Past Special Seminar

18 June 2015
15:00
Dr Ciara Kennefick
Abstract

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.

18 May 2015
11:00
Adrian Rice
Abstract

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.

5 July 2014
00:00
to
8 July 2014
00:00
Various
Abstract

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

11 March 2014
15:30
Abstract

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.

11 March 2014
12:00
Jeremiah Zartman
Abstract

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.

4 March 2014
15:30
Abstract
<p><span>&nbsp;Nature and the world of human technology are full of</span><br /><span>networks. People like to draw diagrams of networks: flow charts,</span><br /><span>electrical circuit diagrams, signal flow diagrams, Bayesian networks,</span><br /><span>Feynman diagrams and the like. Mathematically-minded people know that</span><br /><span>in principle these diagrams fit into a common framework: category</span><br /><span>theory. But we are still far from a unified theory of networks.</span></p>
25 February 2014
15:30
Abstract

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.

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