|Kolchin Seminar in Differential Algebra|
|The Graduate Center|
365 Fifth Avenue, New York, NY 10016-4309
General Telephone: 1-212-817-7000
Last updated on September 20, 2014. For
lecture notes and additional material, see under (or click):
• Current Schedule • Past Lectures–Fall 2014 • Past Years
The start times of most talks have been moved to 12:30 pm. Talks are scheduled for 90 minutes each.
(Friday Schedule), September 23, 2014, 12:30 –2:00 p.m. Room 5382
Raymond Hoobler, CCNY and Graduate Center of CUNY
A Differential Poincaré Lemma
Let X be a smooth scheme over a field k of characteristic 0. I will show
that the complex
0 → OΔX → OX → Ω1 X/k → …
constructed from the de Rham complex of X is exact in the d-finite topology if Δ consists of all "derivations" of X. In particular, this means that the d-finite cohomology of a variety matches the singular cohomology of X with complex coefficients and agrees with the étale cohomology of X with torsion coefficients. Most of the talk will be an outline of the necessary steps that lead up to this result. Potential applications will be described.
Friday, September 26 and October 3, 2014, School Holidays, no seminar.
Thursday, October 2, 2014, 1:00 –2:00 p.m. Room 6/113 North Academic Center, CITY COLLEGE
David Marker, University of Illinois at Chicago
Model Theory and Exponentiation
Methods from mathematical logic have proved surprisingly useful in understanding the geometry and topology of sets definable in the real field with exponentiation. When looking at the complex exponential field, the definability of the integers is a seemingly insurmountable impediment, but a novel approach due to Zilber leads to a large number of interesting new questions.
This is a cross-listing from Model Theory Seminar and the CCNY Mathematics Colloquium.
Friday, October 10, 2014, 2:00 –3:30 p.m. Room 6417
Alice Medvedev, City College, CUNY
This is a cross-listing from CUNY Logic Workshop.
Friday, October 10, 2014, 12:30 –2:00 p.m. Room 5382
Joseph Gunther, Baruch College and the Graduate Center, CUNY
Friday, October 17, 2014, 11:00 –12:30 p.m. Room 5382(?)
Alice Medvedev, City College, CUNY
This is a cross-listing from Model Theory Seminar.
Friday, October 17, 2014, 12:30 –2:00 p.m. Room 5382
William Keigher, Rutgers University at Newark
Friday, October 24, 2014, 12:30 –2:00 p.m. Room 5382
Li Guo, Rutgers University at Newark
Friday, October 31, 2014, 12:30 –2:00 p.m. Room 5382
Anand Pillay, University of Notre Dame
Friday, November 7, 2014, 12:30 –2:00 p.m. Room 5382
Michael Singer, North Carolina State University
Friday, November 14, 2014, 12:30 –2:00 p.m. Room 5382
Rahim Moosa, University of Waterloo
Friday, November 14, 2014, 2:15 –3:45 p.m. Room 5382
Uma Iyer, Bronx Community College, CUNY
Saturday, November 15, 2014, 11:00 a.m.–12:30 p.m. Hunter College E920
Andrei Minchenko, Weizmann Institute
Friday, December 5, 2014, 12:30 –2:00 p.m. Room 5382
Carlos Arreche, North Carolina State University
Friday, December 12, 2014, 12:30 –2:00 p.m. Room 5382
Wei Li, KLMM, Chinese Academy of Sciences, and University of California at Berkeley,
Kolchin Seminar in Differential Algebra. For 2014 Fall Semester, KSDA meets most Fridays from 12:30 PM to 2:00 PM at the Graduate Center, with occasion talks also from 2:15 PM to 3:45 PM and at Hunter College, on some Saturdays. 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. Occasionally, for various reasons, we may also schedule guest speakers in the afternoon. It normally goes from 2:30–4:00 pm (please check with organizers). All are welcome.
Unless the contrary is indicated, all 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 (updated September 1, 2013).
Occasionally, we also meet on a Saturday at
Hunter College, 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
Friday, September 5, 2014, 1:00 –2:30 p.m. Room 5382
Richard Churchill, Graduate Center and Hunter College, CUNY
Kolchin's Proof that Differential Galois Groups are Algebraic
Kolchin's 1948 proof that differential Galois groups are algebraic appeals to a formulation of algebraic geometry which is no longer in fashion. Modern proofs require considerable knowledge of the Grothendieck approach to that subject, which takes considerable time to digest. In this talk I hope to convince those attending that Kolchin's proof can be understood in contemporary terms with only minor appeals to algebraic geometry, i.e. the definition of an algebraic set and the Hilbert Basis Theorem.
For lecture notes, please click here.
Friday, September 12, 2014, 12:30 –2:00 p.m. Room 5382
James Freitag, University of California at Berkeley
Effective Bounds For Finite Differential-Algebraic Varieties (Part I)
Given a differential algebraic variety over a partial differential field, can one give a bound for the degree of its Zariski closure that depends only on the order and degree of the differential polynomials (but not the parameters) which determine the variety? We will discuss the general theory of prolongations of differential algebraic varieties as developed by Moosa and Scanlon, and use this theory to reduce the problem to a combinatorial problem (which will be discussed in detail in the second part of the talk). Along the way we will give numerous examples of the usefulness of the result, some of an arithmetic flavor. We will also describe some other applications of the theory of prolongations.
This is joint work with Omar Sanchez. For a video recording of the talk, please click here.
Friday, September 12, 2014, 2:15 –3:45 p.m. Room 5382
Omar Leon Sanchez, McMaster University
Effective Bounds For Finite Differential-Algebraic Varieties (Part II)
We will talk about the difficulties that commutativity entails when trying to find points of the form (a, d1(a),...,dm(a)) in algebraic subvarieties of prolongations. We discuss how to deal with these issues by passing to higher order prolongations (where the order is "uniform"). We use this to establish effective bounds for finite differential-algebraic varieties.
This is joint work with James Freitag. For a video recording of the talk, please click here.
Friday, September 19, 2014, 12:30 –2:00 p.m. Room 5382
Ronnie Nagloo, Graduate Center of CUNY
Model Theory and the Painlevé Equations
The Painlevé equations are nonlinear 2nd order ODEs and come in six families P1, …, P6, where P1 consists of the single equation y''=6y2+t, and P2, …, P6 come with some complex parameters. They were discovered strictly for mathematical considerations at the beginning of the 20th century but have arisen in a variety of important physical applications, including for example random matrix theory and general relativity.
To view the video recording of this talk, please click here and here.