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

Academic Year 2013–2014

All morning meetings and all afternoon meetings will be in Room 5382 of the Graduate Center. Morning sessions begin at 10:15 am and last till 11:45 am. Most (informal) afternoon sessions begin at 2:00 pm and are unannounced. Occasionally, we may schedule formal talks on Friday afternoons, or on Saturdays at Hunter College, Room E920, and these will be announced. Cancellation due to inclement weather will follow CUNY guideline and policy and will be posted accordingly.

For Schedules, lecture notes and additional material, see under (or click):
 • Current Schedule   •  Past Lectures–Spring 2014  •  Past Years

Friday, April 25, 2014 at 10:15 a.m. Room 5382

Li Guo, Rutgers University at Newark
Gröbner-Shirshov Bases of Free Integral Differential Algebras

Integro-differential algebras have been introduced recently in the study of boundary problems of differential equations. We will discuss a recent construction of free commutative integro-differential algebras using the method of Gröbner-Shirshov basis based on the construction of free commutative Rota-Baxter algebras via mixable shuffles.


Friday, May 2, 2014 at 10:15 a.m. Room 5382

Benjamin Steinberg, The City College, CUNY
Title TBA

Friday, May 9, 2014 at 10:15 a.m. Room 5382

Taylor Dupuy, University of California at Los Angeles and MSRI
Title TBA

Friday, May 16, 2014 at 10:15 a.m. Room 5382

Victor Kac, Massachusetts Institute of Technology
Title TBA

Friday, May 16, 2014 at 2:00 p.m. Room 5382

Victor Kac, Massachusetts Institute of Technology
Title TBA

Monday, July 7, 2014 at 10:15 a.m. Room TBA

Sonia Rueda, Universidad Politécnica de Madrid
Title TBA

Monday, July 7, 2014 at 2:00 p.m. Room TBA

Markus Rosenkranz, University of Kent at Canterbury, UK
Title TBA

Monday, July 8, 2014 at 9:00–10:30 a.m. Room TBA

Moulay Barkatou, XLIM Research Institute, Limoges, France
Title TBA

Monday, July 8, 2014 at 10:45 a.m.–12:15 p.m. and 2:00–5:00 p.m. Room TBA

Markus Rosenkranz, University of Kent at Canterbury, UK
Title TBA

Monday, July 14, 2014 at 10:00 a.m. Room TBA

Julien Roques, Institut Fourier, Université Grenoble 1
Title TBA


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. Occasionally, for various reasons, we may also schedule guest speakers in the afternoon. 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 (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 corner.


Past Lectures, Spring 2014

Friday, January 31, 2014 at 10:15 a.m. Room 5382

Thomas Dreyfus, Institute of Mathematics of Jussieu
A Density Theorem for Parameterized Differential Galois theory

To a linear differential system with coefficients that are germs of meromorphic functions, we can associate an algebraic group (the differential Galois group), which measures the algebraic relations among the solutions. The Density Theorem of Ramis gives a list of topological generators of this group with respect to the Zariski topology. More recently a Galois theory for parameterized linear differential system has been developed by Cassidy and Singer. In this theory, the Galois group, which is a differential algebraic group (with respect to the parametric derivations), measures the algebraic and the (parametric) differential algebraic relations among the solutions. We will present an analogue of the Density Theorem of Ramis for this theory.

For a copy of the lecture slides, please click here. The full preprint of the paper is available at http://www.math.jussieu.fr/~tdreyfus/ramisparam.pdf,

Friday, February 7, 2014 at 10:15 a.m. Room 5382

Alexey Ovchinnikov, Queens College and The Graduate Center, CUNY
Semigroup Actions on Tannakian Categories

Ostrowski's theorem implies that log(x), log(x +1),... are algebraically independent over ℂ(x). More generally, for a linear differential or difference equation, it is an important problem to find all algebraic dependencies among a non-zero solution y and particular transformations of y, such as derivatives of y with respect to parameters, shifts of the arguments, rescaling, etc. I will discuss a theory of Tannakian categories with semigroup actions, which could be used to attack such questions in full generality. Deligne studied actions of braid groups on categories and obtained a finite collection of axioms that characterizes such actions to apply it to various geometric constructions. In this talk, I will present a finite set of axioms that characterizes actions of semigroups that are finite free products of free finitely generated commutative semigroups on Tannakian categories. This is the class of semigroups that appear in many applications.

Friday, February 14, 2014 at 10:15--11:15 a.m. Room 5382

Carlos Arreche, The Graduate Center, CUNY
A Picard-Vessiot Topology for Differential Schemes

We present a new Grothendieck topology for differential schemes, called the Picard-Vessiot topology, in which every OX-coherent module with a connection is locally trivial (i.e., generated by horizontal sections). The main examples of differential schemes are smooth algebraic varieties and prime spectra of differential rings. We will discuss analogies (and contrasts) with the étale topology, as well as potential applications of the Picard-Vessiot topology to some problems in algebraic geometry and differential algebra. We will motivate the abstract theory with a brief account of the role of étale cohomology in the proof of the Weil conjectures, and we will recall the relevant definitions from (differential) algebraic geometry and the theory of Grothendieck topologies.

Friday, February 21, 2014 at 10:15 a.m. Room 5382

Moshe Kamensky, The Hebrew University, Jerusalem
Picard-Vessiot Structures

A Picard-Vessiot (PV) extension associated to a linear differential equation is the analogue, in differential Galois theory, of the splitting field of a polynomial. A classical result asserts that a PV extension exists, and is unique, so long as the base field of constants is algebraically closed. I will explain a generalisation of this result, for other fields of constants. The proof uses a generalisation of PV extensions in a general first order setting, and a geometric description of the collection of such extensions.

Alert:Video recordings of Moshe Kamensky's talk in both the morning and afternoon sessions are available for viewing Morning and Afternoon.

Friday, February 28, 2014 at 10:15--11:15 a.m. Room 5382

Raymond Hoobler, City College and Graduate Center, CUNY
Carlos Arreche, The Graduate Center, CUNY

A Picard-Vessiot Topology for Differential Schemes, Part II

This is a continuation of the talk given on February 14. We present a new Grothendieck topology for differential schemes, called the Picard-Vessiot topology, in which every OX-coherent module with a connection is locally trivial (i.e., generated by horizontal sections). The main examples of differential schemes are smooth algebraic varieties and prime spectra of differential rings. We will discuss analogies (and contrasts) with the étale topology, as well as potential applications of the Picard-Vessiot topology to some problems in algebraic geometry and differential algebra. We will motivate the abstract theory with a brief account of the role of étale cohomology in the proof of the Weil conjectures, and we will recall the relevant definitions from (differential) algebraic geometry and the theory of Grothendieck topologies.

There will be no scheduled Kolchin Seminar Talk on March 7, 2014. You are invited to attend instead:
Friday, March 7, 2014 at 12:30--2:00 p.m. Room 6417

Russell Miller, The Graduate Center, CUNY
Turing Degree Spectra of Differentially Closed Fields

This is a cross-listing from CUNY Model Theory Seminar. For abstract, click here.

Friday, March 14, 2014 at 10:15 a.m. Room 5382

Andrew Parker, New York City College of Technology, I
Grothendieck Topologies—Sieves, Sites and Sheaves

This talk will serve as an introduction to the category-theoretical foundations necessary for defining Grothendieck Topologies. Starting with the Yoneda embedding, our aim will be to replace the standard notion of "open cover of a topological space X " with that of "covering sieves for a category C " in such a way that the classical formalism of sheaves and sheaf cohomology remain meaningful in a more general context.

Friday, March 21, 2014 at 10:15 a.m.–11:45 a.m., and 2:00 p.m.–5:00 p.m. Room 5382

Alexandru Buium, University of New Mexico
Arithmetic Differential Equations on GLn, Parts I and II

Motivated by the search of a concept of linearity in the theory of arithmetic differential equations, we introduce an arithmetic analogue of Lie algebras and an arithmetic analogue of the Maurer-Cartan connections. There is a family of such arithmetic connections for each of the classical involutions of GLn. Finally we discuss the Galois groups attached to the resulting arithmetic differential equations. These Galois groups (generally) appear as subgroups of GLn over the "algebraic closure of the field with one element".

Alert:Video recordings of Alexandru Buium's talk in both the morning and afternoon sessions are available for viewing Morning and Afternoon

Friday, March 28, 2014 at 10:15 a.m. Room 5382

Andrew Parker, New York City College of Technology
Grothendieck Topologies—Sieves, Sites and Sheaves, II

This talk will serve as an introduction to the category-theoretical foundations necessary for defining Grothendieck Topologies. Starting with the Yoneda embedding, our aim will be to replace the standard notion of "open cover of a topological space X " with that of "covering sieves for a category C " in such a way that the classical formalism of sheaves and sheaf cohomology remain meaningful in a more general context.

Friday, April 4, 2014

There will be no scheduled meeting. Those interested in an informal discussion on Grothendieck Topology are welcome to meet at 10:15 a.m. in Room 5382.

The following is a cross-listing from the Commutative Algebra &  Algebraic Geometry Seminar.

Friday, April 4, 2014 at 4:00 p.m. Room 6417

Andrew Parker, New York City College of Technology, CUNY
A1-Homotopy Theory.

In this talk, we will lay the mathematical foundations for replacing the standard unit interval with the affine line, for the purposes of applying topological arguments in an algebro-geometrical context.

Friday, April 11, 2014 at 10:15 a.m.–11:45 a.m. Room 5382

Omar Sanchez, McMaster University
On Differential Algebraic, But Not Constrained, Families

We will give a negative answer to the question: Is every finitely generated differential algebraic extension, with no new constants, of ℂ, a constrained extension? We then use this to answer a question on Poisson prime ideals of Poisson algebras. This is joint work with J. Bell, S. Launois, and R. Moosa.

A video recording of this talk is available for viewing here.

Friday, April 11, 2014 at 12:30 p.m. –2:00 p.m. Room 5382

Andrey Minchenko, Weizmann Institute of Science
Central Extensions of Simple Linear Differential Algebraic Groups

We will classify central extensions of simple linear differential algebraic groups. In particular, we will see that every simple linear differential algebraic group over a non-ordinary differential field has a perfect linear differential central extension with an infinite center. An important step in our classification is to show that H2(SL2, Ga) is a free Hom(Ga, Ga)=k[Δ]-module generated by m(m-1)/2 independent elements, where k stands for the ground Δ-field and m= |Δ|.

A video recording of this talk is available for viewing here.

Friday, April 11, 2014 at 3:00 p.m. –6:00 p.m. 
Saturday, April 12, 2014 at 10:00–11:50 a.m. and 3:30–5:50 p.m. 

Special Session on Differential Algebra and Galois Theory, at the AMS-Meeting at Lubbock, TX

A video recording of the Special Session I (Friday afternoon) is available here .

A video recording of the Special Session II (Saturday morning) is available here .

A video recording of the Special Session III (Saturday afternoon) is available here .

Slides of the talks will be available here as they are made available from the authors.

Friday, April 18, 2014, No Seminar due to Spring Break.


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Last updated April 23, 2014