**The Kolchin Seminar in Differential
Algebra**

**Saturday February 15 ^{th}
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**