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The Kolchin Seminar in Differential Algebra

Hunter College - Room HW706

Saturday February 15th 2003

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Jerry Ianni
LaGuardia Community College - CUNY
Algorithmic Aspects of Abhyankar's Lemma
2:00 - 3:00 PM

Abstract: Suppose V is a discrete valuation ring with field of fractions K, and suppose L and K' are Galois extensions of K tamely ramified over V. Let L' be a composite extension of L and K' over K. Abhyankar's Lemma specifies conditions that ensure that L' is unramified over the localizations of the integral closure V' of V in K'. The proof of this lemma will be presented in general. Then computational aspects of both the hypotheses and the proof of the lemma will be highlighted for the case of characteristic 0. This lecture is the first of a planned series of reports of work in progress. If intuition prevails, the algorithmic aspects discussed in this talk will be interconnected with the presenter's algorithm for computing normalizations (joint work with Raymond T. Hoobler of CCNY) to yield some generalizations of Abhyankar's Lemma.

Lucia Di Vizio
IAS
Arithmetic Characterization of the Generic q-difference Galois Group
3:30 - 4:30 PM

Abstract: Grothendieck's conjecture on $p$-curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all finite places. It is equivalent to Katz's conjectural description of the generic Galois group. In this talk I'll speak about an analogous statement for arithmetic $q$-difference equations.

Li Guo
Rutgers University - Newark
Baxter Algebras and Stirling Numbers
5:00 - 6:00 PM

Abstract: I will first give an interpretation of Stirling numbers in the context of Baxter algebras. Stirling numbers have been studied for a long time and have played important roles in several areas of pure and applied mathematics, including number theory and combinatorics. This interpretation allows one to view number theoretic properties of the Stirling numbers from an algebraic point of view, and to obtain results on Baxter algebras from known theorems on Stirling number. This connection also suggests a generalization of Stirling numbers.

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Coffee and tea will be served beginning at 1:30 PM
Room HW706

Click here for directions to Hunter College and location of room

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