Forthcoming events in this series

Wed, 21 Feb 2024

14:00 - 15:00
Lecture Theatre 2, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

Classical density-functional theory: from formulation to nanofluidics to machine learning

Serafim Kalliadasis
(Imperial College London)
Further Information

This is an Oxford Solid Mechanics and Mathematics Joint Seminar


We review progress made by our group on soft matter at interfaces and related physics from the nano- to macroscopic lengthscales. Specifically, to capture nanoscale properties very close to interfaces and to establish a link to the macroscale behaviour, we employ elements from the statistical mechanics of classical fluids, namely density-functional theory (DFT). We formulate a new and general dynamic DFT that carefully and systematically accounts for the fundamental elements of any classical fluid and soft matter system, a crucial step towards the accurate and predictive modelling of physically relevant systems. In a certain limit, our DDFT reduces to a non-local Navier-Stokes-like equation that we refer to as hydrodynamic DDFT: an inherently multiscale model, bridging the micro- to the macroscale, and retaining the relevant fundamental microscopic information (fluid temperature, fluid-fluid and wall-fluid interactions) at the macroscopic level.


Work analysing the moving contact line in both equilibrium and dynamics will be presented. This has been a longstanding problem for fluid dynamics with a major challenge being its multiscale nature, whereby nanoscale phenomena manifest themselves at the macroscale. A key property captured by DFT at equilibrium, is the fluid layering on the wall-fluid interface, amplified as the contact angle decreases. DFT also allows us to unravel novel phase transitions of fluids in confinement. In dynamics, hydrodynamic DDFT allows us to benchmark existing phenomenological models and reproduce some of their key ingredients. But its multiscale nature also allows us to unravel the underlying physics of moving contact lines, not possible with any of the previous approaches, and indeed show that the physics is much more intricate than the previous models suggest.


We will close with recent efforts on machine learning and DFT. In particular, the development of a novel data-driven physics-informed framework for the solution of the inverse problem of statistical mechanics: given experimental data on the collective motion of a classical many-body system, obtain the state functions, such as free-energy functionals.

Fri, 23 Jun 2023
Lecture Room 5

Groups and Geometry in the South East

Emmanuel Breuillard (Oxford), Koji Fujiwara (Kyoto), Marc Lackenby (Oxford)

Counting incompressible surfaces in hyperbolic 3-manifolds.


Marc Lackenby (Oxford)

Incompressible embedded surfaces play a central role in 3-manifold theory. It is a natural and interesting question to ask how many such surfaces are contained in a given 3-manifold M, as a function of their genus g. I will present a new theorem that provides a surprisingly small upper bound. For any given g, there a polynomial p_g with the following property. The number of closed incompressible surfaces of genus g in a hyperbolic 3-manifold M is at most p_g(vol(M)). This is joint work with Anastasiia Tsvietkova.


The rates of growth in hyperbolic groups.


Koji Fujiwara (Kyoto)

For a finitely generated group of exponential growth, we study the set of exponential growth rates for all possible finite generating sets. Let G be a hyperbolic group. It turns out that the set of growth rates is well-ordered.  Also, given a number, there are only finitely many generating sets that have this number as the growth rate. I also plan to discuss the set of growth for a family of groups.


Character varieties of random groups.


Emmanuel Breuillard (Oxford)

In joint work with P. Varju and O. Becker we study the representation and character varieties of random finitely presented groups with values in a complex semisimple Lie group.  We compute the dimension and number of irreducible components of the character variety of a random group. In particular we show that random one-relator groups have many rigid Zariski-dense representations. The proofs use a fair amount of number theory and are conditional on GRH. Key to them is the use of expander graphs for finite simple groups of Lie type as well as a new spectral gap result for random walks on linear groups.

Tue, 01 Nov 2022

14:00 - 15:00

HiGHS: From gradware to software and Impact

Dr Julian Hall
(University of Edinburgh)

HiGHS is open-source optimization software for linear programming, mixed-integer programming, and quadratic programming. Created initially from research solvers written by Edinburgh PhD students, HiGHS attracted industrial funding that allowed further development, and saw it contribute to a REF 2021 Impact Case Study. Having been identified as a game-changer by the open-source energy systems planning community, the resulting crowdfunding campaign has received large donations that will allow the HiGHS project to expand and create further Impact.

This talk will give an insight into the state-of-the-art techniques underlying the linear programming solvers in HiGHS, with a particular focus on the challenge of solving sequences of linear systems of equations with remarkable properties. The means by which "gradware" created by PhD students has been transformed into software, generating income and Impact, will also be described. Independent benchmark results will be given to demonstrate that HiGHS is the world’s best open-source linear optimization software.


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.


Friday 9th September, 10:00 - 19:00, Workshop
Expert discussion of items from Oxford's collections and their  broader context: registration details here 

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.


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".


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.


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. 

Fri, 10 Jun 2022

13:30 - 17:00
Lecture Theatre 5

Groups and Geometry in the South East

(Mathematical Institute)
Further Information

Property (T) and random quotients of hyperbolic groups


Calum Ashcroft (Cambridge)

In his original manuscript on hyperbolic groups, Gromov asked whether random quotients of non-elementary hyperbolic groups have Property (T). This question was later refined by Ollivier, and then answered in the case of random quotients of free groups by Zuk (and Kotowski--Kotowski).

In this talk we answer the Gromov--Ollivier question in the affirmative. We will discuss random quotients and some of their properties, in particular with relation to Property (T).

Connections between hyperbolic geometry and median geometry


Cornelia Drutu (Oxford)

In this talk I shall explain how groups endowed with various forms of hyperbolic geometry, from lattices in rank one simple groups to acylindrically hyperbolic groups, present various degrees of compatibility with the median geometry. This is joint work with Indira Chatterji, and with John Mackay.



Division, group rings, and negative curvature


Grigori Avramidi (Bonn)

In 1997 Delzant observed that fundamental groups of hyperbolic manifolds with large injectivity radius have nicely behaved group rings. In particular, these rings have no zero divisors and only the trivial units. In this talk I will explain how to extend this observation to show such rings have a division algorithm (generalizing the division algorithm for group rings of free groups discovered by Cohn) and that these group rings have``freedom theorems’’ showing that all of their ideals that are generated by few elements are free, where the specific value of `few’ depends on the injectivity radius of the manifold (which can be viewed as generalizations from subgroups to ideals of some freedom theorems of Delzant and Gromov). This has geometric consequences to the homotopy classification of 2-complexes with surface fundamental groups and to complexity of cell structures on hyperbolic manifolds.

Tue, 08 Mar 2022

13:00 - 18:00

International Women’s Day

(Oxford University)
Further Information

Please join us to celebrate International Women’s Day on Tuesday the 8th of March.

To address this year’s theme - Break the Bias - we will be hosting two sessions in Lecture Theatre 2:

1-2.30pm - How Women Rise in Professional Services, a focus on gender equality from the perspective of Professional Services Staff

2.45-5pm  - A screening of 'Picture A Scientist' and panel discussion

5pm – Drinks reception

Please sign up here.

Tue, 14 May 2019

17:00 - 18:00

Book launch: The Mathematical World of Charles L. Dodgson (Lewis Carroll)

Robin Wilson
(University of Oxford)
Further Information

There has been much recent interest in the mathematical activities of C. L. Dodgson (Lewis Carroll), especially with the publication of Dodgson’s diaries and my popular paperback, ‘Lewis Carroll in Numberland’ which described his mathematical ‘day job’ in the context of Victorian Oxford and his role as Mathematical Lecturer at Christ Church. But for some time there’s been a need for a more serious single-volume book that covers all aspects of his mathematical activities, written by experts from around the world, and this was achieved in February with the publication of this book by Oxford University Press edited by Robin Wilson and Amirouche Moktefi.

This talk will outline his mathematical career and specifically his work in geometry, algebra, logic, voting theory and recreational mathematics, and will be followed by an opportunity to acquire the book at a reduced cost.

Fri, 11 Jan 2019

09:30 - 17:00

SIAM UKIE Annual Meeting 2019

(University of Cambridge and others)

The 23rd Annual Meeting of the SIAM UKIE Section will take place on Friday 11th January 2019 at the Mathematical Institute at the University of Oxford.

The meeting will feature five invited speakers covering a broad range of industrial and applied mathematics: 

- Lisa Fauci, Tulane University, Incoming SIAM President
- Des Higham, Strathclyde University 
- Carola-Bibiane Schoenlieb (IMA sponsored speaker), University of Cambridge 
- Kirk Soodhalter, Trinity College Dublin 
- Konstantinos Zygalakis, University of Edinburgh 

There will also be a poster session, open to PhD students and postdocs. Travel support will be available for PhD students with an accepted poster presentation, and Best Poster prizes will be awarded. 

All talks will take place in room L3 in the Andrew Wiles Building (Mathematical Institute, University of Oxford). 

09:30 - 10:00 Registration, tea/coffee 
10:00 - 10:15 Welcome 
10:15 - 11:00 Des Higham: Our Friends are Cooler than Us 
11:00 - 11:45 Lisa Fauci: Complex dynamics of fibers in flow at the microscale 
11:45 - 12:15 Poster Blitz 
12:15 - 13:30 Lunch and Poster session 
13:30 - 14:00 SIAM UKIE Business Meeting, open to all 
14:00 - 14:45 Kirk Soodhalter: Augmented Arnoldi-Tikhonov Methods for Ill-posed Problems 
14:45 - 15:30 Konstantinos Zygalakis: Explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems 
15:30 - 16:00 Tea/coffee 
16:00 - 16:45 Carola-Bibiane Schoenlieb (IMA sponsored speaker): Variational models and partial differential equations for mathematical imaging 
16:45 - 17:00 Poster prize announcement

Thu, 16 Mar 2017

14:30 - 15:30

"Algebraically closed fields of characteristic 1."

Boris Zilber

 I will start with a motivation of what algebraic and model-theoretic properties an algebraically closed field of characteristic 1 is expected to have. Then I will explain how these properties forces one to follow the route of Hrushovski's construction leading to a a 'pseudo-analytic' structure which we identify as an algebraically closed field of characteristic 1 . Then I am able to formulate very precise axioms that such a field must satisfy.  The main theorem then states that under the axioms the structure has the desired algebraic and analytic properties. The axioms have a form of statements about existence of solutions to systems of equations in terms of a 'multi-dimensional' valuation theory and the validity of these statements is an open problem to be discussed. 
This is a joint work with Alex Cruz Morales.

Thu, 16 Mar 2017

12:00 - 13:00

"Analytic geometry over the field with one element"

Yakov Kremnitzer

1.Kremnitzer. I will explain an approach to constructing geometries relative to a symmetric monoidal 
category. I will then introduce the category of normed sets as a possible analytic geometry over 
the field with one element. I will show that the Fargues-Fontaine curve from p-adic Hodge theory and 
the Connes-Bost system are naturally interpreted in this geometry. This is joint work with Federico Bambozzi and 
Oren Ben-Bassat.

Mon, 23 May 2016

Rediscovering Ada Lovelace's Mathematics

Ursula Martin

Part of the series 'What do historians of mathematics do?'

Ada Lovelace (1815-1852) is famous as "the first programmer" for her prescient writings about Charles Babbage's unbuilt mechanical computer, the Analytical Engine. Biographers have focused on her tragically short life and her supposed poetic approach – one even dismissed her mathematics as "hieroglyphics". This talk will focus on how she learned the mathematics she needed to write the paper – a correspondence course she took with Augustus De Morgan – which is available in the Bodleian Library. I'll also reflect more broadly on things I’ve learned as a newcomer to the history of mathematics.

Tue, 17 May 2016

10:00 - 11:00

Number theory tools for Cryptographic Applications

Giacomo Micheli
((Oxford University))

In this lecture we describe the effective Chebotarev Theorem for global function fields and show how this can be used to describe the statistics of a polynomial map f in terms of its monodromy groups. With this tool in hand, we will provide a strategy to remove the remaining heuristic in the quasi-polynomial time algorithm for discrete
logarithm problems over finite fields of small characteristic.

Mon, 16 May 2016

Four Colours Suffice

Robin Wilson

Part of the series 'What do historians of mathematics do?'

"In this talk I present the history and proof of the four-colour theorem: Can every map be coloured with just four colours so that neighbouring countries are coloured differently?  The proof took 124 years to find, and used 1200 hours of computer time. But what did it involve, and is it really a proof?"

Mon, 09 May 2016

Charles Hutton 'One of the Greatest Mathematicians in Europe'?

Benjamin Wardhaugh

Part of the series 'What do historians of mathematics do?'

I'm currently working on a biography of Charles Hutton (1737–1823): pit lad, FRS, and professor of Mathematics. No-one much has heard of him today, but to his contemporaries he was "one of the greatest mathematicians in Europe". I'll give an outline of his remarkable story and say something about why he's worth my time.

Mon, 02 May 2016

What is the Value of Manuscript Sources and Resources?

Peter M. Neumann
((Oxford University))

Part of the series 'What do historians of mathematics do?' 

" Over the last four centuries a huge amount of mathematics has been published.  Most of it has, however, had little or no influence.  By way of contrast, some mathematics, although unpublished in its time, has had great influence.  My hope is to illustrate this with discussion of manuscript sources and resources that have survived from Thomas Harriot (c.1560--1621), Isaac Newton (1642--1727) and Évariste Galois (1811--1832)."

Thu, 18 Jun 2015

'Law in mathematics and mathematics in law: probability theory and the fair price in contracts in England and France 1700-1850'

Dr Ciara Kennefick

Law in mathematics and mathematics in law: Probability theory and the fair price in contracts in England and France 1700–1850

From the middle of the eighteenth century, references to mathematicians such as Edmond Halley and Abraham De Moivre begin to appear in judgments in English courts on the law of contract and French mathematicians such as Antoine Deparcieux and Emmanuel-Etienne Duvillard de Durand are mentioned in French treatises on contract law in the first half of the nineteenth century. In books on the then nascent subject of probability at the beginning of the eighteenth century, discussions of legal problems and principally contracts, are especially prominent. Nicolas Bernoulli’s thesis at Basle in 1705 on The Use of the Art of Conjecturing in Law was aptly called a Dissertatio Inauguralis Matematico-Juridica. In England, twenty years later, De Moivre dedicated one of his books on probability to the Lord Chancellor, Lord Macclesfield and expressly referred to its significance for contract law.

The objective of this paper is to highlight this textual interaction between law and mathematics and consider its significance for both disciplines but primarily for law. Probability was an applied science before it became theoretical. Legal problems, particularly those raised by the law of contract, were one of the most frequent applications and as such played an essential role in the development of this subject from its inception. In law, probability was particularly important in contracts. The idea that exchanges must be fair, that what one receives must be the just price for what one gives, has had a significant influence on European contract law since the Middle Ages. Probability theory allowed, for the first time, such an idea to be applied to the sale of interests which began or terminated on the death of certain people. These interests, particularly reversionary interests in land and personal property in English law and rentes viagères in French law were very common in practice at this time. This paper will consider the surprising and very different practical effects of these mathematical texts on English and French contract law especially during their formative period in the late eighteenth and nineteenth centuries.

Mon, 18 May 2015

Commutativity and Collinearity: From Diophantus to Pappus via Hilbert

Adrian Rice

This talk investigates the discovery of an intriguing and fundamental connection between the famous but apparently unrelated work of two mathematicians of late antiquity, Pappus and Diophantus. This link went unnoticed for well over 1500 years until the publication of two groundbreaking but again ostensibly unrelated works by two German mathematicians at the close of the 19th century. In the interim, mathematics changed out of all recognition, with the creation of numerous new mathematical subjects and disciplines, without which the connection might never have been noticed in the first place. This talk examines the chain of mathematical events that led to the discovery of this remarkable link between two seemingly distinct areas of mathematics, encompassing number theory, finite-dimensional real normed algebras, combinatorial design theory, and projective geometry, and including contributions from mathematicians of all kinds, from the most distinguished to the relatively unknown.

Adrian Rice is Professor of Mathematics at Randolph-Macon College in Ashland, Virginia, where his research focuses on the history of 19th- and early 20th-century mathematics. He is a three-time recipient of the Mathematical Association of America's awards for outstanding expository writing.

Sat, 05 Jul 2014 00:00 -
Tue, 08 Jul 2014 00:00

Symmetries and Correspondences in Number Theory, Geometry, Algebra and Quantum Computing: Intra-disciplinary Trends (organised by Kobi Kremnitzer et al)


July 5


Robert Langlands (IAS, Princeton)

Problems in the theory of automorphic forms: 45 years later 


Christopher Deninger (Univ. Münster)

Zeta functions and foliations     


Christophe Soulé (IHES, Bures-sur-Yvette)

 A singular arithmetic Riemann-Roch theorem           



Minhyong Kim (Univ. Oxford)

 Non-abelian reciprocity laws and Diophantine geometry


Constantin Teleman (Berkeley/Oxford)           

Categorical representations and Langlands duality 


July 6


Ted Chinburg (Univ. Pennsylvania, Philadelphia)

 Higher Chern classes in Iwasawa theory


Yuri Tschinkel (Courant Institute, New York)

Introduction to almost abelian anabelian geometry


Ralf Meyer (Univ. Göttingen)

Groupoids and higher groupoids


Dennis Gaitsgory (Harvard Univ., Boston)

Picard-Lefschetz oscillators for Drinfeld-Lafforgue compactifications


François Loeser (Univ. Paris 6-7)

Motivic integration and representation theory


July 7


Matthew Morrow (Univ. Bonn)                                                  

On the deformation theory of algebraic cycles


Fedor Bogomolov (Courant Institute, New York/Univ. Nottingham)

On the section conjecture in anabelian geometry                 


Kevin Buzzard (ICL, London)

p-adic Langlands correspondences


Masatoshi Suzuki (Tokyo Institute of Technology)

Translation invariant subspaces and GRH for zeta functions


Edward Frenkel (Univ. California Berkeley)

"Love and Math", the Langlands programme - Public presentation


July 8


Mikhail Kapranov (Kavli IMPU, Tokyo)

Lie algebras and E_n-algebras associated to secondary polytopes                                 


Sergey Oblezin (Univ. Nottingham)

Whittaker functions, mirror symmetry and the Langlands correspondence


Edward Frenkel (Univ. California Berkeley)

The Langlands programme and quantum dualities


Dominic Joyce (Univ. Oxford)

Derived symplectic geometry and categorification


Urs Schreiber (Univ. Nijmegen, The Netherlands)

Correspondences of cohesive linear homotopy types and quantization

Tue, 11 Mar 2014

"Bayesian networks, information and entropy"

John Baez
(University of California)

Nature and the world of human technology are full of
networks. People like to draw diagrams of networks: flow charts,
electrical circuit diagrams, signal flow diagrams, Bayesian networks,
Feynman diagrams and the like. Mathematically-minded people know that
in principle these diagrams fit into a common framework: category
theory. But we are still far from a unified theory of networks.

Tue, 11 Mar 2014

Intrinsic and extrinsic regulation of epithelial organ growth

Jeremiah Zartman
(University of Notre Dame)

The revolution in molecular biology within the last few decades has led to the identification of multiple, diverse inputs into the mechanisms governing the measurement and regulation of organ size. In general, organ size is controlled by both intrinsic, genetic mechanisms as well as extrinsic, physiological factors. Examples of the former include the spatiotemporal regulation of organ size by morphogen gradients, and instances of the latter include the regulation of organ size by endocrine hormones, oxygen availability and nutritional status. However, integrated model platforms, either of in vitro experimental systems amenable to high-resolution imaging or in silico computational models that incorporate both extrinsic and intrinsic mechanisms are lacking. Here, I will discuss collaborative efforts to bridge the gap between traditional assays employed in developmental biology and computational models through quantitative approaches. In particular, we have developed quantitative image analysis techniques for confocal microscopy data to inform computational models – a critical task in efforts to better understand conserved mechanisms of crosstalk between growth regulatory pathways. Currently, these quantitative approaches are being applied to develop integrated models of epithelial growth in the embryonic Drosophila epidermis and the adolescent wing imaginal disc, due to the wealth of previous genetic knowledge for the system. An integrated model of intrinsic and extrinsic growth control is expected to inspire new approaches in tissue engineering and regenerative medicine.