Kolchin Seminar in Differential Algebra
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The Graduate Center
365 Fifth Avenue, New York, NY 10016-4309
General Telephone: 1-212-817-7000
KSDA will meet most Fridays at 10:30 AM at the Graduate Center. The purpose of these meetings is to introduce the audience to differential algebra. The lectures will be suitable for graduate students and faculty and will often include open problems. Presentations will be made by visiting scholars, local faculty, and graduate students.

All meetings will be in Room 6421. This room may be difficult to find; please read the following directions.
When you exit the elevator on the 6th floor, there will be doors both to your left and to your right. Go through the doors where you see the computer monitors, turn right and then immediately left near the drinking fountains. At the end of the corridor turn left, and then left again into a short hallway just past the drinking fountains. The room is at the end of this short corridor.

When you go to the GC you will have to sign in, and it is required that you have some photo ID with you. For directions to the Graduate Center, please click here, and for more on security requirements for entering the premise, please click here.

Academic Year 2008-2009

We welcome Professor Michael Singer, North Carolina State University, as a visiting member of KSDA. The Fall semester will be mainly devoted to studying the notes on Differential Algebraic Groups by Bernard Malgrange, beginning with prerequisites. A copy of the notes is available on request.

For past lecture notes and additional material, see below under "Other Academic Years".

Current Schedule

Friday, October 17, 2008, 10:30 AM

Camilo Sanabria, Graduate Center, CUNY
Entrée to Malgrange ideas: General Involutivity Theorem, III

Abstract: I will motivate through various examples the meaning of Malgrange's Involutivity Theorem. I will expose the curvature as a particular case. The computations involved will smoothly lead to Malgrange's use of the Koszul Complex and its homology.

Friday, October 24, 2008, 10:30 AM

Graduate Center, CUNY
General Discussions: Malgrange ideas: General Involutivity Theorem
Past Lectures, Fall 2008

Friday, September 5, 2008, 10:30 AM

Camilo Sanabria, Graduate Center, CUNY
Hors d'oeuvre to Malgrange ideas: Jet Bundles

Abstract:

Jet Bundles are heavily used in Malgrange's later work. The purpose of the talk is to familiarize the audience with the concept of Jet Bundles and its basic properties.

For lecture notes, please click here.

Friday, September 12, 2008, 10:30 AM

Camilo Sanabria, Graduate Center, CUNY
Hors d'oeuvre to Malgrange ideas: Jet Bundles (continued)

For lecture notes, please click here.

Friday, September 19, 2008, 10:30 AM

Graduate Center, CUNY
General Discussions: Malgrange ideas: Jet Bundles

Abstract:

Jet bundles are heavily used in Malgrange's later work. The purpose of these discussions is to continue to review the concept of jet bundles and their basic properties.

Friday, September 26, 2008, 10:30 AM

Varadharaj Ravi Srinivasan, University of Oklahoma
On Certain Towers of Extensions by Antiderivatives

Abstract: Let F be a characteristic zero differential field with an algebraically closed field of constants, E be a no-new-constant extension of F by antiderivatives of F and let y1, ..., yn be antiderivatives of E. The antiderivatives y1, ..., yn of E are called J-I-E antiderivatives if yi in E satisfies certain conditions. We will discuss a new proof for the Kolchin-Ostrowski theorem and generalize this theorem for a tower of extensions by J-I-E antiderivatives and use this generalized version of the theorem to classify the finitely differentially generated subfields of this tower. In the process, we will show that the J-I-E antiderivatives are algebraically independent over the ground differential field. An example of a J-I-E tower is extensions by iterated logarithms. We will discuss the normality of extensions by iterated logarithms and produce an algorithm to compute the finitely differentially generated subfields of these extensions.

For lecture notes, please click here.

For further information please visit http://math.ou.edu/~vsrinivasan/Thesis-I.pdf.

Friday, October 3, 2008, 10:30 AM

Camilo Sanabria, Graduate Center, CUNY
Entrée to Malgrange ideas: General Involutivity Theorem, I

Abstract: I will motivate through various examples the meaning of Malgrange's Involutivity Theorem. I will expose the curvature as a particular case. The computations involved will smoothly lead to Malgrange's use of the Koszul Complex and its homology.

For lecture notes, please click here.

Friday, October 10, 2008, 10:30 AM

Camilo Sanabria, Graduate Center, CUNY
Entrée to Malgrange ideas: General Involutivity Theorem, II
Other Academic Years

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Created by the KSDA Organizing Committee
Last updated October 12, 2008