Kolchin Seminar in Differential Algebra
KSDA Home     Graduate Center Series     Hunter College Series
People     Posted Papers     Conferences
The Graduate Center
365 Fifth Avenue, New York, NY 10016-4309
General Telephone: 1-212-817-7000

Academic Year 2016–2017

Alerts: Spring Kolchin Workshops and AMS Special Sessions: See workshops below, or click workshops.
The Eighth International Workshop on Differential Algebra and Related Topics (DART VIII) will be held at Johannes Kepler University, Linz, Austria from September 11 to 14, 2017. Click DART VIII for details and updates.


Last updated on April 24, 2017. For Schedules, lecture notes and additional material, see under (or click):
 •  Current Schedule  •   Spring, 2017   •   Past Lectures–Spring, 2017  •  Past Years

Friday, April 28, 2017, 10:15–11:30 a.m. Room 5382

Informal Session.

Informal sessions at the Kolchin Seminar are open to all and attendees may bring short presentations and questions for discussion.


Kolchin Research and Training Workshop III, May 5 and 7, 2017.
Also, Special Sessions on Differential and Difference Algebra at the AMS Sectional Meeting at Hunter College on May 6 and May 7.

For the three combined daily programs, please click May 5, May 6, May 7.

Friday, May 5, 2017, 10:00–17:40, Room 5382 at the Graduate Center  (Kolchin Workshop III)

Saturday, May 6, 2017, 08:00–17:00,  Room HN504 atHunter College AMS Spring Eastern Sectional Meeting #1129

Differential and Difference Algebra: Recent Developments, Applications, and Interactions
Special Sessions I and II, organized by Omár León-Sanchez, McMaster University and Alexander Levin, The Catholic University of America.

All lectures are given in Room HN504 (Hunter North Building). Speaker is marked by an asterisk when there are multiple authors. Each title is preceded by an AMS code in the form of AA-BBB, where AA is MSC 2-digit classification and BBB is a sequence number with a variable number of digits. Abstracts are from AMS official site for abstracts as of April 24, 2017, reproduced below in html format for convenience.

Sunday, May 7, 2017, 08:00–15:30,  Room HN504 at Hunter College AMS Spring Eastern Sectional Meeting #1129

Differential and Difference Algebra: Recent Developments, Applications, and Interactions
Special Sessions III and IV, organized by Omár León-Sanchez, McMaster University and Alexander Levin, The Catholic University of America.

All lectures are given in Room HN504 (Hunter North Building). Speaker is marked by an asterisk when there are multiple authors. Each title is preceded by an AMS code in the form of AA-BBB, where AA is MSC 2-digit classification and BBB is a sequence number with a variable number of digits. Abstracts are from AMS official site for abstracts as of April 24, 2017, reproduced below in html format for convenience.

Sunday, May 7, 2017, 15:30–TBD, Room HN504, Hunter College North Building (Kolchin Research and Training Workshop III)


The Kolchin Seminars

Kolchin Seminar in Differential Algebra. For 2016 Spring Semester, KSDA meets most Fridays from 10:15 AM to 11:45 AM at the Graduate Center, with occasional talks also from 2:00 PM to 3:30 PM and at Hunter College or other venues on some Saturdays and Sundays. The purpose of these meetings is to introduce the audience to differential algebra and related topics. Most 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 although unannounced normally, has been held regularly since. Occasionally, for various reasons, we may also schedule guest speakers in the afternoon. Informal sessions run from 2:00 pm. to 4:00 p m. in Room 5382 and sometimes start earlier and ends much later. The start time and topics will be announced during the morning sessions (and if not, check with the 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.
We sometimes hold joint seminars with the Model Theory and Logic Workshop in Room 6417, which is on the 6th floor.

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, and for more on security requirements for entering the premise, please click here (updated September 1, 2015).

For other seminars of the Mathematics Department at the Graduate Center, please click here.

Hunter College meetings. Occasionally, we also meet on a Saturday and/or Sunday at Hunter College. Hunter College is on 68th Street and Lexington Avenue, where the No. 4,5,6 subways stop. Hunter College has several buildings, including Hunter East (HE), Hunter West (HW), and Hunter North (HN). On weekends, you need to enter from the West Building (a photo ID is required), go up the escalator to the third floor (if necessary, walk across the bridge over Lexington Avenue to the East Building, or across the bridge over 68th Street to the North Building), and take the elevator (ask for direction to the bank of elevators) or escalator to the floor of the meeting room (for example, HN 1036 is on the 10th floor of the North Building).


Past Lectures, Spring 2017

February 3, 2017, 10:15–11:30 a.m. Room 5382

Informal Session
Rota-Baxter (Type) Algebras

Friday, February 10, 2017, 10:15–11:30 a.m. Room 5382

Jim Freitag, University of Illinois at Chicago
Revisiting the Model Theory of Painlevé Equations

The Painlevé equations are six families of nonlinear order two ODEs with complex parameters. Around the start of the last century, the equations were isolated for foundational reasons in the analysis of ODEs. Since the 1970s, interest in the equations has steadily increased due in part to their connections with various areas of mathematics (e.g. monodromy of linear differential equations, mathematical physics, and diophantine geometry). In a recent series of works, Nagloo and Pillay established the algebraic independence of solutions of a Painlevé equation, at least when the coefficients are assumed to be transcendental, algebraically independent complex numbers. Later, Nagloo established results of a similar nature for algebraic relations between solutions of equations from different families. In this talk, we will build on the theme of Nagloo and Pillay, answering several questions left open by their work. One of the surprising aspects of the work of Nagloo and Pillay, as well as the present work, is the application of deep structural classification results from model theory to concrete problems on transcendence.

For a review of the lecture, please click video.

Friday, February 17, 2017, 10:15–11:30 a.m. Room 5382

Peter Thompson, Graduate Center, CUNY
Non-Existence of Independent Commuting Derivations

Let K be a field. A derivation d1 on K[x1,…,xn] is said to be integrable if there exist derivations d2, …, dn such that all di commute pairwise and the set of di is linearly independent over K[x1,…,xn]. Let K be a field of characteristic 0. We present a class of derivations on K[x, y] that is not integrable.
This is joint work with Joel Nagloo and Alexey Ovchinnikov.

Friday, February 24, 2017, 10:15–11:30 a.m. Room 5382

Informal Session

Informal sessions at the Kolchin Seminar are open to all and attendees may bring short presentations and questions for discussion. In this informal session we expect to explore the algebraic approach to integral equations along the recent development in integral differential algebras of Rosenkranz et al.

Friday, March 3, 2017, 10:15–11:45 a.m. Room 5382

Peter Thompson, Graduate Center, CUNY
Non-Existence of Independent Commuting Derivations, Part II

Let K be a field. A derivation d1 on K[x1,…,xn] is said to be integrable if there exist derivations d2, …, dn such that all di commute pairwise and the set of di is linearly independent over K[x1,…,xn]. Let K be a field of characteristic 0. We present a class of derivations on K[x, y] that is not integrable.
This is joint work with Joel Nagloo and Alexey Ovchinnikov.

Friday, March 3, 2017, 2:00–4:00 p.m. Room 5382

Richard Gustavson (Graduate Center, CUNY)*
Elimination for Systems of Algebraic Differential Equations

We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, whether the given system of differential equations has a solution. We first look solely at the "algebraic data" of the system of differential equations through the theory of differential kernels to provide a new upper bound for proving the consistency of the system. We then prove a new upper bound for the effective differential Nullstellensatz, which determines a sufficient number of times to differentiate the original system in order to prove its inconsistency. Finally, we study the Rosenfeld-Gröbner algorithm, which approaches differential elimination by decomposing the given system of differential equations into simpler systems. We analyze the complexity of the Rosenfeld-Gröbner algorithm by computing an upper bound for the orders of the derivatives in all intermediate steps and in the output of the algorithm.
*This talk will be the doctoral dissertation defense of the speaker in the Mathematics Department at the Graduate Center. All are welcome.

Friday, March 10, 2017, CUNY Math Fest Day, NO SEMINAR

Friday, March 17, 2017, 10:15–11:30 a.m. Room 5382

Informal Session

Instead of the previously announced talk (see below), Peter Thompson will instead participate in an informal session, which is open to all and attendees may bring short presentations and questions for discussion.

Peter Thompson, Graduate Center, CUNY
Non-Existence of Independent Commuting Derivations, Part III

Let K be a field. A derivation d1 on K[x1,…,xn] is said to be integrable if there exist derivations d2, …, dn such that all di commute pairwise and the set of di is linearly independent over K[x1,…,xn]. Let K be a field of characteristic 0. We present a class of derivations on K[x, y] that is not integrable.
This is joint work with Joel Nagloo and Alexey Ovchinnikov.

Friday, March 24, 2017, 10:15–11:30 a.m. Room 5382

Due to a family emergency, the talk by William Keigher has been CANCELED.

Until further notice, we will have instead an
Informal Session.

Informal sessions at the Kolchin Seminar are open to all and attendees may bring short presentations and questions for discussion.

Friday, March 31 2017, 10:15–11:30 a.m. Room 5382

Informal Session.

Informal sessions at the Kolchin Seminar are open to all and attendees may bring short presentations and questions for discussion. In this session, the topic is expected to be an introduction to ultra-filters.

Friday, April 7, 2017, 10:00–17:20. All lectures in Room 5382, Graduate Center

Kolchin Research and Training Workshop I, April 7–9, 2017.

For the three daily programs, please click April 7, April 8, April 9.

Saturday, April 8, 2017, 10:00–17:45, All meetings in Room 6-215 at Baruch College

Sunday, April 9, 2017, 9:15–12:30, All meetings in Room 6-215 at Baruch College

Friday, April 14, 2017, Spring Recess, No Seminar

Kolchin Research and Training Workshop II, April 21–23, 2017.

For the three daily programs, please click April 21, April 22, April 23.

Friday, April 21, 2017, 10:00–17:30, Graduate Center

Saturday, April 22, 2017, 10:00–18:00, All meetings in Room 6-215 at Baruch College

Sunday, April 23, 2017, 9:15–13:15, All meetings in Room 6-215 at Baruch College


Other Academic Years

   2005–2006    2006–2007    2007–2008    2008–2009    2009–2010    2010–2011    2011–2012    2012–2013    2013–2014    2014–2015    2015–2016    2016–2017


Hosted by
Created by the KSDA Organizing Committee
Please submit web page problems to William Sit