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 -
Mon, 30 Jun 2025 17:00
Mathematical Institute

Cascading Principles - a major mathematically inspired art exhibition by Conrad Shawcross - extended until June 2025

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 2025. 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

Fri, 28 Feb 2025 09:00 -
Wed, 31 Dec 2025 00:00
Mezzanine

Kathleen Hyndman - Nature+Maths=Art

Further Information

The Mathematical Institute is delighted to be hosting a major exhibition of artist Kathleen Hyndman's mathematically inspired work.

The exhibition of drawings and paintings illustrate Hyndman’s desire to see nature and the world around her in mathematical sequences and geometrical patterns. Golden Section proportions and angles, prime numbers as well as Fibonacci numbers and eccentric constructions are all used to create works achieving a calm and balanced unity.

Born in Essex, Hyndman trained at Kingston-upon-Thames School of Art and exhibited widely in the UK and abroad, including MOMA Oxford and the Hayward Annual in London. As well as a full time artist, she was also a teacher and mother of two. She lived and had her studio in Kingston Bagpuize in Oxfordshire and had exhibitions at Zuleika Gallery in Woodstock until her death in 2022.

The exhibition is curated by Zuleika Gallery and Professor Martin Kemp FBA, and will run until the end of the year.

Exhibition brochure

Bottom from left:  Hot Breeze, 1994; Heat, 1976; Exit (a seventeen sided work), 1993; Straight Line Rotation, White on Black. Forest, 1986

Below: film of the exhibition by Evan Nedyalkov

Mon, 28 Apr 2025

14:00 - 15:00
Lecture Room 3

Deep Learning for Inverse Problems: Theoretical Perspectives, Algorithms, and Applications

Professor Miguel Rodrigues, PhD, FIEEE
(University College London)
Abstract

Recent years have witnessed a surge of interest in deep learning methods to tackle inverse problems arising in various domains such as medical imaging, remote sensing, and the arts and humanities. This talk offers an overview of recent advances in the foundations and applications of deep learning for inverse problems, with a focus on model-based deep learning methods. Concretely, this talk will overview our work relating to theoretical advances in the area of mode-based learning, including learning guarantees; algorithmic advances in model-based learning; and, finally it will showcase a portfolio of emerging signal & image processing challenges that benefit from model based learning, including image separation / deconvolution challenges arising in the arts and humanities.

 

 

Bio:

Miguel Rodrigues is a Professor of Information Theory and Processing at University College London; he leads the Information, Inference and Machine Learning Lab at UCL, and he has also been the founder and director of the master programme in Integrated Machine Learning Systems at UCL. He has also been the UCL Turing University Lead and a Turing Fellow with the Alan Turing Institute — the UK National Institute of Data Science and Artificial Intelligence.

He held various appointments with various institutions worldwide including Cambridge University, Princeton University, Duke University, and the University of Porto, Portugal. He obtained the undergraduate degree in Electrical and Computer Engineering from the Faculty of Engineering of the University of Porto, Portugal and the PhD degree in Electronic and Electrical Engineering from University College London.

Dr. Rodrigues's research lies in the general areas of information theory, information processing, and machine learning. His most relevant contributions have ranged from the information-theoretic analysis and design of communications systems, information-theoretic security, information-theoretic analysis and design of sensing systems, and the information-theoretic foundations of machine learning.

He serves or has served as Editor of IEEE BITS, Editor of the IEEE Transactions on Information Theory, and Lead Guest Editor of various Special Issues of the IEEE Journal on Selected Topics in Signal Processing, Information and Inference, and Foundations and Trends in Signal Processing.

Dr. Rodrigues has been the recipient of various prizes and awards including the Prize for Merit from the University of Porto, the Prize Engenheiro Cristian Spratley, the Prize Engenheiro Antonio de Almeida, fellowships from the Portuguese Foundation for Science and Technology, and fellowships from the Foundation Calouste Gulbenkian. Dr. Rodrigues research on information-theoretic security has also attracted the IEEE Communications and Information Theory Societies Joint Paper Award 2011.  

He has also been elevated to Fellow of the Institute of Electronics and Electrical Engineers (IEEE) for his contributions to the ‘multi-modal data processing and reliable and secure communications.’

Mon, 28 Apr 2025
16:30
L4

Wave localization at subwavelength scales

Habib Amari
(ETH)
Abstract

Systems of high-contrast resonators can be used to control and manipulate wave-matter interactions at scales that are much smaller than the operating wavelengths. The aim of this talk is to review recent studies of ordered and disordered systems of subwavelength resonators and to explain some of their topologically protected localization properties. Both reciprocal and non-reciprocal systems will be considered.
 

Tue, 29 Apr 2025
13:00
L5

Non-perturbative Topological Strings from M-theory

Eran Palti
(Ben Gurion)
Further Information
Topological strings are simplified versions of full string theories. Like all string theories, they admit a perturbative genus expansion in their coupling. In this talk, I will describe a new approach to go beyond this expansion and gain exact full non-perturbative information on their partition function. The approach utilizes an identification between the topological string free energy and certain F-terms in the effective action of full type IIA strings. The latter are known to be calculable in a perturbative approach by uplifting IIA to M-theory and integrating out M2 branes. This is the famous calculation of Gopakumar and Vafa. I will describe recent results which show that integrating out the M2 branes infact yields not only the perturbative (asymptotic) expansion but the full exact non-perturbative free energy. The resulting expression manifests features expected from an exact expression, such as certain strong-weak coupling dualities, and special behaviour at self-dual values of the coupling. 


 

Tue, 29 Apr 2025
14:00
L6

On the mod-$p$ cohomology of certain $p$-saturable groups.

Konstantin Ardakov
((University of Oxford))
Abstract

The mod-$p$ cohomology of uniform pro-$p$ groups has been calculated by Lazard in the 1960s. Motivated by recent considerations in the mod-$p$ Langlands program, we consider the problem of extending his results to the case of compact $p$-adic Lie groups $G$ that are $p$-saturable but not necessarily uniform pro-$p$: when $F$ is a finite extension of $\mathbb{Q}_p$ and $p$ is sufficiently large, this class of groups includes the so-called pro-$p$ Iwahori subgroups of $SL_n(F)$. In general, there is a spectral sequence due to Serre and Lazard that relates the mod-$p$ cohomology of $G$ to the cohomology of its associated graded mod-$p$ Lie algebra $\mathfrak{g}$. We will discuss certain sufficient conditions on $p$ and $G$ that ensure that this spectral sequence collapses. When these conditions hold, it follows that the mod-$p$ cohomology of $G$ is isomorphic to the cohomology of the Lie algebra $\mathfrak{g}$.

Tue, 29 Apr 2025
15:00
L6

Cannon-Thurston maps for the Morse boundary

Matthew Cordes
Abstract

Fundamental to the study of hyperbolic groups is their Gromov boundaries. The classical Cannon--Thurston map for a closed fibered hyperbolic 3-manifolds relates two such boundaries: it gives a continuous surjection from the boundary of the surface group (a circle) to the boundary of the 3-manifold group (a 2-sphere). Mj (Mitra) generalized this to all hyperbolic groups with hyperbolic normal subgroups. A generalization of the Gromov boundary to all finitely generated groups is called the Morse boundary. It collects all the "hyperbolic-like" rays in a group. In this talk we will discuss Cannon--Thurston maps for Morse boundaries. This is joint work with Ruth Charney, Antoine Goldsborough, Alessandro Sisto and Stefanie Zbinden.

Tue, 29 Apr 2025
16:00
L6

Thick points of the planar Gaussian free field 

Ellen Powell
(Durham University)
Abstract
The Gaussian Free Field (GFF) in two dimensions is a random field which can be viewed as a multidimensional analogue of Brownian motion, and appears as a universal scaling limit of a class of discrete height functions. Thick points of the GFF are points where, roughly speaking, the field is atypically high. They provide key insights into the geometric properties of the field, and are the basis for construction of important associated objects in random planar geometry. The set of thick points with thickness level a is a fractal set with Hausdorff dimension 2-a^2/2. In this talk I will discuss another fundamental property, namely, that the set is almost surely disconnected for all non-zero a. This is based on joint work with Juhan Aru and Léonie Papon, and uses a remarkable relationship between the GFF and the "conformal loop ensemble" of parameter 4. 
Tue, 29 Apr 2025
16:00
C3

The nuclear dimension of C*-algebras of groupoids, with applications to C*-algebras of directed graphs

Astrid an Huef
(Victoria University of Wellington Te Herenga Waka)
Abstract

Guentner, Willet and Yu defined a notion of dynamic asymptotic dimension for an étale groupoid that can be used to bound the nuclear dimension of its groupoid C*-algebra.  To have finite dynamic asymptotic dimension, the isotropy subgroups of the groupoid must be locally finite.  I will discuss 1) how to use similar ideas to bound the nuclear dimension of the C*-algebra of a groupoid with `large' isotropy subgroups and 2) the limitations of that approach. In an application to the C*-algebra of a directed graph,  if the C*-algebra is stably finite, then its nuclear dimension is at most 1.  This is joint work with Dana Williams. 

Wed, 30 Apr 2025
16:00
L3

TBA

Gargi Biswas
(University of Oxford)
Abstract

TBA

Wed, 30 Apr 2025
17:00
Lecture Theatre 1, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

Natural tilings: from hard rock to soft cells - Gábor Domokos

Gábor Domokos
(Budapest University of Technology and Economics)
Further Information

In this lecture Gábor Domokos will use the geometric theory of tilings to describe natural patterns ranging from nanoscale to planetary scale, appearing in physics, biology, and geology.  Rock fragments can be modelled by polyhedra having, on average, six flat faces and eight sharp vertices, reflecting Plato’s postulate of pairing the element Earth with the cube.  If we depart from polyhedra and admit curved faces then we can tile space without any sharp corners with a new class of shapes, called soft cells, which appear in both living and non-living nature.

Gábor Domokos is a research professor at the Budapest University of Technology and Economics.  He is best known for proving a conjecture of V.I. Arnold by constructing, with Péter Várkonyi, the Gömböc, the first homogeneous, convex shape with just one stable and one unstable static equilibrium. Since then he has developed geometrical models of natural shapes and their evolution, including Martian pebbles, turtles shells, planetary crack patterns, rock fragments, asteroids, ooids, supramolecular structures and, most recently,  soft cells. 

Please email @email to register.

This lecture will be premiered on our YouTube Channel on Thursday 22 May at 5pm (and any time after). No need to register for the online version.

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

Thu, 01 May 2025

12:00 - 13:00
L3

Do Plants Know Math?: Adventures of a Mathematician in Science Writing

Christophe Golé
(Smith College)

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

Further Information

Short Bio
Christophe Golé is a mathematician originally from France, with academic positions held at institutions including ETH Zurich and UC Santa Cruz. He is the author of Symplectic Twist Maps, a book on dynamical systems, and coined the term “ghost tori” in this context. His recent work focuses on mathematical biology, particularly plant pattern formation (phyllotaxis) and the occurrence of Fibonacci numbers in nature. He co-founded the NSF-funded 4 College Biomath Consortium, which led to the Five College Biomathematical Sciences Certificate Program.

Abstract

"Do Plants Know Math?" is the title of a book I co-authored with physicist Stéphane Douady, biologist Jacques Dumais, and writer Nancy Pick. Written for a general audience with a historical perspective, the book primarily explores phyllotaxis—the arrangement of leaves and other organs around plant stems—while also examining plant fractals, kirigami models of leaf formation, and related phenomena.

To our knowledge, phyllotaxis represents the first historical intersection of biological and mathematical research. Delving into its history uncovers remarkable treasures: phyllotaxis studies led to the first formulation of renormalization (van Iterson, 1907) and inspired one of the earliest computer programs (developed by Turing in the last years of his life).

In this talk, I will highlight several of these hidden historical gems while discussing the productive symbiosis between our scientific research on phyllotaxis and the creation of our book.

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Thu, 01 May 2025

14:00 - 15:00
Lecture Room 3

Adventures in structured matrix computations

Gunnar Martinsson
(UT Austin)
Abstract

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.

Thu, 01 May 2025
16:00
Lecture Room 4

TBA

Antonio Cauchi
(University College Dublin)
Fri, 02 May 2025

11:00 - 12:00
L4

Do the shapes of tumour cell nuclei influence their infiltration?

Professor Karthik Bharath
(School of Mathematical Sciences University of Nottingham)
Abstract

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.  

Fri, 02 May 2025

12:00 - 13:00
Quillen Room

TBD

Tim Gehrunger
(ETH Zurich)
Abstract

TBD

Fri, 02 May 2025
12:00
L4

The structure of spatial infinity

Dr Mariem Magdy
(Perimeter)
Abstract
Penrose's conformal approach to the study of asymptotics leads to a singular conformal structure at spatial infinity, particularly in spacetimes with non-vanishing ADM mass. Two widely used formulations to resolve this singularity were developed by A. Ashtekar et al. and H. Friedrich. In this talk, I will discuss the details of these two approaches and their relation,  on Minkowski spacetime and in a more general setting.
 
Mon, 05 May 2025
15:30
L3

TBC

Dr. Ana Djurdjevac
(Freie Universität Berlin)
Tue, 06 May 2025
16:00
C3

Z-stability for twisted group C*-algebras of nilpotent groups

Eduard Vilalta Vila
( Chalmers University of Technology and University of Gothenburg)
Abstract

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.

Wed, 07 May 2025
16:00
L3

TBA

Samuel Ketchell
(University of Oxford)
Abstract

TBA

Thu, 08 May 2025

12:00 - 13:00
L3

Low-rank methods for discovering structure in data tensors in neuroscience

Alex Cayco-Gajic
(École Normale Supérieure Paris)

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

Further Information

Short Bio

Alex Cayco Gajic is a Junior Professor in the Department of Cognitive Studies at ENS, with a background in applied mathematics and a PhD from the University of Washington. Her research bridges computational modelling and data analysis to study cerebellar function, exploring its roles beyond motor control in collaboration with experimental neuroscientists.

Abstract

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.

Thu, 08 May 2025

12:00 - 12:30
L4

TBA

Nick Trefethen
(Harvard University)
Abstract

TBA

Thu, 08 May 2025
12:00
C6

Sard properties for polynomial maps in infinite dimension

Daniele Tiberio
(University of Padova)
Abstract

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.

Thu, 08 May 2025
14:00
(This talk is hosted by Rutherford Appleton Laboratory)

Multilevel Monte Carlo Methods with Smoothing

Aretha Teckentrup
(University of Edinburgh)
Abstract

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

 

 

 

Thu, 08 May 2025
16:00
Lecture Room 4, Mathematical Institute

TBA

Lasse Grimmelt
(University of Oxford)
Abstract

TBA

Fri, 09 May 2025

11:00 - 12:00
L4

5 years after COVID: what did modellers get right and wrong?

Professor Matt Keeling
(Dept of Mathematics University of Warwick)
Abstract
The COVID-19 pandemic represented a major challenge to many sectors of society. It also provided the opportunity for epidemiological modellers to prove their worth. Much of the modelling was performed to extremely tight deadlines and was underpinned by noisy and often biased data. 
5 years on, and with the benefit of hindsight, I’ll present a personal perspective of what went well, what went badly and lessons for next time. I’ll cover many aspects, but pay particular attention to vaccination, roadmaps, Omicron and building collaborative networks.