Forthcoming events in this series
Seminar series `Symmetries and Correspondences'
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.
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.
July 5
9:30-10:30
Robert Langlands (IAS, Princeton)
Problems in the theory of automorphic forms: 45 years later
11:00-12:00
Christopher Deninger (Univ. Münster)
Zeta functions and foliations
13:30-14:30
Christophe Soulé (IHES, Bures-sur-Yvette)
A singular arithmetic Riemann-Roch theorem
14:40-15:40
Minhyong Kim (Univ. Oxford)
Non-abelian reciprocity laws and Diophantine geometry
16:10-17:10
Constantin Teleman (Berkeley/Oxford)
Categorical representations and Langlands duality
July 6
9:30-10:30
Ted Chinburg (Univ. Pennsylvania, Philadelphia)
Higher Chern classes in Iwasawa theory
11:00-12:00
Yuri Tschinkel (Courant Institute, New York)
Introduction to almost abelian anabelian geometry
13:30-14:30
Ralf Meyer (Univ. Göttingen)
Groupoids and higher groupoids
14:40-15:40
Dennis Gaitsgory (Harvard Univ., Boston)
Picard-Lefschetz oscillators for Drinfeld-Lafforgue compactifications
16:10-17:10
François Loeser (Univ. Paris 6-7)
Motivic integration and representation theory
July 7
9:00-10:00
Matthew Morrow (Univ. Bonn)
On the deformation theory of algebraic cycles
10:30-11:30
Fedor Bogomolov (Courant Institute, New York/Univ. Nottingham)
On the section conjecture in anabelian geometry
13:15-14:15
Kevin Buzzard (ICL, London)
p-adic Langlands correspondences
14:45-15:45
Masatoshi Suzuki (Tokyo Institute of Technology)
Translation invariant subspaces and GRH for zeta functions
16:00-17:00
Edward Frenkel (Univ. California Berkeley)
"Love and Math", the Langlands programme - Public presentation
July 8
9:15-10:15
Mikhail Kapranov (Kavli IMPU, Tokyo)
Lie algebras and E_n-algebras associated to secondary polytopes
10:45-11:45
Sergey Oblezin (Univ. Nottingham)
Whittaker functions, mirror symmetry and the Langlands correspondence
13:30-14:30
Edward Frenkel (Univ. California Berkeley)
The Langlands programme and quantum dualities
14:40-15:40
Dominic Joyce (Univ. Oxford)
Derived symplectic geometry and categorification
16:10-17:10
Urs Schreiber (Univ. Nijmegen, The Netherlands)
Correspondences of cohesive linear homotopy types and quantization
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.
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.
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.
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.
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.
The fundamental mechanisms of microorganism motility have been extensively studied in the past. Most previous work focused on cell locomotion in simple (Newtonian) fluids.
However, in many cases of biological importance (including mammalian reproduction and bacterial infections), the fluids that surround the organisms are strongly non-Newtonian (so-called complex fluids), either because they have shear-dependent viscosities, or because they display an elastic response. These non-Newtonian effects challenge the most fundamental intuition in fluid mechanics, resulting in our incapacity to predict its implications in biological cell locomotion. In this talk, our on-going experimental investigation to quantify the effect of non-Newtonian behavior on the locomotion and fluid transport of microorganisms will be described. Several types of magnetic micro-robots were designed and built. These devices were actuated to swim or move in a variety of fluids : Newtonian, elastic with constant viscosity (Boger fluids) or inelastic with shear-thinning viscosity. We have found that, depending on the details of locomotion, the swimming performance can either be increased, decreased or remain unaffected by the non Newtonian nature of the liquid. Some key elements to understand the general effect of viscoelasticity and shear-thinning viscosity of the motility of microorganisms will be discussed.
Question: Is it a realistic proposition for a mathematician to use his/her skills to make a living from sports betting? The introduction of betting exchanges have fundamentally changed the potential profitability of gambling, and a professional mathematician's arsenal of numerical and theoretical weapons ought to give them a huge natural advantage over most "punters", so what might be realistically possible and what potential risks are involved? This talk will give some idea of the sort of plan that might be required to realise this ambition, and what might be further required to attain the aim of sustainable gambling profitability.
A workshop on different aspects of deformation theory in various fields
A workshop on different aspects of deformation theory in various fields
A workshop on different aspects of deformation theory in various fields
A workshop on different aspects of deformation theory in various fields
Exhibitors will be here along with recruiters from different sectors. There will also be panel talks. For further information see http://www.careers.ox.ac.uk/wp-content/uploads/2012/02/JobsForMathemati… and in particular last year brochure for the event at http://www.careers.ox.ac.uk/wp-content/uploads/2012/04/MathsPrintII.pdf
We consider two independent random sequences of length n.
We consider optimal alignments according to a scoring function S.
We show that when the scoring function S is chosen at random
then with probability 1, the frequency of the aligned letter pairs
converges to a unique distribution as n goes to infinity. We also show
some concentration of measure phenomena.
Nodes in complex networks organize into communities of nodes that share a common property, role or function, such as social communities, functionally related proteins, or topically related webpages. Identifying such communities is crucial to the understanding of the structural and functional roles of networks.
Current work on overlapping community detection (often implicitly) assumes that community overlaps are less densely connected than non-overlapping parts of communities. This is unnatural as it means that the more communities nodes share, the less likely it is they are linked. We validate this assumption on a diverse set of large networks and find an increasing relationship between the number of shared communities of a pair of nodes and the probability of them being connected by an edge, which means that parts of the network where communities overlap tend to be more densely connected than the non-overlapping parts of communities.
Existing community detection methods fail to detect communities with such overlaps. We propose a model-based community detection method that builds on bipartite node-community affiliation networks. Our method successfully detects overlapping, non-overlapping and hierarchically nested communities. We accurately identify relevant communities in networks ranging from biological protein-protein interaction networks to social, collaboration and information networks. Our results show that while networks organize into overlapping communities, globally networks also exhibit a nested core-periphery structure, which arises as a consequence of overlapping parts of communities being more densely connected.
We show how the reduction procedure for generalized Kahler
structures can be used to recover Hitchin's results about the
existence of a generalized Kahler structure on the moduli space of
instantons on bundle over a generalized Kahler manifold. In this setup
the proof follows closely the proof of the same claim for the Kahler
case and clarifies some of the stranger considerations from Hitchin's
proof.
In recent years, surprising connections between type theory and homotopy theory have been discovered. In this talk I will recall the notions of intensional type theories and identity types. I will describe "infinity groupoids", formal algebraic models of topological spaces, and explain how identity types carry the structure of an infinity groupoid. I will finish by discussing categorical semantics of intensional type theories.
The talk will take place in Lecture Theatre B, at the Department of Computer Science.