Discrete Integrable Systems
Created: | 2009-03-13 09:28 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |
Description: | The theory of (ordinary and partial) differential equations is well-established and to some extent standardised. By contrast, the theory of difference equations, while more fundamental, has until recently been in its infancy, in spite of a major effort at the beginning of the 20th Century by N"orlund and the school of G.D. Birkhoff to establish the linear theory. Discrete systems can appear in two main guises: in the first case the independent variable is discrete, taking values on a lattice (e.g. finite-difference equations, such as recurrence relations and dynamical mappings), in the second case the independent variable is continuous (e.g. analytic difference equations and even functional equations).
Very recently, however, mainly through advances in the theory of exactly integrable discrete systems and the theory of (linear and nonlinear) special functions, the study of difference equations has undergone a true revolution. For the first time good and interesting examples of nonlinear difference equations admitting exact, albeit highly nontrivial, solutions were found and this has led to the formulation of novel approaches to the classification and treatment of such equations. Thus, an area has developed where several branches of mathematics and physics, that are usually distinct, come together: complex analysis, algebraic geometry, representation theory, Galois theory, spectral analysis and the theory of special functions, graph theory, and difference geometry. Read more at: www.newton.ac.uk/programmes/DIS/ |
Media items
This collection contains 155 media items.
Media items
QRT Maps & Elliptic Surfaces
Johannes Jisse Duistermaat (Universiteit Utrecht)
Monday 18 May 2009, 17:00-18:00
Collection: Rothschild Seminars
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 16 Mar 2011
A completeness study on a class of Lax pairs
Hay, M (Kyushu)
Thursday 02 July 2009, 11:30-12:00
Discrete Systems and Special Functions
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 15 Mar 2011
A discrete system from the recurrence coefficients of 2-variable elliptic orthogonal polynomials
Spicer, P (KL Leuven)
Tuesday 30 June 2009, 14:00-14:30
Discrete Systems and Special Functions
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 15 Mar 2011
A Galois D-groupoid for q-difference equations
Granier, A (Institut de Mathematiques de Toulouse)
Tuesday 09 June 2009, 11:00-12:00
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 24 Jun 2009
A new extended discrete KP hierarchy and its solutions
Yao, Y (Tsinghua)
Thursday 02 July 2009, 14:30-15:00
Discrete Systems and Special Functions
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 16 Mar 2011
Abelian Integrals over Complex Curves and Lattice Integrals over Tropical Curves
Shinsuke Iwao (Tokyo)
Thursday 02 April 2009, 16:15-17:00
Geometric Aspects of Discrete and Ultra-discrete Integrable Systems
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 10 Mar 2011
Abelian solutions of difference equations
Krichever, I (Columbia)
Wednesday 10 June 2009, 14:00-14:50
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 24 Jun 2009
Admissibility of solutions of discrete dynamical systems
Halburd, R (UCL)
Thursday 14 May 2009, 16:30-17:30
Algebraic Theory of Difference Equations
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 14 Mar 2011
Algebra and algorithms for the classification of differential invariants
Hubert, E (INRIA Sophia Antipolis)
Monday 29 June 2009, 15:30-16:30
Discrete Systems and Special Functions
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 15 Mar 2011
Algebra and geometry of Somos sequences
Hone, A (Kent)
Wednesday 04 March 2009, 15:10-16:00
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 7 Mar 2011
An unification of field, lattice and q-deformed soliton systems as integrable evolution equations on regular times...
Blazej Szablikowski (Glasgow)
Monday 30 March 2009, 16:15-17:00
Geometric Aspects of Discrete and Ultra-discrete Integrable Systems
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 10 Mar 2011
Analytic solutions to the q-Painlevé equations around the origin
Ohyama, Y (Osaka)
Friday 03 July 2009, 14:00-14:30
Discrete Systems and Special Functions
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 16 Mar 2011
Area-perimeter generating functions of lattice walks: q-series and their asymptotics
Prellberg, T (QMUL)
Wednesday 01 July 2009, 11:30-12:00
Discrete Systems and Special Functions
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 15 Mar 2011
Arithmetic theory of q-difference equations
di Vizio, L (CNRS, IMJ, Paris)
Thursday 14 May 2009, 11:00-12:00
Algebraic Theory of Difference Equations
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 14 Mar 2011
Ax's theorem for additive power series
Kowalski, P (Wroclaw)
Thursday 14 May 2009, 14:00-15:00
Algebraic Theory of Difference Equations
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 14 Mar 2011
Bianchi (hyper-)cubes and a geometric unification of the Hirota and Miwa equations
Schief, W (University of New South Wales)
Monday 08 July 2013, 11:00-11:30
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 12 Jul 2013
Bilinearization and soliton solutions for the ABS list
Hietarinta, J (Turku)
Wednesday 11 February 2009, 14:00-14:50
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 7 Mar 2011
Bispectral quantum KZ equations and their solutions
Stokman, J (Universiteit van Amsterdam)
Thursday 02 July 2009, 09:00-10:00
Discrete Systems and Special Functions
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 15 Mar 2011
Bletchley Park 1942 - 1945
Loewe, M
Tuesday 16 June 2009, 17:00-18:00
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 3 Jul 2009
Box-Ball system and Toda equation
Tetsuji Tokihiro (Tokyo)
Monday 30 March 2009, 11:30-12:15
Geometric Aspects of Discrete and Ultra-discrete Integrable Systems
Collection: Discrete Integrable Systems
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 1 May 2009