Advanced Studies) observed in May 2019: ”Artificial intelligence is in its adolescent phase, characterised by trial and error, self-aggrandisement, credulity and lack of systematic understanding.” Mathematics can contribute to the much-needed systematic understanding of AI, for example, greatly improving reliability and robustness of AI algorithms, understanding the operation and sensitivity of networks, reducing the need for abundant data sets, or incorporating physical properties into neural networks needed for super-fast and accurate simulations in the context of digital twinning.

Mathematicians absolutely recognize the potential of artificial intelligence, machine learning and (deep) neural networks for future developments in science, technology and industry. At the same time, a sound mathematical treatment is essential for all aspects of artificial intelligence, including imaging, speech recognition, analysis of texts or autonomous driving, implying it is essential to involve mathematicians in all these areas. In this presentation, we highlight the role of mathematics as a key enabling technology within the emerging field of scientific machine learning. Or, as I always say: ”Real intelligence is needed to make artificial intelligence work.”

 

Thu, 02 May 2024
16:00
L4

Robust Duality for multi-action options with information delay

Dr Anna Aksamit
(University of Sydney)
Further Information

Please join us for reshments outside the lecture room from 1530.

Abstract

We show the super-hedging duality for multi-action options which generalise American options to a larger space of actions (possibly uncountable) than {stop, continue}. We put ourselves in the framework of Bouchard & Nutz model relying on analytic measurable selection theorem. Finally we consider information delay on the action component of the product space. Information delay is expressed as a possibility to look into the future in the dual formulation. This is a joint work with Ivan Guo, Shidan Liu and Zhou Zhou.

Thu, 02 May 2024
16:00
Lecture Room 4, Mathematical Institute

Twisted correlations of the divisor function via discrete averages of $\operatorname{SL}_2(\mathbb{R})$ Poincaré series

Jori Merikoski
(University of Oxford)
Abstract

The talk is based on joint work with Lasse Grimmelt. We prove a theorem that allows one to count solutions to determinant equations twisted by a periodic weight with high uniformity in the modulus. It is obtained by using spectral methods of $\operatorname{SL}_2(\mathbb{R})$ automorphic forms to study Poincaré series over congruence subgroups while keeping track of interactions between multiple orbits. This approach offers increased flexibility over the widely used sums of Kloosterman sums techniques. We give applications to correlations of the divisor function twisted by periodic functions and the fourth moment of Dirichlet $L$-functions on the critical line.

Fri, 03 May 2024

14:00 - 15:00
L3

Epidemiological modelling with behavioural considerations and to inform policy making

Dr Edward Hill
(Dept of Mathematics University of Warwick)
Abstract
Many problems in epidemiology are impacted by behavioural dynamics, whilst in response to health emergencies prompt analysis and communication of findings is required to be of use to decision makers. Both instances are likely to benefit from interdisciplinary approaches. This talk will feature two examples, one with a public health focus and one with a veterinary health focus.
 
In the first part, I will summarise work originally conducted in late 2020 that was contributed to Scientific Pandemic Influenza Group on Modelling, Operational sub-group (SPI-M-O) of SAGE (Scientific Advisory Group for Emergencies) on Christmas household bubbles in England. This was carried out in response to a policy involving a planned easing of restrictions in England between 23–27 December 2020, with Christmas bubbles allowing people from up to three households to meet throughout the holiday period. Using a household model and computational simulation, we estimated the epidemiological impact of both this and alternative bubble strategies that allowed extending contacts beyond the immediate household.

(Associated paper: Modelling the epidemiological implications for SARS-CoV-2 of Christmas household bubbles in England in December 2020. https://doi.org/10.1016/j.jtbi.2022.111331)

In the second part, I will present a methodological pipeline developed to generate novel quantitative data on farmer beliefs with respect to disease management, process the data into a form amenable for use in mathematical models of livestock disease transmission and then refine said mathematical models according to the findings of the data. Such an approach is motivated by livestock disease models traditionally omitting variation in farmer disease management behaviours. I will discuss our application of this methodology for a fast, spatially spreading disease outbreak scenario amongst cattle herds in Great Britain, for which we elicited when farmers would use an available vaccine and then used the attained behavioural groups within a livestock disease model to make epidemiological and health economic assessments. 

(Associated paper: Incorporating heterogeneity in farmer disease control behaviour into a livestock disease transmission model. https://doi.org/10.1016/j.prevetmed.2023.106019)
Fri, 03 May 2024

15:00 - 16:00
L5

Local systems for periodic data

Adam Onus
(Queen Mary University of London)

The join button will be published 30 minutes before the seminar starts (login required).

Abstract

 

Periodic point clouds naturally arise when modelling large homogenous structures like crystals. They are naturally attributed with a map to a d-dimensional torus given by the quotient of translational symmetries, however there are many surprisingly subtle problems one encounters when studying their (persistent) homology. It turns out that bisheaves are a useful tool to study periodic data sets, as they unify several different approaches to study such spaces. The theory of bisheaves and persistent local systems was recently introduced by MacPherson and Patel as a method to study data with an attributed map to a manifold through the fibres of this map. The theory allows one to study the data locally, while also naturally being able to appeal to local systems of (co)sheaves to study the global behaviour of this data. It is particularly useful, as it permits a persistence theory which generalises the notion of persistent homology. In this talk I will present recent work on the theory and implementation of bisheaves and local systems to study 1-periodic simplicial complexes. Finally, I will outline current work on generalising this theory to study more general periodic systems for d-periodic simplicial complexes for d>1.