Session 1.  Monday, 4:10-6:10 pm, 335 Harrelson Hall
Chair: Irina Kogan
 

Peter Olver (University of Minnesota) Moving Frames for Pseudogroups Abstract: In this talk, I will present new computational algorithms for        infinite-dimensional Lie pseudo-groups.  I will begin with a brief        introduction to pseudo-groups, and then develop the equivariant         moving frame method.  Applications include the classification of         differential invariants and the structure of symmetry groups of        differential equations and variational problems arising in geometry        and physics.

Agnes Szanto (NCSU) Over-constrained Weierstrass iterations computes the distance to consistent systems Abstract: In this talk we present a new result concerning a generalization      of the classical Weierstrass iteration for over-constrained multivariate      systems. We prove that given an over-constrained system of polynomials      as input, our method iterates the common roots of a system which has k      common roots and has minimal distance from the input, if the minimum      exist. This result gives an improved iterative method to find the      approximate GCD of univariate polynomials, and allows a completely new      generalization to the multivariate case. This work is a collaboration with      Olivier Ruatta and Mark Sciabica.

Session 2. Tuesday, 10am-12pm, 330 Harrelson Hall
Chair: Liz Mansfield
 

Irina Kogan (NCSU) Noether correspondence for group-invariant variational problems Abstract: It was shown by S. Lie that almost every  variational problem, invariant with respect to a group of point transformations,  and  the corresponding Euler-Lagrange equations, can  be written in terms of differential invariants and invariant differential forms, and thus reduced by the symmetry group. In this talk we  define infinitesimal variational symmetries of  the reduced variational problem and show that they lead to conservation laws  for  both,  the reduced and the original system of Euler-Lagrange equations.  Computational aspects of this approach will be also  discussed.

Michael Singer (NCSU) Inverse Problems in Differential Galois Theory Abstract: I will give a introduction to the Galois theory of linear differential equations from  both an analytic and algebraic point of view.  I will then discuss the problem of constructing a differential equation having a given group as its differential Galois group and presents some recent results in this area.

Session 3. Wednesday, 2-4pm, 314 Harrelson Hall
Chair: Michael Singer
 

Evelyne Hubert (INRIA, Sophia-Antipolis, France) Differential Algebra for Derivations with Nontrivial Commutation Rules Abstract: The classical assumption of differential algebra and differential elimination is that the derivations do commute [Kolchin 1973, Boulier 97, Hubert 2000]. That is the standard case arising from systems of partial differential equations. We inspect here the case where the derivations satisfy nontrivial commutation rules. That situation arises naturally in some applications or is of use to make computations more amenable.     This work is part of a project initiated by E. Mansfield and in collaboration with I. Kogan to treat differential systems that are invariant under a Lie group action. The moving frame construction of differential invarariants and invariant derivations [Fels & Olver 99] allows us to rewrite the system in a more intrinsic way but with derivations that do not commute.     If time permits I shall  illustrate the differential elimination software developed for this new situation.

Elizabeth L. Mansfield (University of Kent, United Kingdom) Difference Forms - from local to global Abstract: When modelling systems using difference equations, global phenomena can become important. For example, in many studies periodicity is used instead of boundary conditions. This introduces the topology of a torus and hence periodic increments in the evaluation of conserved quantities. These increments can appear as mysterious errors if they are not recognised for what they are. Or in other examples, for difference approximations of systems defined originally on surfaces, it may be important to maintain globally defined constraints.      In this talk we show that difference forms defined locally on pieces of lattice can be pieced together in much the same way that local smooth forms can, with strongly analogous results in the resulting cohomology. The method, based on a celebrated line of argument due to Weyl, shows how global constraints and conservation laws for smooth systems and their difference approximations can be matched through "the combinatorics of a good cover".  This is a joint work with Peter Hydon, University of Surrey.