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Mini-Programme on the Algebraic
Theory of Differential Equations

Heriot-Watt University, Edinburgh
31 July to 11 August 2006

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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)
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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)
Return to Monday

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)
Return to Monday |Return to Tuesday

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)
Return to Monday |Return to Tuesday | Return to Wednesday

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)
Return to Monday |Return to Tuesday | Return to Wednesday | Return to Thursday

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
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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
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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
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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
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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
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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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