University of Minnesota
University of Minnesota
http://www.umn.edu/
IMA Web

2006 IMA Summer Program:

Symmetries and Overdetermined Systems of Partial Differential Equations

July 17-August 4, 2006
This summer program is dedicated to the memory of Thomas P. Branson, who played
a leading role in its conception and organization, but did not live to see its realization.

Organizers:

Michael Eastwood

Department of Pure Mathematics
University of Adelaide
http://www.maths.adelaide.edu.au/pure/staff/meastwood.html

Willard Miller, Jr.

Institute for Mathematics & Its Applications
University of Minnesota
http://www.ima.umn.edu/~miller/

Schedule Participants Program Application Feedback
IMA Live Streaming and Webcasting Maps
Abstracts and Talk Materials Dining Guide
Summer Guest Housing
Photo Gallery

Description:

The symmetries to be studied in the this Summer Program naturally arise in several different ways. Firstly, there are the symmetries of a differential geometric structure. By definition, these are the vector fields that preserve the structure in question—the Killing fields of Riemannian differential geometry, for example. Secondly, the symmetries can be those of another differential operator. For example, the Riemannian Killing equation itself is projectively invariant whilst the ordinary Euclidean Laplacian gives rise to conformal symmetries. In addition, there are higher symmetries defined by higher order operators. Physics provides other natural sources of symmetries, especially through string theory and twistor theory.

These symmetries are usually highly constrained—viewed as differential operators, they themselves are overdetermined or have symbols that are subject to overdetermined differential equations. As a typical example, the symbol of a symmetry of the Laplacian must be a conformal Killing field (or a conformal Killing tensor for a higher order symmetry). The Summer Program will consider the consequences of overdeterminacy and partial differential equations of finite type.

The question of what it means to be able to solve explicitly a classical or quantum mechanical system, or to solve it in multiple ways, is the subject matter of the integrability theory and superintegrability theory of Hamiltonian systems. Closely related is the theory of exactly solvable and quasi-exactly solvable systems. All of these approaches are associated with the structure of the spaces of higher dimensional symmetries of these systems.

Symmetries of classical equations are intimately connected with special coordinate systems, separation of variables, conservation laws and integrability. But only the simplest equations are currently understood from these points of view. The Summer Program will provide an opportunity for comparison and consolidation, especially in relation to the Dirac equation and massless fields of higher helicity.

Parabolic differential geometry provides a synthesis and generalization of various classical geometries including conformal, projective, and CR. It also provides a very rich geometrical source of overdetermined partial differential operators. Even in the flat model G/P, for G a semisimple Lie group with P a parabolic subgroup, there is much to be gleaned from the representation theory of G. In particular, the Bernstein-Gelfand-Gelfand (BGG) complex is a series of G-invariant differential operators, the first of which is overdetermined. Conformal Killing tensors, for example, may be viewed in this way. Exterior differential systems provide the classical approach to such overdetermined operators. But there are also tools from representation theory and especially the cohomology of Lie algebras that can be used. The Summer Program will explore these various approaches.

There are many areas of application. In particular, there are direct links with physics and especially conformal field theory. The AdS/CFT correspondence in physics (or Fefferman-Graham ambient metric construction in mathematics) provides an especially natural route to conformal symmetry operators. There are direct links with string theory and twistor theory. Also, there are numerical schemes based on finite element methods via the BGG complex, moving frames, and other symmetry based methods. The BGG complex arises in many areas of mathematics, both pure and applied. When it is recognized as such, there are immediate consequences.

There are close connections and even overlapping work being done in several areas of current research related to the topics above. The main idea of this Summer Program is to bring together relevant research groups for the purpose of intense discussion, interaction, and fruitful collaboration.

In summary, topics to be considered in the Summer Program include:

  • Symmetries of geometric structures and differential operators.
  • Overdetermined systems of partial differential equations.
  • Separation of variables and conserved quantities.
  • Integrability, superintegrability and solvable systems.
  • Parabolic geometry and the Bernstein-Gelfand-Gelfand complex.
  • Interaction with representation theory.
  • Exterior differential systems.
  • Finite element schemes, discrete symmetries, moving frames, and numerical analysis.
  • Interaction with string theory and twistor theory.

Organization:

The first week will be devoted to expository/overview sessions. This week will be particularly valuable for people new to the subject to get an overall understanding of overdetermined systems and their applications. The following two weeks will focus on more specialized research talks with one or two themes each day. These talks will be intermixed with discussions, aimed at assessing what has been learned and pointing out the most promising areas for further research. We will overlap themes in several areas to stimulate interaction between different groups where we expect this interaction to be most productive. We will publish an IMA volume of refereed papers, consisting of expository/survey talks for the entire field, followed by more specialized research contributions.

Proceedings:

Proceedings of the Summer Program will be published in the IMA Volume Series and we now invite participants to submit articles. Though there is no absolute limit on the length of a submission, in order to make this the quality volume that it should be, please try to make your contribution as concise as possible. The volume will include expository lectures from the first week and we are aiming for a particularly useful volume. The volume will be dedicated to the memory of Thomas Branson. All submissions will be refereed and the deadline for submission is Friday, October 20, 2006. Please use LaTeX or similar (TeX, AMS-TeX, etc.). See here for further details. Submissions should be sent by email directly to one of Michael Eastwood ( ) or Willard Miller ( ), who will edit the proceedings.

Schedule
Monday, July 17
8:15a-9:10a Registration and Coffee   EE/CS 3-176
9:10a-9:20a Welcome to the IMA Douglas N. Arnold (University of Minnesota Twin Cities) EE/CS 3-180
9:20a-9:30a Introduction by the Organizers Michael Eastwood (University of Adelaide), Willard Miller Jr. (University of Minnesota Twin Cities) EE/CS 3-180
9:30a-10:30a Exterior differential systems for ordinary differential equations Boris Doubrov (Belarus State University) EE/CS 3-180
10:30a-11:00a Break   EE/CS 3-176
11:00a-12:00p Superintegrable classical and quantum systems Pavel Winternitz (University of Montreal) EE/CS 3-180
12:00p-2:00p Lunch Break    
2:00p-3:00p Introduction to Moving Frames and Pseudo-Groups Peter J. Olver (University of Minnesota Twin Cities) EE/CS 3-180
3:05p-3:30p Break   EE/CS 3-176
3:30p-4:30p Projective differential geometry without moving frames Michael Eastwood (University of Adelaide) EE/CS 3-180
5:00p-6:30p Reception and Poster Session
Lind Hall 400
Partially invariant solutions to ideal magnetohydrodynamics Sergey Golovin (Queen's University)
Q-curvature and holography Andreas Juhl (Uppsala University)
The SsTools environment for classification of integrable super-equations Arthemy V. Kiselev (Ivanovo State Power University)
Thomas Wolf (Brock University)
Algebraic properties of Gardner's deformations Arthemy V. Kiselev (Ivanovo State Power University)
About conformal SU(p,q)-holonomy Felipe Leitner (Universität Stuttgart)
Polynomial Poisson and Associative Algebras for Classical and Quantum Superintegrable Systems with a Third Order Integral of Motion Ian Marquette (University of Montreal)
New integrable system on the sphere Vladimir S. Matveev (Katholieke Universiteit Leuven)
Low-dimensional Lie algebras Anatoly Nikitin (National Academy of Sciences of Ukraine)
Symmetries, Associated Conservation Laws and Double Reductions of PDEs Astri Sjoberg (University of Johannesburg)
The Uniqueness of the Joseph Ideal for the Classical Groups Petr Somberg (Karlovy (Charles) University)
A Method to Find Symmetries of the Yamabe Operator Alfredo Villanueva (University of Iowa)
Tuesday, July 18
9:15a-9:30a Coffee   EE/CS 3-176
9:30a-10:30a Superintegrable classical and quantum systems (continued) Pavel Winternitz (University of Montreal) EE/CS 3-180
10:30a-11:00a Break   EE/CS 3-176
11:00a-12:00p Exterior differential systems for ordinary differential equations (continued) Boris Doubrov (Belarus State University) EE/CS 3-180
12:00p-2:00p Lunch Break    
2:00p-3:00p Superintegrable classical and quantum systems (continued) Pavel Winternitz (University of Montreal) EE/CS 3-180
3:00p-3:30p Break   EE/CS 3-176
3:30p-4:30p Pseudogroups, moving frames, invariants, and symmetries (continued) Peter J. Olver (University of Minnesota Twin Cities) EE/CS 3-180
Wednesday, July 19
9:15a-9:30a Coffee   EE/CS 3-176
9:30a-10:30a Ambient metric constructions in CR and conformal geometry Kengo Hirachi (University of Tokyo) EE/CS 3-180
10:30a-11:00a Break   EE/CS 3-176
11:00a-12:00p Projective differential geometry without moving frames (continued) Michael Eastwood (University of Adelaide) EE/CS 3-180
12:00p-2:00p Lunch Break    
2:00p-3:00p Overdetermined systems, conformal differential geometry, and the BGG complex Andreas Cap (Universität Wien) EE/CS 3-180
3:00p-3:30p Break   EE/CS 3-176
3:30p-4:30p Projective differential geometry with moving frames Joseph Landsberg (Texas A & M University) EE/CS 3-180
6:30p-8:30p Workshop Dinner    
Thursday, July 20
9:15a-9:30a Coffee   EE/CS 3-176
9:30a-10:30a Pseudogroups, moving frames, invariants, and symmetries (continued) Peter J. Olver (University of Minnesota Twin Cities) EE/CS 3-180
10:30a-11:00a Break   EE/CS 3-176
11:00a-12:00p Geometry of linear differential systems - towards "contact geometry of second order" Keizo Yamaguchi (Hokkaido University) EE/CS 3-180
12:00p-2:00p Lunch Break    
2:00p-3:00p Variable separation and second order superintegrability Willard Miller Jr. (University of Minnesota Twin Cities) EE/CS 3-180
3:00p-3:30p Break   EE/CS 3-176
3:30p-4:30p Ambient metric constructions in CR and conformal geometry (continued) Kengo Hirachi (University of Tokyo) EE/CS 3-180
Friday, July 21
9:15a-9:30a Coffee   EE/CS 3-176
9:30a-10:30a Overdetermined systems, conformal differential geometry, and the BGG complex (continued) Andreas Cap (Universität Wien) EE/CS 3-180
10:30a-11:00a Break   EE/CS 3-176
11:00a-12:00p Projective differential geometry with moving frames (continued) Joseph Landsberg (Texas A & M University) EE/CS 3-180
12:00p-2:00p Lunch Break    
2:00p-3:00p Geometry of linear differential systems - towards "contact geometry of second order" (continued) Keizo Yamaguchi (Hokkaido University) EE/CS 3-180
3:00p-3:30p Break   EE/CS 3-176
3:30p-4:30p Topics in superintegrability and quasi-exact solvability Ernie Kalnins (University of Waikato) EE/CS 3-180
Saturday, July 22
All Day No scheduled activity    
Sunday, July 23
All Day No scheduled activity    
Monday, July 24
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a Symplectification procedure for the equivalence problem of vector distributions Igor Zelenko (International School for Advanced Studies (SISSA/ISAS)) EE/CS 3-180
9:45a-10:00a Break   EE/CS 3-176
10:00a-10:45a The Structure of Continuous Pseudogroups Juha Pohjanpelto (Oregon State University) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p The rigidity problem for Carnot groups Michael Cowling (University of New South Wales) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p Analogues of the Dolbeault complex and the separation of variables Vladimir Soucek (Karlovy (Charles) University) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
3:15p-4:00p Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces and Lie groups Stephen Anco (Brock University) EE/CS 3-180
4:30p-6:00p Reception and Poster Session
Lind Hall 400
Symmetries of the Square of the Laplacian Michael Eastwood (University of Adelaide)
Differential invariants of Lie pseudogroups in mechanics of fluids Sergey Golovin (Queen's University)
The SsTools environment for classification of integrable super-equations Arthemy V. Kiselev (Ivanovo State Power University)
Thomas Wolf (Brock University)
Ambient connections realising conformal Tractor holonomy Thomas Leistner (University of Adelaide)
Projectively equivalent metrics on closed manifolds Vladimir S. Matveev (Katholieke Universiteit Leuven)
Transformation to pseudo-Cartesian coordinates in locally flat pseudo-Riemannian spaces Ray McLenaghan (University of Waterloo)
Symmetry groups of the integro-differential equations and an approach for solutions of nonlocal determining equations Teoman Ozer (Istanbul Technical University)
Resolution on n-order functional differential equations with operator coefficients and delay in Hilbert spaces Chan Roath (Ministry of Education, Youth and Sport)
Symmetries, Associated Conservation Laws and Double Reductions of PDEs Astri Sjoberg (University of Johannesburg)
New superintegrable potentials in Euclidean 2D and 3D spaces Roman Smirnov (Dalhousie University)
The Uniqueness of the Joseph Ideal for the Classical Groups Petr Somberg (Karlovy (Charles) University)
The 1856 Lemma of Cayley Revisited, II. Fundamental Invariants Jin Yue (Dalhousie University)
Tuesday, July 25
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a The ambient metric to all orders in even dimensions Robin Graham (University of Washington) EE/CS 3-180
9:45a-10:00a Break   EE/CS 3-176
10:00a-10:45a Rigidity of the adjoint varieties Colleen Robles (University of Rochester) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p Second order superintegrable systems in two and three dimensions. (Solving a system in multiple ways) Willard Miller Jr. (University of Minnesota Twin Cities) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p Galilean vector fields: tensor products and invariants with using moving frames approach Anatoly Nikitin (National Academy of Sciences of Ukraine) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
3:15p-4:00p Exterior differential systems with symmetry Mark Fels (Utah State University) EE/CS 3-180
Wednesday, July 26
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a Exact and quasi-exact solvability superintegrability in Euclidean space George Pogosyan (Yerevan State University) EE/CS 3-180
9:45a-10:00a Break   EE/CS 3-176
10:00a-10:45a Quadratic algebras and superintegrable systems Jonathan Kress (University of New South Wales) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p Multiplication of solutions for systems of partial differential equations Jens Jonasson (Linköping University) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p A geometric approach to Kalnins and Miller non-regular separation Claudia Chanu (Università di Torino) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
3:15p-4:00p Discrete symmetries and Lie algebra automorphisms Peter Hydon (University of Surrey) EE/CS 3-180
Thursday, July 27
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a Separation of variables for systems of first-order Partial Differential Equations: the Dirac equation in two-dimensional manifolds Giovanni Rastelli (Università di Torino) EE/CS 3-180
9:45a-10:00a Break   EE/CS 3-176
10:00a-10:45a Classification of 3-dimensional scalar discrete integrable equations Thomas Wolf (Brock University) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p Involutive differential systems and tableaux over Lie algebras Lorenzo Nicolodi (Università di Parma) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p Projective-type differential invariants and geometric evolutions of KdV-type Gloria Mari Beffa (University of Wisconsin) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
3:15p-4:00p Complex variables for separation of Hamilton-Jacobi equation on real pseudo-Riemannian manifolds Luca Degiovanni (Università di Torino) EE/CS 3-180
Friday, July 28
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a Separation of variables theory for the Hamilton-Jacobi equation from the perspective of the invariant theory of Killing tensors Ray McLenaghan (University of Waterloo) EE/CS 3-180
9:45a-10:00a Break   EE/CS 3-176
10:00a-10:45a Geometry "a la Cartan" revisited: Hamilton-Jacobi theory in moving frames Roman Smirnov (Dalhousie University) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p The KillingTensor package (presented by Roman Smirnov on behalf of Joshua Horwood) Roman Smirnov (Dalhousie University) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p Globally hyperbolic Lorentzian manifolds with special holonomy Helga Baum (Humboldt-Universität) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
3:15p-4:00p Integrable equations of the dispersionless Hirota type and hypersurfaces of the Lagrangian Grassmanian Eugene Ferapontov (Loughborough University) EE/CS 3-180
Saturday, July 29
Sunday, July 30
Monday, July 31
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a Finite element exterior calculus and its applications Douglas N. Arnold (University of Minnesota Twin Cities) EE/CS 3-180
9:45a-10:00a Break   EE/CS 3-176
10:00a-10:45a A simple criterion for involutivity Elizabeth L. Mansfield (University of Kent at Canterbury) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p Differential and variational calculus in invariant frames Irina Kogan (North Carolina State University) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p Algorithmic Symmetry Analysis and Overdetermined Systems of PDE Gregory J. Reid (University of Western Ontario) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
3:15p-4:00p Rational and Algebraic Invariants of a Group Action Evelyne Hubert (Institut National de Recherche en Informatique Automatique (INRIA)) EE/CS 3-180
Tuesday, August 1
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a Overdetermined elliptic boundary value problems Jukka Tuomela (University of Joensuu) EE/CS 3-180
9:45a-10:00a Break   EE/CS 3-180
10:00a-10:45a Geometric integration and control Debra Lewis (University of Minnesota Twin Cities) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p Overdetermined systems, invariant connections, and short detour complexes A. Rod Gover (University of Auckland) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p Higher spin gauge theories and unfolded dynamics Mikhail Vasiliev (P. N. Lebedev Physics Institute) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
3:15p-4:00p Special polynomials associated with rational solutions of the Painleve equations and applications to soliton equations Peter A. Clarkson (University of Kent at Canterbury) EE/CS 3-180
Wednesday, August 2
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a CR-manifolds, differential equations and multicontact structures (tentative) Gerd Schmalz (University of New England) EE/CS 3-180
9:45a-10:00a Break   EE/CS 3-176
10:00a-10:45a Wünsch's calculus for parabolic geometries Jan Slovak (Masaryk University) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p Differential equations and conformal structures Pawel Nurowski (University of Warsaw) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p Symmetry algebras for even number of vector fields and for linearly perturbed complex structures Chong-Kyu Han (Seoul National University) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
3:15p-4:00p Superintegrable systems and the solution of a S. Lie problem Vladimir S. Matveev (Katholieke Universiteit Leuven) EE/CS 3-180
Thursday, August 3
8:45a-9:00a Coffee   EE/CS 3-176
9:00a-9:45a The Work of Thomas P. Branson
(Michael Eastwood, moderator)
Michael Eastwood (University of Adelaide) EE/CS 3-180
10:00a-10:45a Break   EE/CS 3-176
10:00a-10:45a Geometric analysis in parabolic geometries Bent Orsted (Aarhus University) EE/CS 3-180
10:45a-11:15a Break   EE/CS 3-176
11:15a-12:00p Equivariant differential operators, classical invariant theory, unitary representations, and Macdonald polynomials Siddhartha Sahi (Rutgers University) EE/CS 3-180
12:00p-2:00p Lunch    
2:00p-2:45p The Uniqueness of the Joseph Ideal for the Classical Groups Petr Somberg (Karlovy (Charles) University) EE/CS 3-180
2:45p-3:15p Break   EE/CS 3-176
Friday, August 4
9:00a-10:00a Coffee   EE/CS 3-176
10:00a-11:05a Final Discussion Group
Willard Miller Jr., moderator

EE/CS 3-180
Final Discussion Session Michael Eastwood (University of Adelaide)
Final Discussion Session Jonathan Kress (University of New South Wales)

LIST OF CONFIRMED PARTICIPANTS

Name Department Affiliation
Stephen Anco Department of Mathematics Brock University
Douglas N. Arnold Institute for Mathematics and its Applications University of Minnesota Twin Cities
Donald G. Aronson Institute for Mathematics and its Applications University of Minnesota Twin Cities
Helga Baum Institute for Mathematics Humboldt-Universität
Gloria Mari Beffa Department of Mathematics University of Wisconsin
Melisande Fortin Boisvert Department of Mathematics and Statistics McGill University
Andreas Cap Erwin Schrodinger Institute Universität Wien
Mark Chanachowicz Physics Department University of Waterloo
Claudia Chanu Department of Mathematics Università di Torino
Jeongoo Cheh Department of Mathematics University of St. Thomas
Peter A. Clarkson Institute of Mathematics, Statistics & Actuarial Science University of Kent at Canterbury
Michael Cowling School of Mathematics University of New South Wales
Luca Degiovanni Department of Mathematics Università di Torino
Hongjie Dong Department of Mathematics University of Chicago
Boris Doubrov International Sophus Lie Centre Belarus State University
Michael Eastwood Department of Pure Mathematics University of Adelaide
Mark Fels Department of Mathematics and Statistics Utah State University
Eugene Ferapontov Department of Mathematical Sciences Loughborough University
Peter Franek Department of Mathematics Karlovy (Charles) University
Michal Godlinski Institute pf Theoretical Physics University of Warsaw
Hubert Goldschmidt Department of Mathematics Columbia University
Sergey Golovin Department of Mathematics and Statistics Queen's University
A. Rod Gover Department of Mathematics University of Auckland
Robin Graham Department of Mathematics University of Washington
Robert Gulliver School of Mathematics University of Minnesota Twin Cities
Hazem Hamdan School of Mathematics University of Minnesota Twin Cities
Chong-Kyu Han Department of Mathematical Sciences Seoul National University
Kengo Hirachi Graduate School of Mathematical Sciences University of Tokyo
Doojin Hong Algebra and Geometry Eduard Cech Center
Evelyne Hubert Project CAFE Institut National de Recherche en Informatique Automatique (INRIA)
Peter Hydon Department of Mathematics and Statistics University of Surrey
Jens Jonasson Department of Mathematics Linköping University
Andreas Juhl Matematiska institutionen Uppsala University
Ernie Kalnins Department of Mathematics and Statistics University of Waikato
Joseph Kenney Department of Mathematics University of Minnesota Twin Cities
Irina Kogan Department of Mathematics North Carolina State University
Jonathan Kress School of Mathematics University of New South Wales
Svatopluk Krysl Mathematical Institute Karlovy (Charles) University
Joseph Landsberg Department of Mathematics Texas A & M University
Guang-Tsai Lei   GTG Research
Thomas Leistner Department of Mathematics University of Adelaide
Felipe Leitner Institute for Geometry and Topology Universität Stuttgart
Debra Lewis   University of Minnesota Twin Cities
Xiaolong Liu Department of Physics and Astronomy University of Iowa
Elizabeth L. Mansfield Institute of Mathematics and Statistics University of Kent at Canterbury
Ian Marquette Department of Physics University of Montreal
Jose Kenedy Martins Department of Mathematics University of Minnesota Twin Cities
Vladimir S. Matveev Department of Geometry Katholieke Universiteit Leuven
Bonnie McAdoo Department of Mathematical Sciences Clemson University
Ray McLenaghan Department of Applied Mathematics University of Waterloo
Willard Miller Jr. Institute for Mathematics and its Applications University of Minnesota Twin Cities
Emilio Musso Department of Mathematics Università di L'Aquila
Lorenzo Nicolodi Department of Mathematics Università di Parma
Anatoly Nikitin Institute of Mathematics National Academy of Sciences of Ukraine
Pawel Nurowski Institute of Theoretical Physics University of Warsaw
Luke Oeding Department of Mathematics Texas A & M University
Peter J. Olver School of Mathematics University of Minnesota Twin Cities
Bent Orsted Institut for Matematiske Fag Aarhus University
Saadet S. Ozer Department of Mathematics Yeditepe University
Teoman Ozer Division of Mechanics Istanbul Technical University
Lawrence J. Peterson Department of Mathematics University of North Dakota
George Pogosyan Department of Physics Yerevan State University
Juha Pohjanpelto Department of Mathematics Oregon State University
Arvind Satya Rao Department of Mathematics University of Iowa
Giovanni Rastelli Department of Mathematics Università di Torino
Gregory J. Reid Department of Applied Mathematics University of Western Ontario
Chan Roath Scientific Research Ministry of Education, Youth and Sport
Colleen Robles Department of Mathematics University of Rochester
Siddhartha Sahi Department of Mathematics Rutgers University
Arnd Scheel Institute for Mathematics and its Applications University of Minnesota Twin Cities
Gerd Schmalz School of Mathematics, Statistics and Computer Science University of New England
Neil Seshadri Graduate School of Mathematics University of Tokyo
Astri Sjoberg Department of Applied Mathematics University of Johannesburg
Jan Slovak Department of Algebra and Geometry Masaryk University
Dalibor Smid Mathematical Institute Karlovy (Charles) University
Roman Smirnov Department of Mathematics and Statistics Dalhousie University
Shane Smith    
Petr Somberg Mathematical Institute Karlovy (Charles) University
Vladimir Soucek Mathematical Institute Karlovy (Charles) University
Dennis The Department of Mathematics and Statistics McGill University
Frédérick Tremblay Mathematics and Statistics University of Montreal
Jukka Tuomela Department of Mathematics University of Joensuu
Francis Valiquette School of Mathematics University of Minnesota Twin Cities
Mikhail Vasiliev Theory Department P. N. Lebedev Physics Institute
Raphael Verge-Rebelo Centre de Recherches Mathematiques University of Montreal
Alfredo Villanueva Department of Mathematics University of Iowa
Ben Warhurst School of Mathematics University of New South Wales
Pavel Winternitz Centre de Resherches Mathematiques University of Montreal
Thomas Wolf Department of Mathematics Brock University
Keizo Yamaguchi Department of Mathematics Hokkaido University
Jin Yue Department of Mathematics and Statistics Dalhousie University
Ismet Yurdusen Centre de Recherches Mathematiques University of Montreal
Igor Zelenko Sector of Functional Analysis and its Applications International School for Advanced Studies (SISSA/ISAS)
Renat Zhdanov   Bio-Key International