Mini-Programme on the
Algebraic
Theory of
Differential Equations
Heriot-Watt University, Edinburgh
31 July to 11 August 2006
Home Page | Workshop Arrangements | Scientific Programme and Participants
Scientific Programme and Participants
The LMS Invited Lecture Series will start in the morning of Monday 31 July and end in the afternoon of Friday 4 August. The workshop will begin in the early morning of Monday 7 August and end in the afternoon of Friday 11 August. All talks will be held in the ground floor lecture theatre of the Colin MacLaurin Building at Heriot-Watt University.For photographs and links to some presentations please visit this page.
For Week 2 Programme click here.
For list of participants click here.
Programme
Week One: 2006 LMS Invited Lecture Series on the Galois Theory of Differential and Difference Equations
Monday 31 July
| 08.30-09.20 | Registration for those unable to register on Sunday evening |
| 09.20-09.30 | Introduction |
| 09.30-10.30 | Michael Singer What is a differential equation? |
| 10 30-11 00 | Coffee break |
| 11.00-12.00 | Michael Singer Basic theorems and applications (I) |
| 12.00-1400 | Lunch break |
| 14.00-15.00 | Alexandre Mikhailov/Vladimir Sokolov tba |
| 15.00-15.30 | Coffee break |
| 15.30-16.30 | Anton Leykin Introduction to the theory of D-modules and its algorithmic aspects (I) |
Tuesday 1 August
| 09.30-10.30 | Michael Singer Basic theorems and applications (II) |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Michael Singer Analytic theory (I) |
| 12.00-14.00 | Lunch break |
| 14.00-15.00 | Alexandre Mikhailov/Vladimir Sokolov tba |
| 15.00-15.30 | Coffee break |
| 15.30-16.30 | Anton Leykin Introduction to the theory of D-modules and its algorithmic aspects (II) |
Wednesday 2 August
| 09.30-10.30 | Michael Singer Analytic theory (II) |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Michael Singer Algorithms (I) |
| 12.00-14.00 | Lunch break |
| 14.00-15.00 | Anand Pillay Model theory and differential algebra |
| 15.00-15.30 | Coffee break |
| 15.30-16.30 | Anton Leykin Introduction to the theory of D-modules and its algorithmic aspects (III) |
Thursday 3 August
| 09.30-10.30 | Michael Singer Algorithms (II) |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Michael Singer Inverse problems |
| 12.00-14.00 | Lunch break |
| 14.00-15.00 | Anand Pillay A generalized differential Galois theory |
| 15.00-15.30 | Coffee break |
| 15.30-16.30 | Sergey Tsarev Factorisation of linear partial differential equations (I) |
Friday 4 August
| 09.30-10.30 | Michael Singer Families of differential equations (I) |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Michael Singer Families of differential equations (II) |
| 12.00-14.00 | Lunch break |
| 14.00-15.00 | Anand Pillay Differential algebra and diophantine geometry |
| 15.00-15.30 | Coffee break |
| 15.30-16.30 | Sergey Tsarev Factorisation of linear partial differential equations (II) |
Week Two: Workshop on the Algebraic Theory of Differential Equations
Monday 7 August
| 08.30-09.30 | Registration for new arrivals for Workshop only |
| Chair: | Michael Singer |
| 09.30-10.30 | Daniel Bertrand Abelian integrals, Picard-Vessiot groups and the Schanuel conjecture |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Felix Ulmer
Formulas for Liouvillian solutions for higher order equations |
| 12.00-14.00 | Lunch break |
| Chair: | Daniel Bertrand |
| 14.00-15.00 | Anand
Pillay Around Grothendiek’s conjecture on the arithmetic of linear differential equations and nonlinear generalisations |
| 15.00-16.00 | George Shabat Dessins d’enfants and algebraic solutions of Painleve-VI |
| 16.00-16.30 | Coffee break |
| 16.30-17.30 | Charlotte Hardouin Galois groups and hyper transcendancy |
| 17.35 | Hired coach outside Colin Maclaurin building for travel to India Street |
| 18.00-19.00 | Reception at 14 India Street |
Tuesday 8 August
| Chair: | Yuji Kodama |
| 09.30-10.30 | Jarmo Hietarinta Searching for integrable (P)DEs using algebraic conditions: two examples |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Vladimir Novikov Symmetry structure of non-evolutionary equations |
| 12.00-14.00 | Lunch break |
| Chair: | Jarmo Hietarinta |
| 14.00-15.00 | Jing Ping Wang On the structure of (2+1)-dimensional commutative and noncommutative integrable equations |
| 15.00-16.00 | Vladimir Sokolov Compatible associative algebras and non-abelian integrable ODEs |
| 16.00-16.30 | Coffee break |
| 16.30-17.30 | Anton Leykin Algorithms in algebraic analysis |
Wednesday 9 August
| Chair: | Chris Eilbeck |
| 09.30-10.30 | Martin Kruskal Surreal numbers – a new number system for a new century |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Alex Buium Arithmetic differential equations |
| 12.00-13.30 | Lunch break |
| Chair: | Chris Athorne |
| 13.30-14.00 | Georg
Regensburger Boundary value problems for nonlinear first-order ODEs - constructing generalised solution via the maxplus algebra |
| 14.00-14.30 | Olga Efimovskaya Factorization of loop algebras over so(4) and integrable nonlinear differential equations |
| 14.30-15.00 | Guowu Meng The generalized Kepler problem |
| 15.00-15.30 | Sonia Reuda Polyhedral representations of invariant differential operators |
| 15.30-16.00 | Coffee break |
| Chair: | Jacques-Arthur Weil |
| 16.00-16.30 | Alexey Ovchinnikov Characteristic sets for ordinary algebraic differential equations |
| 16.30-17.00 | Sara Lombardo Automorphic Lie Algebras and the problem of reductions for integrable equations |
| 17.00-17.30 | Eugeny Pankratiev Conditions of finiteness for differential standard bases |
| 17.30-18.00 | Ruyong Feng The rational solutions of first order autonomous algebraic ordinary difference equations |
Thursday 10 August
| Chair: | Iskander Taimanov |
| 09.30-10.30 | Jan Sanders Transvectants |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Chris Athorne Applications of transvectants |
| 12.00-14.00 | Lunch break |
| Chair: | Sasha Mikhailov |
| 14.00-15.00 | Iskander Taimanov Singular curves in the finite gap integration method |
| 15.00-16.00 | Yuji Kodama Grassmannains and soliton solutions of the KP equation |
| 16.00-16.30 | Coffee break |
| 16.30-17.30 | Chris Eilbeck PDEs and addition formulae associated with trigonal curves |
| 19.00 | Workshop Dinner - Scholars Restaurant |
Friday 11 August
| Chair: | Malcolm MacCallum |
| 09.30-10.30 | Jacques-Arthur Weil Variational (Galoisian) methods for complete integrability of dynamical systems |
| 10.30-11.00 | Coffee break |
| 11.00-12.00 | Xiao-Shan Gao Decomposition of differential and difference polynomials |
| 12.00-14.00 | Lunch break |
| Chair: | Sergey Tsarov |
| 14.00-15.00 | Moulay Barkatou Direct algebraic methods for solving systems of linear differential equations |
| 15.00-16.00 | Kai Gehrs Some practical algorithms for the solution of ODEs via symmetry methods and integrating factors |
| 16.00-16.30 | Coffee break |
| 16.30-17.30 | Markus Rosenkranz Symbolic computation with two-point boundary value problems – a novel operator-based approach |
Return to Thursday
Provisional List of Participants
19 July
| Name | Institution | Dates |
| Athorne, Chris | University of Glasgow | 07 Aug - 11 Aug |
| Bardavid, Colas | IRMAR | 30 Jul - 12 Aug |
| Barkatou, Moulay | Limoges University | 30 Jul - 12 Aug |
| Benoist, Frank | University Paris 7 | 30 Jul - 11 Aug |
| Bertrand, Daniel | Université de Paris 6 | 07 Aug - 11 Aug |
| Braden, Harry | University of Edinburgh | 31 Jul - 09 Aug |
| Buium, Alex | University of New Mexico | 06 Aug - 12 Aug |
| Burovskiy, Pavel | Loughborough University | 30 Jul - 12 Aug |
| Bury, Rhys | University of Leeds | 30 Jul - 05 Aug |
| Christopher, Colin | University of Plymouth | 31 Jul - 04 Aug |
| Covarrubias, Enrique | University of Edinburgh | 31 Jul - 04 Aug |
| Efimovskaya, Olga | Moscow State University | 30 Jul - 11 Aug |
| Eilbeck, Chris | Heriot-Watt University | 31 Jul - 11 Aug |
| Feng, Ruyong | Chinese Academy of Sciences | 30 Jul - 12 Aug |
| Ferapontov, Eugene | University of Loughborough | 09 Aug - 11 Aug |
| Ferguson, James | University of Glasgow | 31 Jul - 04 Aug |
| Figueroa-O'Farrill, Jose Miguel | University of Edinburgh | 31 Jul - 04 Aug |
| Fordy, Allan | University of Leeds | 30 Jul - 11 Aug |
| Gao, Xiao-Shan | Chinese Academy of Sciences | 06 Aug - 12 Aug |
| Gehrs, Kai | University of Paderborn | 06 Aug - 12 Aug |
| Gratus, Jonathan | University of Lancaster | 30 Jul - 04 Aug |
| Hardouin, Charlotte | Institut de Mathématiques de Jussieu | 06 Aug - 12 Aug |
| Hietarinta, Jarmo | University of Turku | 30 Jul - 11 Aug |
| Kamensky, Moshe | University of East Anglia | 29 Jul - 05 Aug |
| Khodabakhshi, Alireza | Imperial College London | 31 Jul - 04 Aug |
| Kiripichnikova, Anna | Loughborough University | 30 Jul - 04 Aug |
| Knops, Robin | Heriot-Watt University | 31 Jul - 04 Aug |
| Kodama, Yuji | Ohio State University | 06 Aug - 12 Aug |
| Kruskal, Martin | Rutgers University | 01 Aug - 11 Aug |
| Leykin, Anton | University of Illinois at Chicago | 30 Jul - 09 Aug |
| Lobb, Sarah | University of Leeds | 30 Jul - 05 Aug |
| Lombardo, Sara | Vrije Universiteit Amsterdam | 30 Jul - 12 Aug |
| MacCallum, Malcolm | Queen Mary, University of London | 30 Jul - 11 Aug |
| Marshall, Dave | Loughborough University | 30 Jul - 04 Aug |
| Mazzocco, Marta | University of Manchester | 30 Jul - 05 Aug |
| Meng, Guowu | Hong Kong University of Science & Technology | 30 Jul - 12 Aug |
| Mikhailov, Alexander | University of Leeds | 30 Jul - 12 Aug |
| Nguyen, Khuong An | University of Groningen | 30 Jul - 12 Aug |
| Novikov, Vladimir | University of Kent at Canterbury | 30 Jul - 12 Aug |
| Ovchinnikov, Alexey | North Carolina State University | 30 Jul - 14 Aug |
| Pankratiev, Eugeny | Moscow State University | 06 Aug - 12 Aug |
| Pillay, Anand | University of Leeds | 02 Aug - 09 Aug |
| Regensburger, Georg | Austrian Academy of Sciences | 30 Jul - 12 Aug |
| Rosenkranz, Markus | Austrian Academy of Sciences | 30 Jul - 12 Aug |
| Rueda, Sonia | Universidad Politecnica de Madrid | 06 Aug - 14 Aug |
| Sanders, Jan | Vrije Universiteit Amsterdam | 06 Aug - 12 Aug |
| Shabat, George | ITEP Moscow | 04 Aug - 11 Aug |
| Shah, Mitul | University of Oxford | 29 Jul - 06 Aug |
| Singer, Michael F | North Carolina State University | 30 Jul - 12 Aug |
| Sokolov, Vladimir | Landau Institute | 30 Jul - 11 Aug |
| Taimanov, Iskander | Institute of Mathematics, Novosibirsk | 06 Aug - 11 Aug |
| Tsarev, Sergey | Krasnoyarsk State Pedagogical University | 30 Jul - 12 Aug |
| Ulmer, Felix | Université de Rennes 1 | 06 Aug - 12 Aug |
| Wallace, David | Universities of Loughborough & Cambridge | 3 Aug - 11 Aug |
| Wang, Jing Ping | University of Kent | 30 Jul - 12 Aug |
| Weil, Jacques-Arthur | Université de Limoges | 30 Jul - 12 Aug |
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