Thu, 06 Oct 2022

12:00 - 13:00
L2

Some Entropy Rate Approaches in Continuum Mechanics

Prof. Hamid Said
(Kuwait University)
Abstract

Irreversible processes are accompanied by an increase in the internal entropy of a continuum, and as such the entropy production function is fundamental in determining the overall state of the system. In this talk, it will be shown that the entropy production function can be utilized for a variational analysis of certain dissipative continua in two different ways. Firstly, a novel unified Lagrangian-Hamiltonian formalism is constructed giving phase space extra structure, and applied to the study of fluid flow and brittle fracture.  Secondly, a maximum entropy production principle is presented for simple bodies and its implications to the study of fluid flow discussed. 

Thu, 06 Oct 2022

11:00 - 12:00
L2

Second-order regularity properties of solutions to nonlinear elliptic problems

Prof. Andrea Cianchi
(Universita' di Firenze)
Abstract

Second-order regularity results are established for solutions to elliptic equations and systems with the principal part having a Uhlenbeck structure and square-integrable right-hand sides. Both local and global estimates are obtained. The latter apply to solutions to homogeneous Dirichlet problems under minimal regularity assumptions on the boundary of the domain. In particular, if the domain is convex, no regularity of its boundary is needed. A critical step in the approach is a sharp pointwise inequality for the involved elliptic operator. This talk is based on joint investigations with A.Kh.Balci, L.Diening, and V.Maz'ya.

Wed, 05 Oct 2022
17:00
Lecture Theatre 1, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

The million-dollar shuffle: symmetry and complexity - Colva Roney-Dougal

Colva Roney-Dougal
(University of St Andrews)
Further Information

In 1936, Alan Turing proved the startling result that not all mathematical problems can be solved algorithmically. For those which can be, we still do not always know when there's a clever technique which could give us the answer quickly. In particular, the famous "P = NP" question asks whether, for problems where the correct solution has a proof which can easily be checked, in fact there's a quick way to find the answer.

Many difficult problems become easier if they have symmetries: finding the shortest route to deliver many parcels would be easy if all the houses were neatly arranged in a circle. This lecture will explore the interactions between symmetry and complexity.

Colva Roney-Dougal is Professor of Pure Mathematics at the University of St Andrews and Director of the Centre for Interdisciplinary Research in Computational Algebra.

Please email @email to register.

The lecture will be available on our Oxford Mathematics YouTube Channel on 12 October at 5 pm.

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

Mon, 03 Oct 2022

14:00 - 15:00
L1

Theory and Practice of Infinitely Wide Neural Networks

Roman Novak
(Google)
Abstract

A common observation that wider (in the number of hidden units/channels/attention heads) neural networks perform better motivates studying them in the infinite-width limit.

Remarkably, infinitely wide networks can be easily described in closed form as Gaussian processes (GPs), at initialization, during, and after training—be it gradient-based, or fully Bayesian training. This provides closed-form test set predictions and uncertainties from an infinitely wide network without ever instantiating it (!).

These infinitely wide networks have become powerful models in their own right, establishing several SOTA results, and are used in applications including hyper-parameter selection, neural architecture search, meta learning, active learning, and dataset distillation.

The talk will provide a high-level overview of our work at Google Brain on infinite-width networks. In the first part I will derive core results, providing intuition for why infinite-width networks are GPs. In the second part I will discuss challenges and solutions to implementing and scaling up these GPs. In the third part, I will conclude with example applications made possible with infinite width networks.

The talk does not assume familiarity with the topic beyond general ML background.

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

Tue, 20 Sep 2022 09:00 -
Wed, 21 Sep 2022 17:00
L1 and L5

4th IMA Conference on The Mathematical Challenges of Big Data

Please see the programme.
Abstract

4th IMA Conference on The Mathematical Challenges of Big Data


The 4th Ima Conference on The Mathematical Challenges of Big Data is issuing a Call For Papers for both contributed talks and posters. Mathematical foundations of data science and its ongoing challenges are rapidly growing fields, encompassing areas such as: network science, machine learning, modelling, information theory, deep and reinforcement learning, applied probability and random matrix theory. Applying deeper mathematics to data is changing the way we understand the environment, health, technology, quantitative humanities, the natural sciences, and beyond ‐ with increasing roles in society and industry. This conference brings together researchers and practitioners to highlight key developments in the state‐of‐the art and find common ground where theory and practice meet, to shape future directions and maximize impact. We particularly welcome talks aimed to inform on recent developments in theory or methodology that may have applied consequences, as well as reports of diverse applications that have led to interesting successes or uncovered new challenges.

Contributed talks and posters are welcomed from the mathematically oriented data science community. Contributions will be selected based on brief abstracts and can be based on previously unpresented results, or recent material originally presented elsewhere. We encourage contributions from both established and early career researchers. Contributions will be assigned to talks or posters based on the authors request as well as the views of the organizing committee on the suitability of the results. The conference will be held in person with the option to attend remotely where needed.

 

Inducement of sparsity, Heather Battey
Sparsity, the existence of many zeros or near-zeros in some domain, is widely assumed throughout the high-dimensional literature and plays at least two roles depending on context. Parameter orthogonalisation (Cox and Reid, 1987) is presented as inducement of population-level sparsity. The latter is taken as a unifying theme for the talk, in which sparsity-inducing parameterisations or data transformations are sought. Three recent examples are framed in this light: sparse parameterisations of covariance models; systematic construction of factorisable transformations for the elimination of nuisance parameters; and inference in high-dimensional regression. The solution strategy for the problem of exact or approximate sparsity inducement appears to be context specific and may entail, for instance, solving one or more partial differential equation, or specifying a parameterised path through transformation or parameterisation space.

 

Confirmed Invited Speakers
Dr Heather Battey, Imperial College London
Prof. Lenka Zdebrova, EPFL (Swiss Federal Institute Technology)
Prof. Nando de Freitas, Google Deep Mind
Prof. Tiago de Paula Peixoto, Central European University

Please follow the link below for Programme and Registration:

https://ima.org.uk/17625/4th-ima-conference-on-the-mathematical-challen…

 

Thu, 15 Sep 2022

17:00 - 18:00
Lecture Theatre 1, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

A mathematical journey through scales - Martin Hairer

Martin Hairer
(Imperial College)
Further Information

Oxford Mathematics Public Lecture

A mathematical journey through scales - Martin Hairer

The tiny world of particles and atoms and the gigantic world of the entire universe are separated by about forty orders of magnitude. As we move from one to the other, the laws of nature can behave in drastically different ways, sometimes obeying quantum physics, general relativity, or Newton’s classical mechanics, not to mention other intermediate theories.

Understanding the transformations that take place from one scale to another is one of the great classical questions in mathematics and theoretical physics, one that still hasn't been fully resolved. In this lecture, we will explore how these questions still inform and motivate interesting problems in probability theory and why so-called toy models, despite their superficially playful character, can sometimes lead to certain quantitative predictions.

Professor Martin Hairer is Professor of Pure Mathematics at Imperial College London. He was awarded the Fields Medal in 2014.

Please email @email to register.

The lecture will be available on our Oxford Mathematics YouTube Channel on 22 September at 5 pm.

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

Banner for lecture

Fri, 09 Sep 2022

10:00 - 19:00
Bodleian Weston Library

Imagining AI

Troy Astarte (Swansea); David Brock (Computer History Museum); Kanta Dihal (Cambridge); David Dunning (Pennsylvania); Sharon Ruston (Lancaster); and Máté Szabó (Greenwich)
Further Information

Image from Charles Babbage's Passages from the life of a philosopher, London 1864.


EVENTS

Friday 9th September, 10:00 - 19:00, Workshop
Expert discussion of items from Oxford's collections and their  broader context: registration details here https://visit.bodleian.ox.ac.uk/event/sep22/imagining-ai-a-view-from-the-archive 

The event will be chaired by Professor Ursula Martin of Wadham College and Oxford Mathematics.   Speakers include:

  • Troy Astarte (Swansea) on Christopher Strachey's 1950s experiments with computer poetry and chess
  • David Brock (Computer History Museum, Mountain View) on the curation of AI experiments
  • Kanta Dihal (Cambridge), editor AI Narratives (2020, OUP) and Imagining AI (2023, OUP)
  • Sharon Ruston (Lancaster) author of “The science of life and death in Frankenstein" (Bodleian)
  • Máté Szabó (Oxford, Greenwich) on "Max Newman's influence on Turing's early work"

A panel discussion chaired by Professor Rob Iliffe, Head of the Faculty of History, will explore how the history and philosophy of AI and computing can enrich contemporary conversations about the use of these transformative technologies.

See titles, abstracts and more about our speakers here.


Saturday 10 September, Imagining AI demonstrations with Oxford Open Doors

Encounter a world of AI at the Weston Library. 

Meet Ai-Da – booking essential, 11.00 – 12.00 Sir Victor Blank Lecture Theatre    Meet Ai-Da, the world’s first ultra-realistic robot artist, for a Q&A and live art session hosted by Cheney School’s Rumble Museum Council students.  If you have a question for Ai-Da please send it to @email  by Friday 27 August with the subject line ‘Question for Ai-Da’. More here 

Encounter AI – drop-in 10.30 – 15.30  Blackwell Hall.  

  • See a demonstration of a Difference Engine in action, inspired by Charles Babbage's work, courtesy of Royal Holloway, University of London. More here.
  • Discover a cybernetic ladybug that responds to light, sound and interaction. This model provided courtesy of the John von Neumann Computer Society is based on the Hungarian original from the late 1950s. More here.
  • Students from Cheney School will exhibit artwork and creative writing responding to artificial intelligence in our lives today and in the future.
  • Ai-Da will be in Blackwell Hall 13.30 – 15.30 for photographs only.

DISPLAYS OPENING 9th SEPTEMBER

Blackwell Hall, Weston Library  Explore the ideas that led to contemporary AI  with manuscripts of computer pioneer Ada Lovelace; pages from Mary Shelley's draft of "Frankenstein", and notes on computer poetry and draughts from Turing's collaborator Christopher Strachey. The History of Science Museum are lending Stanley Jevons's remarkable mechanical “reasoning piano” from the 1860s, and an even earlier pocket logic calculator.

History of Science Museum See the earliest plans and prototypes of Charles Babbage's computers, and Ada Lovelace's so-called "first programme".


OTHER

13th June and afterwards online, Meet the machines Sharon Ruston and Ursula Martin take a closer look at manuscripts of Mary Shelley, Humphry Davy and Ada Lovelace. Online link to follow.

cs4fn magazine  Cunning Computational Contraptions: Issue 28 of the cs4fn magazine from Queen Mary University of London  looks at some of the machines contrived in earlier times  to support dreams of artificial intelligence. 

The project acknowledges support from UKRI, Oxford's Faulty of History and Mathematical Institute, Wadham College Oxford and the HAPOC Commission. With thanks to David Dunning,  Máté  Szabó, Colin Williams and colleagues at the Bodleian Libraries, History of Science Museum,  Oxford History and Oxford Mathematics.



Friday 9th September, 09.30-17.30, Workshop, Further details

09.30 Register, Blackwell Hall Cafe open.  

10.00 Welcome and introduction. Professor Ursula Martin, Wadham College Oxford and Oxford Mathematics

10.10 Professor Sharon Ruston,  ‘Minds and Machines in Mary Shelley’s Frankenstein and beyond’

Abstract: The question of whether the Creature in Frankenstein is human is one that continues to be asked. Is he more like a man or a machine? In what ways is he like or like us? How much humanity does his maker, Victor Frankenstein, demonstrate in the novel? In this talk, I’ll consider how Mary Shelley’s novel discusses concepts such as the mind, morality, and the soul. I’ll look at other literary examples of apparently mindless states of being, such as suspended animation, somnambulism, and automata. I will also examine some unpublished manuscript notebook pages of the young Davy as he reflects on the dangerous idea that the mind might be thought of as merely a thinking machine. A page of Mary Shelley's manuscript can be seen in the accompanying display.

Biography: Professor Ruston is Chair in Romanticism at Lancaster University. She has published The Science of Life and Death in Frankenstein (2021), Creating Romanticism (2013), Romanticism: An Introduction (2010), and Shelley and Vitality (2005). She co-edited the Collected Letters of Sir Humphry Davy for Oxford University Press (2020). She currently leads an AHRC-funded project to transcribe all of the notebooks of Sir Humphry Davy (and urges everyone to help with this task!), details are here: Davy Notebooks Project | Zooniverse - People-powered research.

10.50 Dr David E Dunning, "A Purely Mechanical Form”: William Stanley Jevons and the Materiality of Reasoning

Abstract: In the 1860s, philosopher of science and political economist William Stanley Jevons (1835–1882) designed a Logic Machine that, he claimed, reduced deduction “to a purely mechanical form.” As a box with a keyboard that mechanically spits out solutions to problems input by a user, this Logical Piano (as it is also known) readily evokes an embryonic idea of the digital computer when viewed with modern eyes. But perhaps what links this device most profoundly to today's computers is, ironically, the fact that it was not really about computing. While the digital computer’s better known predecessors (such as Babbage’s engines) were concerned with numerical calculation, Jevons pursued a more philosophical goal, aiming to show that reasoning was a fundamentally material process. Like the notions of AI that emerged in the second of half of the twentieth century, his project envisioned a form of computing far more expansive than number crunching. In this talk I will situate Jevons’s machine in the context of early symbolic logic that produced it, focusing on the novel techniques of writing that he built on, and built into his device. I will use this history to understand the role of material processes such as instruction, display, and memory in the context of machines and the intelligence we imagine them to possess. The machine can be seen in the accompanying display.

Biography: David E. Dunning is a Lecturer in the Integrated Studies Program at the University of Pennsylvania and the 2022–23 IEEE Life Member History Fellow. He is a historian of science, technology, and mathematics, whose research focuses on the material and social dimensions of abstract knowledge. He co-developed the  Imagining AI display while at the Mathematical Institute at the University of Oxford. 

11.30 David C. Brock, Learning from AI’s Eternal Recurrence: Documenting the History of Expert Systems at the Computer History Museum

Abstract: The starting point for some of the Computer History Museum’s most recent work to document the history of artificial intelligence – through proactive collecting and oral histories – was recognizing a striking recurrence of both rhetoric and action in and around the artificial intelligence community. Increasingly over the past decade, researchers and commentators alike have hailed the combination of neural networks with large data sets and vast amounts of computing resources as a fundamental break with the past, with transformative sociopolitical implications for the near and far futures. The current CEO of Google recently went so far as to compare this to the first human control of fire. This same rhetoric – and the same flurry of action spanning commercialization and expanded government, especially military, interest and investment – can be found in the artificial intelligence community and commentators of the 1980s. Then, the past-shattering and future-altering combination was expert systems and advanced computing resources. In this talk, I will attempt to elucidate this recurrence, and will argue that one of the most celebrated achievements of the expert systems era – the military logistics system, DART, deployed by the US in the Gulf War of 1990-1991 – shows one possible future for our current moment.

Biography: David C. Brock is the Director of Curatorial Affairs, and the Director of the Software History Center, for the Computer History Museum in Mountain View, California. He is the co-author of Moore’s Law: The Life of Gordon Moore, Silicon Valley’s Quiet Revolutionary (Basic Books, 2015) and of Makers of the Microchip: A Documentary History of Fairchild Semiconductor (MIT Press, 2010).

12.10 Break Lunch can be purchased in the Blackwell Hall Cafe, or elsewhere. Dedicated seating available.

13.30 Dr Troy Astarte, Christopher Strachey and the “thinking” machine 

Abstract: As the electronic calculator of the 1940s was replaced by the computer of the 1950s, and its flexibility was slowly revealed, comparisons to human cognition were immediate: Giant Brains and Faster than Thought. While most who worked with computers knew this was little but a metaphor, the question of whether machines could really think was a good route for exploring their capabilities. This was certainly the case for Christopher Strachey (1916–1975), with a Bloomsbury Group pedigree and protean curiosity. In 1950, he was a schoolmaster at Harrow, but managed to find himself time to experiment with computers. While most computer applications were still numerical, Strachey explored games, literature, and music, alongside systems to make programming easier. These various programs, some of them almost unique in their time, gave Strachey ample opportunity to ruminate on the question of computers and their ability to think—or lack thereof. Strachey's notes can be seen in the accompanying display.

Biography: Troy Kaighin Astarte is a teaching-focused lecturer in computer science at Swansea University. Educated in computing at Newcastle University, their research interest moved to the history of computing and computer science in particular. Building on research on the history of formal semantics of programming languages, and the history of concurrency, Troy is interested in questions about the role of computer science in shaping the world and vice-versa. 

14.10 Dr Máté Szabó, Max Newman's Influence on Turing's Early Work

Abstract: In 1936 Turing published his groundbreaking article “On Computable Numbers”, in which he described a mathematical model of machine computation that later became known as Turing Machines. Turing became interested in the topic while attending Max Newman’s course on logic and foundations of mathematics a year earlier. In this talk I will take a look at little known early works of Newman and show how they ifluenced Turing’s seminal paper. 

Biography: Máté Szabó is a historian and philosopher of computing and mathematical logic. He earned his PhD in "Logic, Computation and Methodology" from the Department of Philosophy at Carnegie Mellon University. He co-developed the  Imagining AI display while at the Mathematical Institute at the University of Oxford, and is currently he is a lecturer at the University of Greenwich.

14.50 Dr Kanta Dihal, How the world sees intelligent machines

Abstract: People have been imagining intelligent machines for millennia, in ways that vary greatly across cultures. Yet as artificial intelligence begins to fulfil its potential as a technology, spreading across the globe from its origins in 1950s America, many of these perspectives are marginalised. These stories, films, and visions matter: they are entangled in broader cultural attitudes and approaches to AI, reflecting or inspiring, embedding or disputing them. I will introduce such visions from across the globe, and what they can tell us now that AI is becoming a technological reality. I will draw out three themes: real and apparent differences between ‘Eastern’ and ‘Western’ portrayals of AI; visions of AI in communist states; and narratives of AI that explicitly aim to reject colonialist views of the technology.

Biography: Dr Kanta Dihal is a Senior Research Fellow at the Leverhulme Centre for the Future of Intelligence, University of Cambridge. Her research focuses on science narratives, particularly those that emerge from conflict. She currently manages the project ‘Desirable Digitalisation’, an international research collaboration that investigates intercultural perspectives on AI and fundamental rights and values. She is co-editor of the books AI Narratives (2020) and Imagining AI (2023) and has advised the World Economic Forum, the UK House of Lords, and the United Nations. She obtained her DPhil on the communication of quantum physics at Oxford in 2018.

15.30 Break, refreshments can be purchased at the cafe. Dedicated seating available.

16.00 Panel discussion hosted by the Faculty of History  The panel will explore how the history and philosophy of AI and computing can enrich contemporary conversations about the use of these transformative technologies.  

Chair: Professor Rob Iliffe, Head of Oxford's Faculty of History  Panellists:  Al Brown, Visiting Fellow, University of Oxford.; Dr Keith Dear, Defence & National Security, Fujitsu; Dr Kanta Dihal, University of Cambridge; Dr Philip Garnett, University of York; Professor Sharon Ruston, University of Lancaster; Dr Keith Scott, De Montfort University; Colin Williams, University of Oxford.

17.30 -  19.00 Reception: wine, soft drinks and snacks.

Abstract

Join us in Oxford in September 2022  for displays, demonstrations and a lively workshop discussions celebrating the minds, manuscripts and machines that made the dreams and realities that  we now call artificial intelligence. 

Mon, 15 Aug 2022 09:30 -
Fri, 19 Aug 2022 15:00
L3

PDE WORKSHOP: Stability Analysis for Nonlinear PDEs

((Department of Mathematics)
Further Information

 

Monday 15th August

09:30     10:30     Morning Refreshments

10:30     11:20     Session 1: Mikhail Feldman

11:30     12:20     Session 2: Cleopatra Christoforou

12:30     14:30     Lunch Break

14:30     15:20     Session 3: Jiang-Lun Wu

 

Tuesday 16th August

09:30     10:30     Morning Refreshments

10:30     11:20     Session 4: Jonathan Ben-Artzi

11:30     12:20     Session 5: Mikhail Perepelita

12:30     14:30     Lunch Break

14:30     15:20     Session 6: Monica Torres

 

Wednesday 17th August

09:30     10:30     Morning Refreshments

10:30     11:20     Session 7: Aram Karakhanyan

11:30     12:20     Session 8: Piotr Gwiazda

12:30     14:30     Lunch Break

14:30     15:20     Session 9: Cheng Yu

15:30     16:20     Session 10: Steve Shkoller (UC-Davis, USA) [online]

 

Thursday

09:30     10:00     Morning Refreshments

10:00     10:50     Session 11: Susana Gutierrez

11:00     11:25     Session 12: Matthew Schrecker

11:30     12:00     Morning Break (30mins)

12:00     12:25     Session 13: Timon Salar Gutleb

12:30     12:55     Session 14: Yucong Huang

13:00     14:30     Conference Lunch (90mins)

14:30     15:20     Session 15: Nicolas Dirr

15:30     16:20     Session 16: Dehua Wang (U. Pittsburgh, USA) [online]

16:30     17:00     Afternoon Break (20mins)

17:00     17:50     Session 17: Pierre-Emmanuel Jabin (Penn State, USA) [online]

18:30     21:00     Conference Dinner

 

Friday

09:30   10:30   Morning Refreshments

10:30   11:20   Session 18: Ewelina Zatorska 

11:30   12:20   Session 19: Alexis Vasseur

12:30   12:45  Closing Remarks

13:00    ** **   Conference Lunch

 

PDE Workshop Programme.pdf

 

Slides: Alexis Vasseur_2.pdf / Cheng Yu_1.pdf / Cleopatra Christoforou_0.pdf / Ewelina Zatorska.pdf / Jiang-Lun Wu.pdf / Jonathan Ben-Artzi.pdf / Matthew Schrecker.pdf / Mikhail Feldman.pdf / Mikhail A Perepelitsa.pdf / Monica Torres.pdf / Nicolas Dirr.pdf / Pierre-Emmanuel.pdf / Susana Gutierrez.pdf / Timon Salar Gutleb.pdf / Yucong Huang.pdf

 

Organisers: 

Prof. Gui-Qiang G. Chen

Prof. José A. Carrillo

Prof. Endre Süli

 

Administrators:

Charlotte Turner-Smith 

Sarah Randall

Kerri Louise Howard FInstAM ACIM

Abstract

Maths PNG

 

 

 

 

 

 

 

 

 

 

PDE Workshop in Stability Analysis for Nonlinear PDEs will be running Monday 15th - Friday 19th August.

Location: L3, AWB

Our goal was to bring together leading experts in the stability analysis of nonlinear partial differential equations across multi-scale applications. Some of the topics to be addressed include: 

  • Stability analysis of shock wave patterns of reflections/diffraction.
  • Stability analysis of vortex sheets, contact discontinuities, and other characteristic discontinuities for multidimensional hyperbolic systems of conservation laws.
  • Stability analysis of particle to continuum limits including the quantifying asymptotic/mean-field/large-time limits for pairwise interactions and particle limits for general interactions among multi-agent systems
  • Stability analysis of asymptotic limits with emphasis on the vanishing viscosity limit of solutions from multidimensional compressible viscous to inviscid flows with large initial data.
Thu, 04 Aug 2022
15:00
S2.27

K-theoretic classification of inductive limit actions of fusion categories on AF-algebras

Roberto Hernandez Palomares
(Texas A&M University)
Abstract

I will introduce a K-theoretic complete invariant of inductive limits of finite dimensional actions of fusion categories on unital AF-algebras. This framework encompasses all such actions by finite groups on AF-algebras. Our classification result essentially follows from applying Elliott's Intertwining Argument adapted to this equivariant context, combined with tensor categorical techniques.

Our invariant roughly consists of a finite list of pre-ordered abelian groups and positive homomorphisms, which can be computed in principle. Under certain conditions this can be done in full detail. For example, using our classification theorem, we can show torsion-free fusion categories admit a unique AF-action on certain AF-algebras.

Connecting with subfactors, inspired by Popa’s classification of finite-depth hyperfinite subfactors by their standard invariant, we study unital inclusions of AF-algebras with trivial centers, as natural analogues of hyperfinite II_1 subfactors. We introduce the notion of strongly AF-inclusions and an Extended Standard Invariant, which characterizes them up to equivalence.

Thu, 07 Jul 2022
12:00
C2

Resonances and unitarity from celestial amplitude

Dr Jinxiang Wu
((Oxford University))

Note: we would recommend to join the meeting using the Zoom client for best user experience.

Abstract

We study the celestial description of the O(N) sigma model in the large N limit. Focusing on three dimensions, we analyze the implications of a UV complete, all-loop order 4-point amplitude of pions in terms of correlation functions defined on the celestial circle. We find these retain many key features from the previously studied tree-level case, such as their relation to Generalized Free Field theories and crossing-symmetry, but also incorporate new properties such as IR/UV softness and S-matrix metastable states. In particular, to understand unitarity, we propose a form of the optical theorem that controls the imaginary part of the correlator based solely on the presence of these resonances. We also explicitly analyze the conformal block expansions and factorization of four-point functions into three-point functions. We find that summing over resonances is key for these factorization properties to hold. This is a joint work with D. García-Sepúlveda, A. Guevara, J. Kulp.

Wed, 06 Jul 2022
12:00
C2

Pushing Forward Rational Differential Forms

Robert Moermann
(University of Hertfordshire)

Note: we would recommend to join the meeting using the Zoom client for best user experience.

Abstract

The scattering equations connect two modern descriptions of scattering amplitudes: the CHY formalism and the framework of positive geometries. For theories in the CHY family whose S-matrix is captured by some positive geometry in the kinematic space, the corresponding canonical form can be obtained as the pushforward via the scattering equations of the canonical form of a positive geometry in the CHY moduli space. In this talk, I consider the general problem of pushing forward rational differential forms via the scattering equations. I will present some recent results (2206.14196) for achieving this without ever needing to explicitly solve any scattering equations. These results use techniques from computational algebraic geometry, and they extend the application of similar results for rational functions to rational differential forms.

Wed, 29 Jun 2022

16:00 - 17:00

Information theory with kernel methods

Francis Bach
(INRIA - Ecole Normale Supérieure)
Further Information
Abstract

I will consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. In this talk, I will show that the von Neumann entropy and relative entropy of these operators are intimately related to the usual notions of Shannon entropy and relative entropy, and share many of their properties. They come together with efficient estimation algorithms from various oracles on the probability distributions. I will also present how these new notions of relative entropy lead to new upper-bounds on log partition functions, that can be used together with convex optimization within variational inference methods, providing a new family of probabilistic inference methods (based on https://arxiv.org/pdf/2202.08545.pdf, see also https://francisbach.com/information-theory-with-kernel-methods/).

Tue, 28 Jun 2022

14:00 - 15:00
C3

The temporal rich club phenomenon

Nicola Pedreschi
(Mathematical Institute (University of Oxford))
Abstract

Identifying the hidden organizational principles and relevant structures of complex networks is fundamental to understand their properties. To this end, uncovering the structures involving the prominent nodes in a network is an effective approach. In temporal networks, the simultaneity of connections is crucial for temporally stable structures to arise. In this work, we propose a measure to quantitatively investigate the tendency of well-connected nodes to form simultaneous and stable structures in a temporal network. We refer to this tendency as the temporal rich club phenomenon, characterized by a coefficient defined as the maximal value of the density of links between nodes with a minimal required degree, which remain stable for a certain duration. We illustrate the use of this concept by analysing diverse data sets and their temporal properties, from the role of cohesive structures in relation to processes unfolding on top of the network to the study of specific moments of interest in the evolution of the network.

Article link: https://www.nature.com/articles/s41567-022-01634-8

Mon, 27 Jun 2022
16:15
St Catherine's

The Reddick Lecture 2022: The Benefits of Applied Mathematics in Product Development

Dr Uwe Beuscher, W.L. Gore & Associates, Inc.
Further Information

For more information, and to register your interest, please visit the Reddick Lecture web page

Abstract

Throughout a product development project, many decisions must be made. These include whether to start, stop, continue, or re-direct a project based on the learnings of the project team. Some of these decisions are related to the risk of achieving certain product performance attributes and they are often based on experimental observations in the laboratory or in field applications of early prototypes. Sometimes, these observations provide sufficient insight but often a significant uncertainty remains. Mathematical simulation can provide deeper insight into the mechanisms, may indicate limiting parameters and transport steps, and allows exploration of novel prototypes without actually making them. This talk will illustrate how Mathematics have been used to inform project development projects and their guiding decisions at WL Gore by describing examples from three very different applications.

Mon, 27 Jun 2022

12:45 - 13:45
L3

Marginal quenches and drives in Tomonaga-Luttinger liquids/free boson CFTs

Apoorv Tivari
(Stockholm)
Abstract

I will discuss the free compact boson CFT thrown out of equilibrium by marginal deformations, modeled by quenching or periodically driving the compactification radius of the free boson between two different values. All the dynamics will be shown to be crucially dependent on the ratio of the compactification radii via the Zamolodchikov distance in the space of marginal deformations. I will present various exact analytic results for the Loschmidt echo and the time evolution of energy density for both the quench and the periodic drive. Finally, I will present a non-perturbative computation of the  Rényi divergence, an information-theoretic distance measure, between two marginally deformed thermal density matrices.

 

The talk will be based on the recent preprint: arXiv:2206.11287

Mon, 27 Jun 2022 09:00 -
Fri, 22 Jul 2022 17:00
Mathematical Institute, Ground and Mezzanine levels

All we ever wanted was everything / 24.02.22 (for Ukraine)

Andy Bullock
Further Information

On June 27th, in the Reception area of the Mathematical Institute, Oxford artist Andy Bullock unveiled his most ambitious knot sculpture to date, a large floor-based work titled ‘All we ever wanted was everything / 24.02.22 (for Ukraine)’ constructed using 70 metres of metal trunking. As with all his knot sculptures they often reference issues of complexity with situations and people, the personal and interpersonal; focusing on what it means to be human.

In a first for the artist, Bullock will be inviting members of the recently arrived Ukrainian refugee community to contribute to the artwork by incorporating items of personal relevance. Bullock is reaching out to Oxfordshire’s Ukrainian community in a collaboration with Yulia Astasheva, a recent arrival herself from the Dnipropetrovsk region, where she still has close family living only miles from the Russian-occupied region.

The idea for the work came initially from a commission from Oxford Mathematics for Bullock to create an exhibition of his maths-related painting, photography and sculpture to be open to the public this summer. The core of his fine art master’s degree show last year was a creative examination and exploration of the topological subject of knot theory, and in particular the work of Clifford Hugh Dowker (1912-82) an eminent mathematician whose work is still studied today. “I find a poetic beauty in the mathematics I researched even though my understanding of the subject is virtually nil” said Bullock. “My final dissertation for my master’s degree examined the similarities in thought of mathematicians working in these areas and that of artists working in a more conceptual arena”.

In the lower ground floor space of the building there is an exhibition of some of Andy Bullock’s ‘knot variation’ paintings and photographs and a display of original handwritten manuscripts from Dowker’s personal archive alongside Andy's own sketchbooks, allowing an insight into the respective processes of mathematician and artist.

For further information:

Andy Bullock - @email - 07582 526957 - www.bullockstudio.com

Yulia Astasheva - @email

Tue, 21 Jun 2022

16:30 - 17:30
C1

Amenable actions and purely infinite crossed products

Julian Kranz
(University of Münster)
Abstract

Since the completion of the Elliott classification programme it is an important question to ask which C*-algebras satisfy the assumptions of the classification theorem. We will ask this question for the case of crossed-product C*-algebras associated to actions of nonamenable groups and focus on two extreme cases: Actions on commutative C*-algebras and actions on simple C*-algebras. It turns out that for a large class of nonamenable groups, classifiability of the crossed product is automatic under the minimal assumptions on the action. This is joint work with E. Gardella, S. Geffen, P. Naryshkin and A. Vaccaro. 

Tue, 21 Jun 2022

14:00 - 15:00
L6

The orbit method and normality of closures of nilpotent orbits

Dan Barbasch
(Cornell University, USA)
Abstract

The work of Kraft-Procesi classifies closures of nilpotent orbits that are normal in the cases of classical complex Lie algebras. Subsequent work of Ranee Brylinsky combines this work with the Theta correspondence as defined by Howe to attach a representation of the corresponding complex group. It provides a quantization of the closure of a nilpotent orbit. In joint work with Daniel Wong, we carry out a detailed analysis of these representations viewed as (\g,K)-modules of the complex group viewed as a real group. One consequence is a "representation theoretic" proof of the classification of Kraft-Procesi.

Tue, 21 Jun 2022

14:00 - 15:00
C6

Sequential Motifs in Observed Walks

Timothy LaRock
(Mathematical Institute (University of Oxford))
Abstract

The structure of complex networks can be characterized by counting and analyzing network motifs, which are small graph structures that occur repeatedly in a network, such as triangles or chains. Recent work has generalized motifs to temporal and dynamic network data. However, existing techniques do not generalize to sequential or trajectory data, which represents entities walking through the nodes of a network, such as passengers moving through transportation networks. The unit of observation in these data is fundamentally different, since we analyze observations of walks (e.g., a trip from airport A to airport C through airport B), rather than independent observations of edges or snapshots of graphs over time. In this work, we define sequential motifs in trajectory data, which are small, directed, and sequenced-ordered graphs corresponding to patterns in observed sequences. We draw a connection between counting and analysis of sequential motifs and Higher-Order Network (HON) models. We show that by mapping edges of a HON, specifically a kth-order DeBruijn graph, to sequential motifs, we can count and evaluate their importance in observed data, and we test our proposed methodology with two datasets: (1) passengers navigating an airport network and (2) people navigating the Wikipedia article network. We find that the most prevalent and important sequential motifs correspond to intuitive patterns of traversal in the real systems, and show empirically that the heterogeneity of edge weights in an observed higher-order DeBruijn graph has implications for the distributions of sequential motifs we expect to see across our null models.

ArXiv link: https://arxiv.org/abs/2112.05642

Mon, 20 Jun 2022
15:30
L5

Coxeter groups acting on CAT(0) cube complexes

Michah Sageev
Abstract

We will give a general overview of how one gets groups to act on CAT(0) cube complexes, how compatible such actions are and how this plays out in the setting of Coxeter groups.

 

Mon, 20 Jun 2022

12:45 - 13:45
L4

Large N Partition Functions, Holography, and Black Holes

Nikolay Bobev
Abstract

I will discuss the large N behavior of partition functions of the ABJM theory on compact Euclidean manifolds. I will pay particular attention to the S^3 free energy and the topologically twisted index for which I will present closed form expressions valid to all order in the large N expansion. These results have important implications for holography and the microscopic entropy counting of AdS_4 black holes which I will discuss. I will also briefly discuss generalizations to other SCFTs arising from M2-branes.

Fri, 17 Jun 2022

16:00 - 17:00
L5

Defect Central Charges

Adam Chalabi
(Southampton University)
Abstract

Conformal defects can be characterised by their contributions to the Weyl anomaly. The coefficients of these terms, often called defect central charges, depend on the particular defect insertion in a given conformal field theory. I will review what is currently known about defect central charges across dimensions, and present novel results. I will discuss many examples where they can be computed exactly without requiring any approximations or limits. Particular emphasis will be placed on recently developed tools for superconformal defects as well as defects in free theories.

Fri, 17 Jun 2022

14:00 - 15:00
L6

Data-driven early detection of potential high risk SARS-CoV-2 variants

Dr Marcin J. Skwark
(InstaDeep)
Abstract

Recent advances in Deep Learning have enabled us to explore new application domains in molecular biology and drug discovery - including those driven by complex processes that defy analytical modelling.  However, despite the combined forces of increased data, improving compute resources and continuous algorithmic innovation all bringing previously intractable problems into the realm of possibility, many advances are yet to make a tangible impact for life science discovery.  In this talk, Dr Marcin J. Skwark will discuss the challenge of bringing machine learning innovation to tangible real-world impact.  Following a general introduction of the topic, as well as newly available methods and data, he will focus on the modelling of COVID-19 variants and, in particular, the DeepChain Early Warning System (EWS) developed by InstaDeep in collaboration with BioNTech.  With thousands of new, possibly dangerous, SARS-CoV-2 variants emerging each month worldwide, it is beyond humanities combined capacity to experimentally determine the immune evasion and transmissibility characteristics of every one.  EWS builds on an experimentally tested AI-first computational biology platform to evaluate new variants in minutes, and is capable of risk monitoring variant lineages in near real-time.  This is done by combining an AI-driven protein structure prediction framework with large, spike protein sequence-oriented Transformer models to allow for rapid simulation-free assessment of the immune escape risk and expected fitness of new variants, conditioned on the current state of the world.  The system has been extensively validated in cooperation with BioNTech, both in terms of host cell infection propensity (including experimental assays of receptor binding affinity), and immune escape (pVNT assays with monoclonal antibodies and real-life donor sera). In these assessments, purely unsupervised, data-first methods of EWS have shown remarkable accuracy. EWS flags and ranks all but one of the SARS-CoV-2 Variants of Concern (Alpha, Beta, Gamma, Delta… Omicron), discriminates between subvariants (e.g. BA.1/BA.2/BA.4 etc. distinction) and for most of the adverse events allows for proactive response on the day of the observation. This allows for appropriate response on average six weeks before it is possible for domain experts using domain knowledge and epidemiological data. The performance of the system, according to internal benchmarks, improves with time, allowing for example for supporting the decisions on the emerging Omicron subvariants on the first days of their occurrence. EWS impact has been notable in general media [2, 3] for the system's applicability to a novel problem, ability to derive generalizable conclusions from unevenly distributed, sparse and noisy data, to deliver insights which otherwise necessitate long and costly experimental assays.