The program will focus on computational algebraic geometry and algebraic properties of differential equations and their solutions. The program committee consists of Marie-Françoise Roy, Michael Singer and Bernd Sturmfels.
In geometry, some of the topics we will emphasize are: Gröbner Bases (both commutative and non-commutative), resultants and residues (relationship to Chow forms, multigraded resultants, ``sparse'' resultants, multisymmetric functions, relations to hypergeometric differential equations), enumerative and combinatorial geometry (effective methods in the Schubert calculus, mixed volumes and toric varieties, relations to integer programming) and real algebraic geometry (real enumerative geometry, fewnomials, root counting, complexity of semi-algebraic sets, certificates for unsolvable systems).
In analysis some of the topics are: linear difference and differential equations (effective methods in the Galois theory, Zeilberger's method, relations to residues and roots of parameterized polynomial equations), systems of differential equations (differential ideal theory, Gröbner-like techniques, involutive systems of partial differential equations, Pfaffian systems), first integrals and symmetry and equivalence methods (Lie and Hopf theoretic techniques, differential invariants, Cartan equivalence).
More information is available at the URL: http://www.msri.org
Contents