Kolchin Seminar in Differential Algebra. KSDA meets most Fridays from 10:15 AM to 11:45 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. Kolchin Afternoon Seminar in Differential Algebra.This informal discussion series began during the Spring Semester of 2009 and will be continued. It normally goes from 2:00-5:00 pm (please check with organizers). All are welcome. Unless the contrary is indicated, all morning and afternoon meetings will be in Room 5382. This room may be difficult to find; please read the following directions. When you exit the elevator on the 5th floor, there will be doors both to your left and to your right. Go through the doors where you see the computer monitors, then turn left and then immediately right through two glass doors. At the end of the corridor, go past another set of glass doors and continue into the short corridor directly in front of you. Room 5382 is the last room on your right. Security. 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.

Occasionally, we also meet on a Saturday at Hunter Colleger, Room E920. Hunter College is on 68th Street and Lexington Avenue, where the No. 4,5,6 subways stop. You need to enter from the West Building (a photo ID is required), go up the escalators to the third floor, walk across the bridge over Lexington Avenue to the East Building, and take the elevator before the Library to the 9th floor. Room 920 is located in a north-east corner.

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Preliminary Schedule

Friday, February 24, 2012 at 10:15 a.m. Room 5382

Andrey Minchenko, University of Western Ontario
TBA

Andrey Minchenko will also be giving a talk at the Representation Theory Seminar, at 1:00 pm, Rm 6493

Friday, March 9, 2012 at 10:15 a.m. Room 5382

William Simmons, University of Illinois, Chicago
TBA

Friday, March 30, 2012 at 10:15 a.m. Room 5382

David Marker, University of Illinois, Chicago
TBA

Past Lectures, Spring 2012

Friday, January 27, 2012 at 10:15 a.m. Room 5382

Nathan Penton, Graduate Center, CUNY
Jet Bundles and PDEs

The language of jet bundles allows a formalization of the geometric aspects of nonlinear partial differential equations, in much the same way that varieties formalize the geometric aspects of polynomials. As such, they provide a natural setting for the application of differential algebra to nonlinear problems. In this talk, I will provide an introduction to PDEs and their symmetries from the jet bundle viewpoint, including details and examples, with the goal of defining some of the differential algebraic structures and transformation groupoids that arise in this study.
Although this talk consists of expansions, clarifications, and corrections of notions touched upon in my talk last month, nothing from that talk will be assumed.

Friday, February 3, 2012 at 10:15 a.m. Room 5382

Christian Dönch, Research Institute for Symbolic Computation. Johannes Kepler University, Linz, Austria
Alexander Levin, The Catholic University of America
Evaluation of the Strength of Systems of Partial Differential and Difference Equations via Differential and Difference Dimension Polynomials, Part I

In the first part of this talk the speakers will review basic facts about univariate and multivariate differential and difference dimension polynomials and their relation to the strength of systems of algebraic differential and difference equations. We will also describe invariants of such polynomials and main methods of their computation.

Friday, February 3, 2012 at 2:00 p.m. Room 5382

Christian Dönch, Research Institute for Symbolic Computation. Johannes Kepler University, Linz, Austria
Alexander Levin, The Catholic University of America
Evaluation of the Strength of Systems of Partial Differential and Difference Equations via Differential and Difference Dimension Polynomials, Part II

In the second part of the talk we will introduce the concepts of a Gröbner basis with respect to several orderings and relative Gröbner basis and show how properties of these bases can be applied to the computation of multivariate dimension polynomials. Then we will present algorithms of computation of such polynomials and use them to determine the strength of several systems of PDEs of mathematical physics and their difference analogs obtained from different types of difference schemes.