The Kolchin Seminar in Differential Algebra

Hunter College - Room HW706

Saturday March 27 - Sunday March 28 2004

Saturday Session

Li Guo
Rutgers University
Differential algebras and dendriform algebras
2:00-3:00pm

Abstract: Dendriform algebras refer to a class of algebra structures introduced by Loday in 1996 with motivation from algebraic K-theory. The field has expanded quite much during the last couple of years, with connections to operad theory, math physics, Hopf algebras and combinatorics. A recent observation is that some basic dendriform algebras are induced by linear operators, such as Baxter and Nijenhuis operators. After an introduction to dendriform algebras, we will describe relations between differential algebras and dendriform algebras, such as dendriform algebras induced by differential operators.

Juan Morales-Ruiz
Universitat Polytècnica de Catalunya, Barcelona, Spain
A Galois differential approach to perturbation of asymptotic surfaces in Hamiltonian systems (I)
3:30-4:30PM

Abstract: The aim of the talk is a report on a joint work in progress with J.-P. Ramis. This work is motivated by my paper, A Note on a Connection Between the Poincaré--Arnold-Melnikov Integral and the Picard-Vessiot Theory, and can be considered also as an extension of my results with Ramis to the variational equations with respect to parameters and to study the splitting of separatrices. As a by product, the differential extensions that we consider are very natural candidates to Kolchin's strongly normal extensions.

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Li Guo
Rutgers University
Differential algebras and dendriform algebras - PartII
5:00-6:00pm

Abstract: In the second part of this talk we will describe relations between differential algebras and dendriform algebras, such as dendriform algebras induced by differential operators.

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Sunday Session

Juan Morales-Ruiz
Universitat Polytècnica de Catalunya, Barcelona, Spain
A Galois differential approach to perturbation of asymptotic surfaces in Hamiltonian systems (II)
10:00-11:00AM

Abstract: The second part of the talk will address the strategy of proofs which are mainly based on the p-adic theory of elliptic curves and modular curves.

Coffee and tea will be served beginning at 1:30 PM on Saturday and at 10 AM on Sunday
Room HW706