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 nearly 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 8 October 2023. You can see and find out more here.

The first of the four public talks about the exhibition (featuring Conrad himself) took place on 23 February. You can watch a recording of the first lecture here.

You can register for the second talk on 27th July here

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

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

Schism Fracture

Axiom Paradigm

Thu, 28 Sep 2023
17:30
Lecture Theatre 1

Patterns in Science and Art -  Liliane Lijn, Marcus du Sautoy and Fatos Ustek with Conrad Shawcross

 Liliane Lijn, Marcus du Sautoy and Fatos Ustek with Conrad Shawcross
Further Information

The search for and creation of patterns is intrinsic to both science and art. But so is the desire to understand how and why those patterns break down and to uncover the implications for the scientist and the artist.

Artist Liliane Lijn, curator Fatos Ustek and mathematician Marcus du Sautoy will share their experience and understanding of pattern and where it has taken them in their scientific and artistic careers. Conrad Shawcross will chair the discussion and provide his own unique perspective as represented by his 'Cascading Principles' Exhibition.

Liliane Lijn is an American-born artist who has exhibited at the Venice Biennale, and was recently short listed for her design for the Fourth Plinth in Trafalgar Square. Marcus Sautoy is a mathematician and Professor for the Public Understanding of Science in Oxford. Fatos Ustek is curator of the 'Cascading Principles' exhibition and curator of the sculpture park at Frieze London. Conrad Shawcross is an artist specialising in mechanical sculptures based on philosophical and scientific ideas.

Please email @email to register.

Tue, 03 Oct 2023
17:00
Lecture Theatre 1

Around the World in 80 Games - Marcus du Sautoy

Marcus du Sautoy
(University of Oxford)
Further Information

Oxford Mathematics Public Lecture: Around the World in 80 Games - Marcus du Sautoy

Join Marcus as he takes us on a mathematical journey across the centuries and through countries, continents and cultures in search of the games we love to play.  Based on his new book, he looks at the way mathematics has always been deeply intertwined with games and investigates how games themselves can provide us with opportunities for mathematical insight into the world.

From backgammon to chess, Catan to Snakes and Ladders, games are not simply an enjoyable diversion. They are rather the height of human ingenuity. Ours is the species that loves playing games: not homo sapiens but homo ludens.  The lecture is suitable for everyone ‘from age 8 to 108.’  Come and join Marcus on his journey Around the World in 80 Games. You simply can’t lose…

Marcus du Sautoy is Charles Simonyi Professor for the Public Understanding of Science in Oxford and Professor of Mathematics.

Please email @email to register.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on 24th October at 5pm, and can be watched any time after.

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

Mon, 09 Oct 2023

14:00 - 15:00
Lecture Room 6

TBA

Prof. Xin Guo
( UC Berkley)
Abstract

TBA

Mon, 09 Oct 2023
15:30
Lecture Theatre 3, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

Compact Brownian surfaces

Professor Grégory Miermont
(École Normale Supérieure de Lyon)
Further Information

Please join us from 1500-1530 for tea and coffee outside the lecture theatre before the talk.

Abstract

We describe the compact scaling limits of uniformly random quadrangulations with boundaries on a surface of arbitrary fixed genus. These limits, called Brownian surfaces, are homeomorphic to the surface of the given genus with or without boundaries depending on the scaling regime of the boundary perimeters of the quadrangulation. They are constructed by appropriate gluings of pieces derived from Brownian geometrical objects (the Brownian plane and half-plane). In this talk, I will review their definition and discuss possible alternative constructions. This is based on joint work with Jérémie Bettinelli.

Mon, 09 Oct 2023

16:30 - 17:30
L5

TBC

Risabh Gvalani
(Max Planck Institute in Leipzig)
Tue, 10 Oct 2023
13:00
L1

Dynamical consequences of Generalized Symmetries in Argyres-Douglas Theories

Alessandro Mininno
(DESY)
Abstract
In this talk, I will discuss the dynamical consequences of having 1-form, 2-group and non-invertible symmetries in Argyres-Douglas (AD) theories.
I will first review how to construct (G,G') and D_p(G) theories from geometric engineering. Then, I will briefly introduce how 1-form symmetries are found in these AD theories, focusing on their dynamical consequences in the study of the Higgs branch for such theories.  Analogously, I will show how certain D_p(G) theories enjoy a 2-group structure due to a non-trivial extension between a discrete 1-form symmetry and a continuous 0-form symmetry, emphasizing the dynamical consequences that a 2-group structure entails, and the family of AD theories that have it. This analysis allowed us to "bootstrap" families of D_p(G) theories sharing the same properties. Finally, I discuss the presence of non-invertible symmetries in AD theories obtained by gauging the flavor symmetry of multiple D_p(SU(N)) theories. 

 

Tue, 10 Oct 2023

14:00 - 15:00
L5

TBC

Mark Pengitore
(University of Virginia)
Abstract

to follow

Tue, 10 Oct 2023

14:00 - 14:30
L4

TBA

Ioannis Papadopoulos
(Imperial)
Abstract

TBA

Tue, 10 Oct 2023
15:00
L1

Rank gradient in higher rank lattices

Mikołaj Frączyk
(Jagiellonian University Cracow)
Abstract

In a recent work with Sam Mellick and Amanda Wilkens, we proved that higher rank semisimple Lie groups satisfy a generalization of Gaboriau fixed price property (originally defined for countable groups) to the setting of locally compact second countable groups. As one of the corollaries, under mild conditions, we can prove that the rank (minimal number of generators) or the first mod-p Betti number of a higher rank lattice grow sublinearly in the covolume.  The proof relies on surprising geometric properties of Poisson-Voronoi tessellations in higher-rank symmetric spaces, which could be of independent interest. 

Thu, 12 Oct 2023

13:00 - 14:00
Lecture Room 3

Surprises in a classic boundary-layer problem

Steven Strogatz
(Cornell University)
Abstract

Over the years, I've often taught a first course in asymptotics and perturbation methods, even though I don't know much about the subject. In this talk, I'll discuss a textbook example of a singularly perturbed nonlinear boundary-value problem that has revealed delightful new surprises, every time I teach it. These include a pitchfork bifurcation in the number of solutions as one varies the small parameter, and transcendentally small terms in the solutions' initial conditions that can be calculated by elementary means.

Thu, 12 Oct 2023

14:00 - 15:00
Lecture Room 3

TBA

Nicole Spillane
(Ecole Polytechnique (CMAP))
Abstract

TBA

Thu, 12 Oct 2023
16:00
Lecture Room 4, Mathematical Institute

Path Shadowing Monte-Carlo: a new approach to prediction

Rudy Morel
(Ecole Normale Superieure)
Abstract

A Path Shadowing Monte-Carlo method provides prediction of future paths given any generative model.

At a given date, it averages future quantities over generated price paths whose past history matches, or “shadows”, the actual (observed) history.

We test our approach using paths generated from a maximum entropy model of financial prices,

based on the recently introduced “Scattering Spectra” which are multi-scale analogues of the standard skewness and kurtosis.

This model promotes diversity of generated paths while reproducing the main statistical properties of financial prices, including stylized facts on volatility roughness.

Our method yields state-of-the-art predictions for future realized volatility. It also allows one to determine conditional option smiles for the S&P500.

These smiles depend only on the distribution of the price process, and are shown to outperform both the current version of the Path Dependent Volatility model and the option market itself.

Fri, 13 Oct 2023

14:00 - 15:00
L3

To be announced

Prof Alexandria Volkening
(Department of Mathematics Weldon School of Biomedical Engineering)
Mon, 16 Oct 2023
15:30
Lecture Theatre 3, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

Non-adversarial training of Neural SDEs with signature kernel scores

Dr Maud Lemercier
(Mathematical Institute (University of Oxford))
Further Information

Please join us from 1500-1530 for tea and coffee outside the lecture theatre before the talk.

Abstract

Neural SDEs are continuous-time generative models for sequential data. State-of-the-art performance for irregular time series generation has been previously obtained by training these models adversarially as GANs. However, as typical for GAN architectures, training is notoriously unstable, often suffers from mode collapse, and requires specialised techniques such as weight clipping and gradient penalty to mitigate these issues. In this talk, I will introduce a novel class of scoring rules on path space based on signature kernels and use them as an objective for training Neural SDEs non-adversarially. The strict properness of such kernel scores and the consistency of the corresponding estimators, provide existence and uniqueness guarantees for the minimiser. With this formulation, evaluating the generator-discriminator pair amounts to solving a system of linear path-dependent PDEs which allows for memory-efficient adjoint-based backpropagation. Moreover, because the proposed kernel scores are well-defined for paths with values in infinite-dimensional spaces of functions, this framework can be easily extended to generate spatiotemporal data. This procedure permits conditioning on a rich variety of market conditions and significantly outperforms alternative ways of training Neural SDEs on a variety of tasks including the simulation of rough volatility models, the conditional probabilistic forecasts of real-world forex pairs where the conditioning variable is an observed past trajectory, and the mesh-free generation of limit order book dynamics.

Mon, 16 Oct 2023

16:30 - 17:30
L5

Plateau's problem via the theory of phase transitions

Stephen Lynch
(Imperial College London )
Abstract

Plateau's problem asks whether every boundary curve in 3-space is spanned by an area minimizing surface. Various interpretations of this problem have been solved using eg. geometric measure theory. Froehlich and Struwe proposed a PDE approach, in which the desired surface is produced using smooth sections of a twisted line bundle over the complement of the boundary curve. The idea is to consider sections of this bundle which minimize an analogue of the Allen--Cahn functional (a classical model for phase transition phenomena) and show that these concentrate energy on a solution of Plateau's problem. After some background on the link between phase transition models and minimal surfaces, I will describe new work with Marco Guaraco in which we produce smooth solutions of Plateau's problem using this approach. 

Tue, 17 Oct 2023
13:00
L1

An exact solution to cosmological bootstrap using 6j symbols

Sourav Sarkar
(Uppsala)
Abstract

We shall consider a crossing equation of the Euclidean conformal group in terms of conformal partial waves and in particular, a position independent representation of this equation. We shall briefly discuss the relevance of this equation to the problem of cosmological bootstrap. Thereafter, we shall sketch the derivation of the Biedenharn-Eliiot identity (a pentagon identity) for the 6j symbols of the conformal group and show how this provides us with an exact solution to said crossing equation. For the conformal group (which is non-compact), this involves some careful bookkeeping of the spinning representations. Finally, we shall discuss some consistency checks on the result obtained, and some open questions. 

Tue, 17 Oct 2023
15:00

Dehn functions of central products of nilpotent groups

Claudio Llosa Isenrich
(KIT)
Abstract

The Dehn function of a finitely presented group provides a quantitative measure for the difficulty of detecting if a word in its generators represents the trivial element of the group. By work of Gersten, Holt and Riley the Dehn function of a nilpotent group of class $c$ is bounded above by $n^{c+1}$. However, we are still far from determining the precise Dehn functions of all nilpotent groups. In this talk, I will explain recent results that allow us to determine the Dehn functions of large classes of nilpotent groups arising as central products. As a consequence, for every $k>2$, we obtain many pairs of finitely presented $k$-nilpotent groups with bilipschitz asymptotic cones, but with different Dehn functions. This shows that Dehn functions can distinguish between nilpotent groups with the same asymptotic cone, making them interesting in the context of the conjectural quasi-isometry classification of nilpotent groups.  This talk is based on joint works with García-Mejía, Pallier and Tessera.

Thu, 19 Oct 2023

12:00 - 13:00
Lecture Room 3

Does Maxwell’s hypothesis of air saturation near the surface of evaporating liquid hold at all spatial scales?

Eugene Benilov
(University of Limerick)
Abstract

The classical model of evaporation of liquids hinges on Maxwell’s assumption that the air near the liquid’s surface is saturated. It allows one to find the evaporative flux without considering the interface separating liquid and air. Maxwell’s hypothesis is based on an implicit assumption that the vapour-emission capacity of the interface exceeds the throughput of air (i.e., its ability to pass the vapour on to infinity). If indeed so, the air adjacent to the liquid would get quickly saturated, justifying Maxwell’s hypothesis.

 

In the present paper, the so-called diffuse-interface model is used to account for the interfacial physics and, thus, derive a generalised version of Maxwell’s boundary condition for the near-interface vapour density. It is then applied to a spherical drop floating in air. It turns out that the vapour-emission capacity of the interface exceeds the throughput of air only if the drop’s radius is rd10μm, but for rd ≈ 2μm, the two are comparable. For rd1μm, evaporation is interface-driven, and the resulting evaporation rate is noticeably smaller than that predicted by the classical model.

Thu, 19 Oct 2023

14:00 - 15:00
Lecture Room 3

Randomized Least Squares Optimization and its Incredible Utility for Large-Scale Tensor Decomposition

Tammy Kolda
(mathsci.ai)
Abstract

Randomized least squares is a promising method but not yet widely used in practice. We show an example of its use for finding low-rank canonical polyadic (CP) tensor decompositions for large sparse tensors. This involves solving a sequence of overdetermined least problems with special (Khatri-Rao product) structure.

In this work, we present an application of randomized algorithms to fitting the CP decomposition of sparse tensors, solving a significantly smaller sampled least squares problem at each iteration with probabilistic guarantees on the approximation errors. We perform sketching through leverage score sampling, crucially relying on the fact that the problem structure enable efficient sampling from overestimates of the leverage scores with much less work. We discuss what it took to make the algorithm practical, including general-purpose improvements.

Numerical results on real-world large-scale tensors show the method is faster than competing methods without sacrificing accuracy.

*This is joint work with Brett Larsen, Stanford University.

Fri, 20 Oct 2023

10:00 - 11:00
L6

Automate algorithm for self-adjusting selections and thresholds in a credit scoring process.

Kal BUKOVSKI
(Sopra Steria)
Further Information

We are looking to find a solution to a multi-stage optimisation problem where all 3 stages define a separate optimisation problem on it’s own which is, however, dependent on the other two. The 3 objectives are:

• Select the most appropriate set of metrics to be included in the scoring process;

• Allocated the most accurate weights to each of these metrics so that if the respective condition for trend or level is triggered, the weight score is added to the individual’s scorecard;

• Based on all final individual scores, find the most accurate classification thresholds’ adjustments to the previous time point of assessment.

The resulting multi-problem optimised solution can be applied in various industrial fields, such as credit scoring process.

Fri, 20 Oct 2023

15:00 - 16:00
Virtual

Machine learning for identifying translatable biomarkers and targets

Professor Daphne Koller
(Department of Computer Science Stanford University)

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

Abstract

Modern medicine has given us effective tools to treat some of the most significant and burdensome diseases. At the same time, it is becoming consistently more challenging and more expensive to develop new therapeutics. A key factor in this trend is that we simply don't understand the underlying biology of disease, and which interventions might meaningfully modulate clinical outcomes and in which patients. To achieve this goal, we are bringing together large amounts of high content data, taken both from humans and from human-derived cellular systems generated in our own lab. Those are then used to learn a meaningful representation of biological states via cutting edge machine learning methods, which enable us to make predictions about novel targets, coherent patient segments, and the clinical effect of molecules. Our ultimate goal is to develop a new approach to drug development that uses high-quality data and ML models to design novel, safe, and effective therapies that help more people, faster, and at a lower cost. 

Fri, 20 Oct 2023

16:00 - 17:00
L1

Generalized Tensor Decomposition: Utility for Data Analysis and Mathematical Challenges

Tamara Kolda
( MathSci.ai)
Further Information

Tamara Kolda is an independent mathematical consultant under the auspices of her company MathSci.ai based in California. From 1999-2021, she was a researcher at Sandia National Laboratories in Livermore, California. She specializes in mathematical algorithms and computation methods for tensor decompositions, tensor eigenvalues, graph algorithms, randomized algorithms, machine learning, network science, numerical optimization, and distributed and parallel computing.

From the website: https://www.mathsci.ai/

Abstract

Tensor decomposition is an unsupervised learning methodology that has applications in a wide variety of domains, including chemometrics, criminology, and neuroscience. We focus on low-rank tensor decomposition using  canonical polyadic or CANDECOMP/PARAFAC format. A low-rank tensor decomposition is the minimizer according to some nonlinear program. The usual objective function is the sum of squares error (SSE) comparing the data tensor and the low-rank model tensor. This leads to a nicely-structured problem with subproblems that are linear least squares problems which can be solved efficiently in closed form. However, the SSE metric is not always ideal. Thus, we consider using other objective functions. For instance, KL divergence is an alternative metric is useful for count data and results in a nonnegative factorization. In the context of nonnegative matrix factorization, for instance, KL divergence was popularized by Lee and Seung (1999). We can also consider various objectives such as logistic odds for binary data, beta-divergence for nonnegative data, and so on. We show the benefits of alternative objective functions on real-world data sets. We consider the computational of generalized tensor decomposition based on other objective functions, summarize the work that has been done thus far, and illuminate open problems and challenges. This talk includes joint work with David Hong and Jed Duersch.