# 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