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, 08 Oct 2023 17:00
Mathematical Institute

Cascading Principles - a major mathematically inspired exhibition by Conrad Shawcross

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 more than 35 sculptures realised by the artist over the last seventeen years. The artworks are placed in public and private areas, forming a web of relationships which emerge as the viewer moves through the building.

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.

Cascading Principles: Expansions within Geometry, Philosophy, and Interference will be accompanied by a four-part symposium, with events taking place throughout the year of the exhibition. Researchers from Oxford Mathematics will be paired with artists and philosophers for talks that will foster cross-fertilisation of thought and creativity. The symposium series is organised in partnership with Modern Art Oxford and Ruskin School of Art, evoking the collaborative ethos of Conrad's artistic practice.

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 8 October 2023.

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

Image of 'off cut axiom' by Conrad Shawcross

Tue, 29 Nov 2022

12:30 - 13:00
C3

Spatial analysis to investigate the emergent dynamics of a cellular automaton model of tumour-immune interactions.

Roisin Stephens
Abstract

Baseline T cell infiltration and the spatial distribution of T cells within a tumour has been found to be a significant indicator of patient outcomes. This observation, coupled with the increasing availability of spatially-resolved imaging data of individual cells within the tumour tissue, motivates the development of mathematical models which capture the spatial dynamics of T cells. Agent-based models allow the simulation of complex biological systems with detailed spatial resolution, and generate rich spatio-temporal datasets. In order to fully leverage the information contained within these simulated datasets, spatial statistics provide methods of analysis and insight into the biological system modelled, by quantifying inherent spatial heterogeneity within the system. We present a cellular automaton model of interactions between tumour cells and cytotoxic T cells, and an analysis of the model dynamics, considering both the temporal and spatial evolution of the system. We use the model to investigate some of the standard assumptions made in these models, to assess the suitability of the models to accurately describe tumour-immune dynamics.

Tue, 29 Nov 2022
14:00
L6

Springer Fibres - Geometrical and Combinatorial Applications

Neil Saunders
(University of Greenwich)
Abstract

Fibres coming from the Springer resolution on the nilpotent cone are incredibly rich algebraic varieties that have many applications in representation theory and combinatorics. Though their geometry can be very difficult to describe in general, in type A at least, their irreducible components can be described using standard Young tableaux, and this can help describe their geometry in small dimensions. In this talk, I will report on recent and ongoing work with Lewis Topley and separately Daniele Rosso on geometrical and combinatorial applications of the classical ‘type A’ Springer fibres and the ‘exotic’ type C Springer fibres coming from Kato’s exotic Springer correspondence.

Tue, 29 Nov 2022

14:00 - 15:00
L5

Distances in colourings of the plane

James Davies
(Cambridge University)
Abstract

We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd (integral) distance from each other. We will also discuss some further results with Rose McCarty and Michal Pilipczuk concerning prime and polynomial distances.

Tue, 29 Nov 2022
15:00
L3

The rates of growth in a hyperbolic group

Koji Fujiwara
Abstract

I discuss the set of rates of growth of a finitely generated 
group with respect to all its finite generating sets. In a joint work 
with Sela, for a hyperbolic group, we showed that the set is 
well-ordered, and that each number can be the rate of growth of at most 
finitely many generating sets up to automorphism of the group. I may 
discuss its generalization to acylindrically hyperbolic groups.

Tue, 29 Nov 2022
16:00
C1

Constructing CFTs

Andre Henriques
(University of Oxford)
Abstract

Since Segal's formulation of axioms for 2d CFTs in the 80s, it has remained a major problem to construct examples of CFTs that satisfy the axioms.

I will report on ongoing joint work with James Tener in that direction.

Wed, 30 Nov 2022
16:00
L4

Handlebody groups and disk graphs

Panagiotis Papadopoulos
(LMU Munich)
Abstract

The handlebody group is defined as the mapping class group of a three-dimensional handlebody. We will survey some geometric and algebraic properties of the handlebody groups and compare them to those of two of the most studied (classes of) groups in geometric group theory, namely mapping class groups of surfaces, and ${\rm Out}(F_n)$. We will also introduce the disk graph, the handlebody-analogon of the curve graph of a surface, and discuss some of its properties.

Thu, 01 Dec 2022

12:00 - 13:00
L6

The inviscid limit of the stochastic Camassa--Holm equation with gradient noise

Peter Pang
Abstract

The Camassa--Holm (CH) equation is a nonlocal equation that manifests supercritical behaviour in ``wave-breaking" and non-uniqueness. In this talk, I will discuss the existence of global (dissipative weak martingale) solutions to the CH equation with multiplicative, gradient type noise, derived as an inviscid limit. The goal of the talk is twofold. The stochastic CH equation will be used to illustrate aspects of a stochastic compactness and renormalisation method which is popularly used to derive well-posedness and continuous dependence results in SPDEs. I shall also discuss how a lack of temporal compactness introduces fundamental difficulties in the case of the stochastic CH equation.

This talk is based on joint works with L. Galimbert and H. Holden, both at NTNU, and with K.H. Karlsen at the University of Oslo. 

Thu, 01 Dec 2022
13:45
L1

2d RCFTs and 3d TQFTs

Palash Singh
Further Information

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.

Thu, 01 Dec 2022

16:00 - 17:00
L3

Convergence of policy gradient methods for finite-horizon stochastic linear-quadratic control problems

Michael Giegrich
Abstract

We study the global linear convergence of policy gradient (PG) methods for finite-horizon exploratory linear-quadratic control (LQC) problems. The setting includes stochastic LQC problems with indefinite costs and allows additional entropy regularisers in the objective. We consider a continuous-time Gaussian policy whose mean is linear in the state variable and whose covariance is state-independent. Contrary to discrete-time problems, the cost is noncoercive in the policy and not all descent directions lead to bounded iterates. We propose geometry-aware gradient descents for the mean and covariance of the policy using the Fisher geometry and the Bures-Wasserstein geometry, respectively. The policy iterates are shown to obey an a-priori bound, and converge globally to the optimal policy with a linear rate. We further propose a novel PG method with discrete-time policies. The algorithm leverages the continuous-time analysis, and achieves a robust linear convergence across different action frequencies. A numerical experiment confirms the convergence and robustness of the proposed algorithm.

This is joint work with Yufei Zhang and Christoph Reisinger.

Thu, 01 Dec 2022
16:00
Virtual

Particle filters for Data Assimilation

Dan Crisan
(Imperial College London)

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

Further Information
Abstract

Modern Data Assimilation (DA) can be traced back to the sixties and owes a lot to earlier developments in linear filtering theory. Since then, DA has evolved independently of Filtering Theory. To-date it is a massively important area of research due to its many applications in meteorology, ocean prediction, hydrology, oil reservoir exploration, etc. The field has been largely driven by practitioners, however in recent years an increasing body of theoretical work has been devoted to it. In this talk, In my talk, I will advocate the interpretation of DA through the language of stochastic filtering. This interpretation allows us to make use of advanced particle filters to produce rigorously validated DA methodologies. I will present a particle filter that incorporates three additional add-on procedures: nudging, tempering and jittering. The particle filter is tested on a two-layer quasi-geostrophic model with O(10^6) degrees of freedom out of which only a minute fraction are noisily observed.

Thu, 01 Dec 2022
16:00
L5

Ihara’s lemma for quaternionic Shimura varieties and special values of L-functions

Matteo Tamiozzo
Abstract

I will talk about work in progress with Ana Caraiani aimed at proving Ihara’s lemma for quaternionic Shimura varieties, generalising the strategy of Manning-Shotton for Shimura curves. As an arithmetic motivation, in the first part of the talk I will recall an approach to the Birch and Swinnerton-Dyer conjecture based on congruences between modular forms, relying crucially on Ihara’s lemma.

Fri, 02 Dec 2022
10:00
L6

Closest Point of Approach problem

Dr. Nikhil Banda MIOA and Dan Pollard
(Drumgrange)
Abstract

Consider an environment with two vehicles/platforms moving at a relative velocity (v). The objective is to predict the Closest Point of Approach (CPA) between the two platforms as defined by the parameters: CPA time (t0), CPA bearing (θ0), CPA distance (r0)[†].The challenge is to identify mathematical operations - either using geometric methods, or by use of tracking algorithms such as Kalman Filters (EKF, UKF), or a combination of both - to estimate the CPA parameters. The statistical errors in estimation of CPA parameters also need to be quantified with each observations at time ti. The signals to be employed are acoustic in nature and the receiver platform has one sensor. The parameters that can extracted from acoustic signals are current relative bearing (θ) and current doppler or range rate (S) 


[†]Defined currently using polar coordinate system.

Fri, 02 Dec 2022

12:00 - 13:00
N3.12

TBA

Finn Wiersig
(University of Oxford)
Abstract

TBA

Fri, 02 Dec 2022

14:00 - 15:00
L5

Shaping of solids under natural convection

Megan Davies Wykes
(University of Cambridge)
Abstract

Fluids sculpt many of the shapes we see in the world around us. We present a new mathematical model describing the shape evolution of a body that dissolves or melts under gravitationally stable buoyancy-driven convection, driven by thermal or solutal transfer at the solid-fluid interface. For high Schmidt number, the system is reduced to a single integro-differential equation for the shape evolution. Focusing on the particular case of a cone, we derive complete predictions for the underlying self-similar shapes, intrinsic scales and descent rates. We will present the results of new laboratory experiments, which show an excellent match to the theory. By analysing all initial power-law shapes, we uncover a surprising result that the tips of melting or dissolving bodies can either sharpen or blunt with time subject to a critical condition.

Fri, 02 Dec 2022

15:00 - 16:00
L6

On the Discrete Geometric Principles of Machine Learning and Statistical Inference

Jesús A. De Loera
(UC Davies)
Further Information

You can find out more about Professor De Loera here: https://www.math.ucdavis.edu/~deloera/ 

Abstract

In this talk I explain the fertile relationship between the foundations of inference and learning and combinatorial geometry.

My presentation contains several powerful examples where famous theorems in discrete geometry answered natural  questions from machine learning and statistical inference:

In this tasting tour I will include the problem of deciding the existence of Maximum likelihood estimator in multiclass logistic regression, the variability of behavior of k-means algorithms with distinct random initializations and the shapes of the clusters, and the estimation of the number of samples in chance-constrained optimization models. These obviously only scratch the surface of what one could do with extra free time. Along the way we will see fascinating connections to the coupon collector problem, topological data analysis, measures of separability of data, and to the computation of Tukey centerpoints of data clouds (a high-dimensional generalization of median). All new theorems are joint work with subsets of the following wonderful folks: T. Hogan, D. Oliveros, E. Jaramillo-Rodriguez, and A. Torres-Hernandez.

Two relevant papers published/ to appear are

https://arxiv.org/abs/1907.09698https://arxiv.org/abs/1907.09698

https://arxiv.org/abs/2205.05743https://arxiv.org/abs/2205.05743

Fri, 02 Dec 2022

16:00 - 17:00
L1

Strong cosmic censorship versus Λ

Mihalis Dafermos
(Cambridge)
Abstract
The strong cosmic censorship conjecture is a fundamental open problem in classical general relativity, first put forth by Roger Penrose in the early 70s. This is essentially the question of whether general relativity is a deterministic theory. Perhaps the most exciting arena where the validity of the conjecture is challenged is the interior of rotating black holes, and there has been a lot of work in the past 50 years in identifying mechanisms ensuring that at least some formulation of the conjecture be true. It turns out that when a nonzero cosmological constant Λ is added to the Einstein equations, these underlying mechanisms change in an unexpected way, and the validity of the conjecture depends on a detailed understanding of subtle aspects of black hole scattering theory, surprisingly involving, in the case of negative Λ, some number theory. Does strong cosmic censorship survive the challenge of non-zero Λ? This talk will try to address this Question!
Mon, 05 Dec 2022
16:00
L4

TBA

Samuel Frengley
(University of Cambridge (DPMMS))
Abstract

TBA

Tue, 06 Dec 2022
14:00
Large Lecture Theatre, Department of Statistics, University of Oxford

CDT in Mathematics of Random Systems December Workshop 2022

Thomas Tendron (Oxford Statistics), Julian Sieber (Imperial Mathematics)
Abstract

2:00 Julian Sieber

On the (Non-)stationary density of fractional SDEs

I will present a novel approach for studying the density of SDEs driven by additive fractional Brownian motion. It allows us to establish smoothness and Gaussian-type upper and lower bounds for both the non-stationary as well as the stationary density. While the stationary density has not been studied in any previous works, the former was the subject of multiple articles by Baudoin, Hairer, Nualart, Ouyang, Pillai, Tindel, among others. The common theme of all of these works is to obtain the results through bounds on the Malliavin derivative. The main disadvantage of this approach lies in the non-optimal regularity conditions on the SDE's coefficients. In case of additive noise, the equation is known to be well-posed if the drift is merely sublinear and measurable (resp. Holder continuous). Relying entirely on classical methods of stochastic analysis (avoiding any Malliavin calculus), we prove the aforementioned Gaussian-type bounds under optimal regularity conditions.

The talk is based on a joint work with Xue-Mei Li and Fabien Panloup.

 

2:45 Thomas Tendron

A central limit theorem for a spatial logistic branching process in the slow coalescence regime

We study the scaling limits of a spatial population dynamics model which describes the sizes of colonies located on the integer lattice, and allows for branching, coalescence in the form of local pairwise competition, and migration. When started near the local equilibrium, the rates of branching and coalescence in the particle system are both linear in the local population size - we say that the coalescence is slow. We identify a rescaling of the equilibrium fluctuations process under which it converges to an infinite dimensional Ornstein-Uhlenbeck process with alpha-stable driving noise if the offspring distribution lies in the domain of attraction of an alpha-stable law with alpha between one and two.

3:30 Break

4:00-5:30 Careers Discussion

babbar image
cora cartis
alisdair wallis
Dr Katia Babbar Professor Coralia Cartis Dr Alisdair Wallis
Tue, 13 Dec 2022
17:00
Lecture Theatre 1, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

Anyone for a mince pi? Mathematical modelling of festive foods - Helen Wilson

Helen Wilson
(University College London)
Further Information

Oxford Mathematics Christmas Public Lecture

In this talk we'll look at a variety of delicious delights through a lens of fluid dynamics and mathematical modelling. From perfect roast potatoes to sweet sauces, mathematics gets everywhere!

Helen Wilson is Head of the Department of Mathematics at UCL. She is best known for her work on the chocolate fountain (which will feature in this lecture) but does do serious mathematical modelling as well.

Please email @email to register. The lecture will be followed by mince pies and drinks for all.

This lecture will be available on our Oxford Mathematics YouTube Channel at 5pm on 20th December.

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

Thu, 19 Jan 2023

14:00 - 15:00
L3

TBA

Misha Kilmer
(Tufts University)
Abstract

TBA

Fri, 20 Jan 2023

14:00 - 15:00
L3

The inevitable emergence of density-dependent diffusion in expanding phage populations

Dr Diana Fusco
(Dept of Physics University of Cambridge)
Abstract

Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit a density-dependent dispersal rate.

Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal and cell lysis caused by viral infection results in an effective density-dependent diffusion rate akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion. Moreover, we find that a second, independent density-dependent effect on phage dispersal spontaneously emerges as a result of the viral incubation period, during which phage is trapped inside the host unable to disperse. Our results indicate both that bacteriophage can be used as a controllable laboratory population to investigate the impact of density-dependent dispersal on evolution, and that the genetic diversity and adaptability of expanding viral populations could be much greater than is currently assumed.