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

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

Mon, 18 Mar 2024 12:30 -
Fri, 22 Mar 2024 13:00
Lecture Room 2, Mathmatical Institute

National PDE Network Meeting: Nonlinear PDEs of Mixed Type in Geometry and Mechanics /Joint with the 13th Oxbridge PDE Conference

Abstract

Meeting Theme:      

Analysis of Nonlinear PDEs of Mixed-Type (esp. Elliptic-Hyperbolic and Hyperbolic-Parabolic Mixed PDEs) and Related Topics

Meeting Place:    

Lecture Theatre 2, Mathematical Institute, University of Oxford

For more information and to view the programme

Registration is now closed.

Mon, 18 Mar 2024 14:15 -
Tue, 19 Mar 2024 15:00
L2

Euler Equations and Mixed-Type Problems in Gas Dynamics and Geometry

Professor Dehua Wang
(University of Pittsburgh)
Further Information

This course is running as part of the National PDE Network Meeting being held in Oxford 18-21 March 2024, and jointly with the 13th Oxbridge PDE conference.

The course is broken into 3 sessions over two days, with all sessions taking place in L2:

14:15-14:55:    Short Course I-1 Monday 18 March

9:45-10:25:    Short Course I-2 Tuesday 19 March

14:15-14:55:    Short Course I-3 Tuesday 19 March

Abstract

 In this short course, we will discuss the Euler equations and applications in gas dynamics and geometry. First, the basic theory of Euler equations and mixed-type problems will be reviewed. Then we will present the results on the transonic flows past obstacles, transonic flows in the fluid dynamic formulation of isometric embeddings, and the transonic flows in nozzles. We will discuss global solutions and stability obtained through various techniques and approaches. The short course consists of three parts and is accessible to PhD students and young researchers.

Mon, 18 Mar 2024 16:15 -
Sun, 19 May 2024 17:00
L2

Characteristic Boundary Value Problems and Magneto-Hydrodynamics

Professor Paolo Secchi
(University of Brescia)
Further Information

This course is running as part of the National PDE Network Meeting being held in Oxford 18-21 March 2024, and jointly with the 13th Oxbridge PDE conference.

The course is broken into 3 sessions over two days, thus, with all sessions taking place in L2:

16:15-16:55:    Short Course II-1 Monday 18 March

11:35-12:15:    Short Course II-2 Tuesday 19 March

16:15-16:55:    Short Course II-3 Tuesday 19 March

Abstract

The course aims to provide an introduction to the theory of initial boundary value problems for Friedrichs symmetrizable systems, with particular interest for the applications to the equations of ideal Magneto-Hydrodynamics (MHD). 

We first analyse different kinds of boundary conditions and present the main results about the well-posedness. In the case of the characteristic boundary, we discuss the possible loss of regularity in the normal direction to the boundary and the use of suitable anisotropic Sobolev spaces in MHD.  

Finally, we give a short introduction to the Kreiss-Lopatinskii approach and discuss a simple boundary value problem for the wave equation that may admit estimates with a loss of derivatives from the data. 

 

Thu, 21 Mar 2024

16:00 - 17:00
C2

Biexact von Neumann algebras

Changying Ding
(UCLA)
Abstract

The notion of biexactness for groups was introduced by Ozawa in 2004 and has since become a major tool used for studying solidity of von Neumann algebras. We introduce the notion of biexactness for von Neumann algebras, which allows us to place many previous solidity results in a more systematic context, and naturally leads to extensions of these results. We will also discuss examples of solid factors that are not biexact. This is a joint work with Jesse Peterson.

Thu, 21 Mar 2024

16:00 - 17:00
Virtual

Data-driven surrogate modelling for astrophysical simulations: from stellar winds to supernovae

Jeremy Yates and Frederik De Ceuster
(University College London)

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

Further Information
Abstract

The feedback loop between simulations and observations is the driving force behind almost all discoveries in astronomy. However, as technological innovations allow us to create ever more complex simulations and make ever more detailed observations, it becomes increasingly difficult to combine the two: since we cannot do controlled experiments, we need to simulate whatever we can observe. This requires efficient simulation pipelines, including (general-relativistic-)(magneto-)hydrodynamics, particle physics, chemistry, and radiation transport. In this talk, we explore the challenges associated with these modelling efforts and discuss how adopting data-driven surrogate modelling and proper control over model uncertainties, promises to unlock a gold mine of future discoveries. For instance, the application to stellar wind simulations can teach us about the origin of chemistry in our Universe and the building blocks for life, while supernova simulations can reveal exotic states of matter and elucidate the formation black holes.

Mon, 25 Mar 2024
15:00
L4

Uhlenbeck compactness theorems and isometric immersions

Professor Siran Li
(Shanghai Jiao Tong University)
Abstract

In this short course, we survey the celebrated weak and strong compactness theorems proved by Karen Uhlenbeck in 1982. These results are fundamental to the gauge theory and have found numerous applications to geometry, topology, and theoretical physics. The proof is based on the ingenious idea of putting connections into ``Uhlenbeck--Coulomb gauge'', which enables the use of standard elliptic and/or nonlinear PDE techniques, as well as involved local-to-global patching arguments. We aim at giving detailed explanation of the proof, and we shall also discuss the relation between Uhlenbeck's compactness and the classical geometric problem of isometric immersions of submanifolds into Euclidean spaces.

Thu, 28 Mar 2024

16:00 - 17:00
Virtual

Differential Equation-inspired Deep Learning for Node Classification and Spatiotemporal Forecasting

Noseong Park

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

Further Information
Abstract

Scientific knowledge, written in the form of differential equations, plays a vital role in various deep learning fields. In this talk, I will present a graph neural network (GNN) design based on reaction-diffusion equations, which addresses the notorious oversmoothing problem of GNNs. Since the self-attention of Transformers can also be viewed as a special case of graph processing, I will present how we can enhance Transformers in a similar way. I will also introduce a spatiotemporal forecasting model based on neural controlled differential equations (NCDEs). NCDEs were designed to process irregular time series in a continuous manner and for spatiotemporal processing, it needs to be combined with a spatial processing module, i.e., GNN. I will show how this can be done. 

Mon, 08 Apr 2024

11:00 - 12:00
Lecture Room 3

Heavy-Tailed Large Deviations and Sharp Characterization of Global Dynamics of SGDs in Deep Learning

Chang-Han Rhee
(Northwestern University, USA)
Abstract

While the typical behaviors of stochastic systems are often deceptively oblivious to the tail distributions of the underlying uncertainties, the ways rare events arise are vastly different depending on whether the underlying tail distributions are light-tailed or heavy-tailed. Roughly speaking, in light-tailed settings, a system-wide rare event arises because everything goes wrong a little bit as if the entire system has conspired up to provoke the rare event (conspiracy principle), whereas, in heavy-tailed settings, a system-wide rare event arises because a small number of components fail catastrophically (catastrophe principle). In the first part of this talk, I will introduce the recent developments in the theory of large deviations for heavy-tailed stochastic processes at the sample path level and rigorously characterize the catastrophe principle for such processes. 
The empirical success of deep learning is often attributed to the mysterious ability of stochastic gradient descents (SGDs) to avoid sharp local minima in the loss landscape, as sharp minima are believed to lead to poor generalization. To unravel this mystery and potentially further enhance such capability of SGDs, it is imperative to go beyond the traditional local convergence analysis and obtain a comprehensive understanding of SGDs' global dynamics within complex non-convex loss landscapes. In the second part of this talk, I will characterize the global dynamics of SGDs building on the heavy-tailed large deviations and local stability framework developed in the first part. This leads to the heavy-tailed counterparts of the classical Freidlin-Wentzell and Eyring-Kramers theories. Moreover, we reveal a fascinating phenomenon in deep learning: by injecting and then truncating heavy-tailed noises during the training phase, SGD can almost completely avoid sharp minima and hence achieve better generalization performance for the test data.  

This talk is based on the joint work with Mihail Bazhba, Jose Blanchet, Bohan Chen, Sewoong Oh, Zhe Su, Xingyu Wang, and Bert Zwart.

 

 

Bio:

Chang-Han Rhee is an Assistant Professor in Industrial Engineering and Management Sciences at Northwestern University. Before joining Northwestern University, he was a postdoctoral researcher at Centrum Wiskunde & Informatica and Georgia Tech. He received his Ph.D. from Stanford University. His research interests include applied probability, stochastic simulation, experimental design, and the theoretical foundation of machine learning. His research has been recognized with the 2016 INFORMS Simulation Society Outstanding Publication Award, the 2012 Winter Simulation Conference Best Student Paper Award, the 2023 INFORMS George Nicholson Student Paper Competition (2nd place), and the 2013 INFORMS George Nicholson Student Paper Competition (finalist). Since 2022, his research has been supported by the NSF CAREER Award.  
 

Mon, 08 Apr 2024

11:00 - 12:00
Lecture Room 3

Heavy-Tailed Large Deviations and Sharp Characterization of Global Dynamics of SGDs in Deep Learning

Chang-Han Rhee
(Northwestern University, USA)
Abstract

While the typical behaviors of stochastic systems are often deceptively oblivious to the tail distributions of the underlying uncertainties, the ways rare events arise are vastly different depending on whether the underlying tail distributions are light-tailed or heavy-tailed. Roughly speaking, in light-tailed settings, a system-wide rare event arises because everything goes wrong a little bit as if the entire system has conspired up to provoke the rare event (conspiracy principle), whereas, in heavy-tailed settings, a system-wide rare event arises because a small number of components fail catastrophically (catastrophe principle). In the first part of this talk, I will introduce the recent developments in the theory of large deviations for heavy-tailed stochastic processes at the sample path level and rigorously characterize the catastrophe principle for such processes. 

The empirical success of deep learning is often attributed to the mysterious ability of stochastic gradient descents (SGDs) to avoid sharp local minima in the loss landscape, as sharp minima are believed to lead to poor generalization. To unravel this mystery and potentially further enhance such capability of SGDs, it is imperative to go beyond the traditional local convergence analysis and obtain a comprehensive understanding of SGDs' global dynamics within complex non-convex loss landscapes. In the second part of this talk, I will characterize the global dynamics of SGDs building on the heavy-tailed large deviations and local stability framework developed in the first part. This leads to the heavy-tailed counterparts of the classical Freidlin-Wentzell and Eyring-Kramers theories. Moreover, we reveal a fascinating phenomenon in deep learning: by injecting and then truncating heavy-tailed noises during the training phase, SGD can almost completely avoid sharp minima and hence achieve better generalization performance for the test data.  

 

This talk is based on the joint work with Mihail Bazhba, Jose Blanchet, Bohan Chen, Sewoong Oh, Zhe Su, Xingyu Wang, and Bert Zwart.

Mon, 08 Apr 2024

11:00 - 12:00
Lecture Room 3

Heavy-Tailed Large Deviations and Sharp Characterization of Global Dynamics of SGDs in Deep Learning

Chang-Han Rhee
(Northwestern University, USA)
Abstract

While the typical behaviors of stochastic systems are often deceptively oblivious to the tail distributions of the underlying uncertainties, the ways rare events arise are vastly different depending on whether the underlying tail distributions are light-tailed or heavy-tailed. Roughly speaking, in light-tailed settings, a system-wide rare event arises because everything goes wrong a little bit as if the entire system has conspired up to provoke the rare event (conspiracy principle), whereas, in heavy-tailed settings, a system-wide rare event arises because a small number of components fail catastrophically (catastrophe principle). In the first part of this talk, I will introduce the recent developments in the theory of large deviations for heavy-tailed stochastic processes at the sample path level and rigorously characterize the catastrophe principle for such processes. 
The empirical success of deep learning is often attributed to the mysterious ability of stochastic gradient descents (SGDs) to avoid sharp local minima in the loss landscape, as sharp minima are believed to lead to poor generalization. To unravel this mystery and potentially further enhance such capability of SGDs, it is imperative to go beyond the traditional local convergence analysis and obtain a comprehensive understanding of SGDs' global dynamics within complex non-convex loss landscapes. In the second part of this talk, I will characterize the global dynamics of SGDs building on the heavy-tailed large deviations and local stability framework developed in the first part. This leads to the heavy-tailed counterparts of the classical Freidlin-Wentzell and Eyring-Kramers theories. Moreover, we reveal a fascinating phenomenon in deep learning: by injecting and then truncating heavy-tailed noises during the training phase, SGD can almost completely avoid sharp minima and hence achieve better generalization performance for the test data.  

This talk is based on the joint work with Mihail Bazhba, Jose Blanchet, Bohan Chen, Sewoong Oh, Zhe Su, Xingyu Wang, and Bert Zwart.
 

Thu, 11 Apr 2024
18:00
The Auditorium, Citigroup Centre, London, E14 5LB

0DTEs: Trading, Gamma Risk and Volatility Propagation

Prof Grigory Vilkov
(Frankfurt School of Finance & Management)
Further Information

Registration is free but required. Register Here.

Abstract

Investors fear that surging volumes in short-term, especially same-day expiry (0DTE), options can destabilize markets by propagating large price jumps. Contrary to the intuition that 0DTE sellers predominantly generate delta-hedging flows that aggravate market moves, high open interest gamma in 0DTEs does not propagate past volatility. 0DTEs and underlying markets have become more integrated over time, leading to a marginally stronger link between the index volatility and 0DTE trading. Nonetheless, intraday 0DTE trading volume shocks do not amplify recent past index returns, inconsistent with the view that 0DTEs market growth intensifies market fragility.

About the speaker
Grigory Vilkov, Professor of Finance at the Frankfurt School of Finance and Management, holds an MBA from the University of Rochester and a Ph.D. from INSEAD, with further qualifications from Goethe University Frankfurt. He has been a professor at both Goethe University and the University of Mannheim.
His academic work focused on improving long-term portfolio strategies by building better expectations of risks, returns, and their dynamics. He is known for practical innovations in finance, such as developing forward-looking betas marketed by IvyDB OptionMetrics, establishing implied skewness and generalized lower bounds as cross-sectional stock characteristics, and creating measures for climate change exposure from earnings calls. His current research encompasses factor dispersions, factor and sector rotation, asset allocation with implied data, and machine learning in options analysis. 

Register Here.

Thu, 18 Apr 2024

16:00 - 17:00
C2

TBD

Thomas Schulmprecht
(Texas A&M University)
Abstract

to follow

Mon, 22 Apr 2024

14:00 - 15:00
Lecture Room 3

Quantization of Bandlimited Graph Signals

Hanna Veselovska
(Technical University of Munich)
Abstract

Graph signals provide a natural representation of data in many applications, such as social networks, web information analysis, sensor networks, and machine learning. Graph signal & data processing is currently an active field of mathematical research that aims to extend the well-developed tools for analyzing conventional signals to signals on graphs while exploiting the underlying connectivity. A key challenge in this context is the problem of quantization, that is, finding efficient ways of representing the values of graph signals with only a finite number of bits.

In this talk, we address the problem of quantizing bandlimited graph signals. We introduce two classes of noise-shaping algorithms for graph signals that differ in their sampling methodologies. We demonstrate that these algorithms can efficiently construct quantized representatives of bandlimited graph-based signals with bounded amplitude.

Inspired by the results of Zhang et al. in 2022, we provide theoretical guarantees on the relative error between the true signal and its quantized representative for one of the algorithms.
As will be discussed, the incoherence of the underlying graph plays an important role in the quantization process. Namely, bandlimited signals supported on graphs of lower incoherence allow for smaller relative errors. We support our findings with various numerical experiments showcasing the performance of the proposed quantization algorithms for bandlimited signals defined on graphs with different degrees of incoherence.

This is joint work with Felix Krahmer (Technical University of Munich), He Lyu (Meta), Rayan Saab (University of California San Diego), and Rongrong Wang (Michigan State University).

Mon, 22 Apr 2024
15:30
L3

TBC

Prof Eduardo Abi Jaber
(Centre de Mathématiques Appliquées, École polytechnique )
Tue, 23 Apr 2024
11:00
TBC

Random Fourier Signature Features.

Csaba Toth
(Mathematical Insittute)
Abstract

Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to compute the signature kernel scale quadratically in terms of the length and the number of the sequences. To mitigate this severe computational bottleneck, we develop a random Fourier feature-based acceleration of the signature kernel acting on the inherently non-Euclidean domain of sequences. We show uniform approximation guarantees for the proposed unbiased estimator of the signature kernel, while keeping its computation linear in the sequence length and number. In addition, combined with recent advances on tensor projections, we derive two even more scalable time series features with favourable concentration properties and computational complexity both in time and memory. Our empirical results show that the reduction in computational cost comes at a negligible price in terms of accuracy on moderate-sized datasets, and it enables one to scale to large datasets up to a million time series.

Please click here to read the full paper.

Tue, 23 Apr 2024

14:00 - 15:00
L5

TBC

Dmitriy Rumynin
(University of Warwick)
Abstract

to follow

Tue, 23 Apr 2024

14:00 - 14:30
L6

TBA

Zangir Iklassov
( Mohamed bin Zayed University of Artificial Intelligence)
Abstract

TBA

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

TBA

Dan Loughran
(University of Bath)
Abstract

TBA

Thu, 25 Apr 2024
16:00
L4

TBC

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

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

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. 
 


 

Mon, 29 Apr 2024

14:00 - 15:00
Lecture Room 3

TBA

Aretha Teckentrup
(University of Edinburgh)
Abstract

TBA 

Mon, 29 Apr 2024
15:30
Lecture Room 3

TBC

Prof. Weijun Xu
(Beijing International Center for Mathematical Research)
Tue, 30 Apr 2024

14:00 - 15:00
tbc

TBC

Lucas Mason-Brown
((Oxford University))
Abstract

to follow

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

TBD

Matteo Pagliero
(KU Leuven)
Abstract

to follow

Thu, 02 May 2024

12:00 - 13:00
L3

OCIAM TBC

Steve Fitzgerald
(University of Leeds)

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