Kolchin Seminar in Differential Algebra 
 The Graduate Center 365 Fifth Avenue, New York, NY 100164309 General Telephone: 12128177000 
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 March 20, 2017. For Schedules, lecture notes and additional material, see under (or click):
• Current Schedule • Spring, 2017 • Past Lectures–Spring, 2017 • Past Years
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.
Kolchin Research and Training Workshop I, April 7–9, 2017.
For the three daily programs, please click April 7, April 8, April 9.
Friday, April 7, 2017, 10:00–TBD, Graduate Center
 10:00–10:50 a.m, Room 5382
Jason Bell, University of Waterloo, Canada
The DixmierMoeglin Equivalence and DgroupsThe DixmierMoeglin equivalence is a result that gives a characterization of annihilators of simple modules in a ring and is the first basic step in understanding the irreducible representations of an algebra. We investigate a differentialalgebraic geometric analogue of this equivalence and show that it holds for Dgroups. We use this to show that the classical DixmierMoeglin equivalence holds for a certain class of Hopf algebras.
This is joint work with Omar Leon Sanchez and Rahim Moosa.
 11:00–11:50 a.m, Room 5382
Michael Singer, North Carolina State University
Walks, Difference Equations and Elliptic CurvesIn the recent years, the nature of the generating series of the walks in the quarter plane has attracted the attention of many authors. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least hyperalgebraic (solutions of algebraic differential equations)?
In a seminal paper, BousquetMélou and Mishna attach a group to any walk in the quarter plane and make the conjecture that a walk has a holonomic generating series if and only if the associated group is finite. They proved that, if the group of the walk is finite, then the generating series is holonomic, except, maybe, in one case, which was solved positively by Bostan, van Hoeij and Kauers. In the infinite group case, Kurkova and Raschel proved that if the walk is in addition nonsingular, then the corresponding generating series is not holonomic. This work is very delicate, and relies on the explicit uniformization of a certain elliptic curve. Recently, Bernardi, BousquetMélou, and Raschel proved that 9 of the 51 such walks have a generating series which is hyperalgebraic.
In this talk, I will discuss how difference Galois theory can be used to show that the remaining 42 walks have a generating series which is not hyperalgebraic, reproving and generalizing the results of Kurkova/Raschel and giving insight into the recent work of Bernardi, BousquetMélou, and Raschel. This is joint work with T. Dreyfus, C. Hardouin and Julien Roques.
Saturday, April 8, 2017, 10:00–TBD, Venue: TBA
 Program
TBA
Sunday, April 9, 2017, 10:00–TBD, Venue: TBA
 Program
TBA
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–TBD, Graduate Center
 12:30–13:45 p.m, Room 6417
Anand Pillay, Notre Dame University
Title: TBAThis is jointly organized with the Model Theory Seminar.
 14:00–14:50, Room TBA
David Harbater, University of Pennsylvania
Title: TBA
Saturday, April 22, 2017, 10:00–TBD, Venue: TBA
 Program
TBA
Sunday, April 23, 2017, 10:00–TBD, Venue: TBA
 Program
TBA
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, 10:00–18:00, Room TBA, Graduate Center (Kolchin Workshop III)
 Program
TBA
Saturday, May 6, 2017, Hunter College (AMS Special Sessions)
 Program
TBA
Sunday, May 7, 2017, Hunter College (AMS Special Sessions)
 Program
TBA
Sunday, May 7, 2017, 15:00–18:00, Venue: TBA (Kolchin Workshop III)
 Program
TBA
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. 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). 
February 3, 2017, 10:15–11:30 a.m. Room 5382
Informal Session
RotaBaxter (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 EquationsThe 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
NonExistence of Independent Commuting DerivationsLet K be a field. A derivation d_{1} on K[x_{1},…,x_{n}] is said to be integrable if there exist derivations d_{2}, …, d_{n} such that all d_{i} commute pairwise and the set of d_{i} is linearly independent over K[x_{1},…,x_{n}]. 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
NonExistence of Independent Commuting Derivations, Part IILet K be a field. A derivation d_{1} on K[x_{1},…,x_{n}] is said to be integrable if there exist derivations d_{2}, …, d_{n} such that all d_{i} commute pairwise and the set of d_{i} is linearly independent over K[x_{1},…,x_{n}]. 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 EquationsWe 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 RosenfeldGröbner algorithm, which approaches differential elimination by decomposing the given system of differential equations into simpler systems. We analyze the complexity of the RosenfeldGröbner 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
NonExistence of Independent Commuting Derivations, Part IIILet K be a field. A derivation d_{1} on K[x_{1},…,x_{n}] is said to be integrable if there exist derivations d_{2}, …, d_{n} such that all d_{i} commute pairwise and the set of d_{i} is linearly independent over K[x_{1},…,x_{n}]. 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.
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