Kolchin Seminar in Differential Algebra
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We will post links to slides, papers, lecture notes on this page as they become available.
Click here for papers posted before 2005.

  • Manuel Campagnolo, DM/ISA, Technical University of Lisbon
       and SQIG/Instituto de Telecomunicações, Lisbon
    Continuous Dynamic Systems and Computation (03/12/2010)
  • Phyllis J. Cassidy, Smith College and CCNY
    Examples as Avatars  (11/18/2011)
    Differentially closed fields  (11/16/2007)
    The logarithmic derivative on the elliptic curve  (11/16/2007)
    Differential Algebraic Geometry, Part 5  (11/9/2007)
    Differential Algebraic Geometry, Part 4  (11/2/2007)
    Differential Algebraic Geometry, Part 3  (10/26/2007)
    Differential Algebraic Geometry, Part 2  (10/19/2007)
    Differential Algebraic Geometry, Part 1  (10/5/2007)
    The Galois group of a Picard-Vessiot extension, Part 3  (12/8/2006)
    The Galois group of a Picard-Vessiot extension, Part 2  (12/1/2006)
    The Galois group of a Picard-Vessiot extension, Part 1  (11/17/2006)
    Introduction to differential algebraic geometry and differential algebraic groups  (Fall, 2005)
  • Shaoshi Chen, North Carolina State University
    Rooks, Recurrences and Residues (10/19/2012), Joint work with Manuel Kauers (RISC) and Michael F. Singer (NCSU)
  • Richard Churchill, Hunter College and The Graduate Center
    Kolchin's Proof that Differential Galois Groups are Algebraic (09/05/2014)
    Transcendentals, The Goldbach Conjecture, and the Twin Prime Conjecture (08/30/2013; updated 09/01/2013)
    A Set-Theoretical Approach to Model Theory (02/08/2013; revised 04/04/2013)
    A Geometric Approach to Classical Galois Theory (08/27/2010). Corrected Aug 28, 2010.
    Differential arithmetic (02/01/08) Corrected May 13, 2008
    A brief introduction to algebraic geometry  (11/25/2007)
    A geometric approach to linear ordinary differential equations  (10/13/2006)
    Introduction to the Galois Theory of Linear Ordinary Differential Equations  (9/8/2006)
    Liouville's theorem on integration in terms of elementary functions  (9/1/2006)
  • Adam Crock, Graduate Center of CUNY
    A brief introduction to schemes  (12/16/2005)
  • Christian Dönch, RISC, Johannes Kepler University, Linz
    Evaluation of the Strength of Systems of Partial Differential and Difference Equations via Differential and Difference Dimension Polynomials  (02/03/2012)
  • Tobias Dyckerhoff, University of Pennsylvania and Universitat Heidelberg
    Picard-Vessiot extensions over number fields  (Diplomarbeit)
  • James Freitag, University of California at Berkeley
    Indecomposability  (11/16/2012)
    A Note on Canonical Bases in Partial Differential Fields (11/16/2012)
  • Xiao-Shan Gao, Institute of Systems Science, Chinese Academy of Sciences
    Differential and Difference Chow Form, Sparse Resultant, and Toric Variety (10/02/2015)
    Characteristic Set and Resolvent for Difference Polynomial Systems  (5/6/2006)
  • Xing GAO, Lanzhou University, China
    Integro-Differential Algebras on Combinatorial Species (09/11/2015)
  • Oleg Golubitsky, Queen's University, Kingston, Ontario
    A bound for the order of derivatives in the Rosenfeld-Gröbner Algorithm  (3/18/2006)
  • Richard Gustavson, Graduate Center
    Order Bounds for the Rosenfeld-Gröbner Algorithm  (02/05/2016)
  • Li Guo, Rutgers University at Newark
    Rota-Baxter Operators on Polynomial Algebras, Integration, and Averaging 0perators;  (10/24/2014; joint work with Markus Rosenkranz and Shanghua Zheng)
    Free Integral Differential Algebras;  (04/25/2014; joint work with G. Regensburger, M. Rosenkranz, X. Gao, and S. Zheng)
    On Integro-Differential Algebras  (05/13/2013; joint work with G. Regensburger and M. Rosenkranz)
    Differential Type Operators, Rewriting Systems and Gröbner-Shirshov Bases  (04/27/12)
    Classification of Rota-Baxter type operators  (04/24/2009; joint work with W. Sit and R. Zhang)
    Introduction to Rota-Baxter algebras  (02/15/08)
  • Raymond Hoobler, City College and Graduate Center, CUNY
    Rethinking Picard-Vessiot Theory  (09/27/2013)
    Cohomology and Differential Schemes  (10/21/2011)
    The Differential Brauer Group (revised version)  (12/11/2009)
    FPQC Descent and Grothendieck Topologies in a Differential Setting (fourth version)  (12/04/2009)
    Differential Spectrum and Other Matters  (03/20/2009)
  • Evelyne Hubert, INRIA, Sophia Antipolis, France
    Rational and algebraic invariants of a group action  (12/16/2006)
    Symbolic computation for overdetermined systems of nonlinear differential equations  (12/15/2006)
  • Miodrag Cristian Iovanov, University of Southern California and Rutgers University at New Brunswick
    Finite Tensor Categories and a Certain Class of Frobenius Algebras  (04/30/2010)
    Why Coalgebras? ---- Frobenius Algebras, Hopf Algebras and Compact Groups via Co-Representation Theory, with Applications  (04/23/2010)
  • Thomas Drefus, Institute of Mathematics of Jussieu
    A Density Theorem for Parameterized Differential Galois Theory  (01/31/2014)
  • Uma Iyer, Bronx Community College, CUNY
    On the Quantum Torus  (04/28/2012)
    Generic Base Algebras and Universal Comodule Algebras for Some Finite Dimensional Hopf Algebras (12/13/2013)
  • Lourdes Juan, Texas Tech University
    The infinite Quaternion group Q\infty and the Airy equation  (5/7/2006)
    On the structure of Picard-Vessiot extensions  (5/6/2006),  see also the web site
    Torsors and Galois cohomology  (5/5/2006)
    Generic Picard-Vessiot extensions for connected by finite groups  (10/22/2005)
  • Victor Kac, Massachusetts Institute of Technology
    Algebraic Theory of Integrable Systems (05/16/2014)
  • William Keigher, Rutgers University at Newark
    Interlacing of Hurwitz Series (12/04/2015)
    Category Theory Meets the First Fundamental Theorem of Calculus (02/20/2015)
    Partitioned Differential Quasifields, I and II (03/27/2009 and 04/03/2009)
  • Jerald Kovacic, CCNY
    Strongly normal extensions (1/25/2008)
    Differential schemes (11/30/2007)
    Existence of a Picard-Vessiot extension (10/27/2006)
    Differential schemes (12/17/2005)
    Picard-Vessiot theory, algebraic groups and group schemes  (Fall, 2005)
    An algorithm for solving second order linear homogeneous differential equations  (9/23/2005)
    An algorithm for solving second order linear homogeneous differential equations  (scan)
  • Igor Krichever, Columbia University
    Analytic Theory of Difference Equations with Rational Coefficients (03/01/2013)
  • Alexander Levin, Catholic University of America
    Differential Dimension Polynomials  (10/22/2005)
  • Wei Li, KLMM, Chinese Academy of Sciences, Beijing
    Sparse Differential Resultant for Laurent Differential Polynomials  (11/11/11)
    Differential Chow Form   (11/18/11)
  • Bernard Malgrange, Université Joseph Fourier, Grenoble, France
    Lie Pseudogroups and Differential Galois Theory  (Posted 04/20/2010)
  • David Marker, University of Illinois at Chicago
    Embedding Differential Algebraic Groups in Algebraic Groups  (05/01/2009, expanded version)
    Embedding Differential Algebraic Groups in Algebraic Groups  (02/20/2009)
  • Alice Medvedev, The City College of The City University of New York
    Difference Algebraic Geometry in/for Hrushovski's Frobenius Paper  (10/04/2013)
  • Sally Morrison, Bucknell University
    A generalization of Rosenfeld's Lemma  (10/22/2005)
    Coherence and prime decomposition  (10/21/2005)
  • John Nahay, Bioenergia America, LLC, Princeton, NJ
    Entropy: Why Doing Nothing at all is Better than Doing Anything (12/14/2012; last revised 03/01/2013)
    The Wall of Complexity: Summations Over Partitions of Integers (10/12/2012)
    Joint Differential Resolvents for Pseudo-Polynomials  (03/01/2008)
  • Alexey Ovchinnikov, Queens College, CUNY
  • Eugeny Pankratiev, Moscow State University
       A. I. Zobnin, Moscow State University
    Standard Differential Bases  (4/7/2006)
  • Laurent Poinsot, Computer Science Laboratory of Paris-North University (LIPN) and French Air Force Academy (CReA)
    Jacobi Algebras, in-between Poisson, Differential, and Lie Algebras  (05/15/2015)
  • Wai-yan Pong, California State University Dominguez Hills
    Bezout-type Theorems for Differential Fields  (03/20/2015)
  • Markus Rosenkranz, University of Kent at Canterbury, UK
    Integro-Differential Polynomials and Free Integro-Differential Algebras  (7/7/2014)
    A Differential Algebra Approach to Linear Boundary Problems  (7/7/2014)
    A Noncommutative Mikusinski Calculus for Linear Boundary Problems  (7/8/2014)
    Software for Symbolic Boundary Problems and Applications in Actuarial Mathematics  (7/8/2014)
    Singular Boundary Problems and Generalized Green's Operators  (7/8/2014)
  • Sonia Luisa Rueda Perez, Universidad Politenica de Madrid
    Sparse Resultant Forumulas for Differential Polynomials  (7/7/2014)
  • Camilo Sanabria, Graduate Center, CUNY
    Symmetries of meromorphic connections over Riemann Surfaces  (02/13/2009 and 02/27/2009)
    Entrée to Malgrange ideas: General Involutivity Theorem, III, IV (10/17/2008; 10/24/2008)
    Entrée to Malgrange ideas: General Involutivity Theorem, I, II  (10/03/2008; 10/10/2008)
    Hors d'oeuvre to Malgrange ideas: Jet Bundles, II (09/12/2008)
    Hors d'oeuvre to Malgrange ideas: Jet Bundles, I (09/05/2008)
  • Thomas Scanlon, University of California at Berkeley
    D-fields as a Common Formalism for Difference and Differential Algebra (10/18/2013)
  • Leonard Scott, University of Virginia
    Algebraic Group Representation, and Related Topics (11/6/2009)
  • William Simmons, University of Pennsylvania
    Identifying Complete Differential Varieties  (03/09/2012)
    A Differential Algebra Sampler  (04/24/2015)
  • Michael F. Singer, North Carolina State University
    Differential Groups and the Gamma Function  (12/12/2008)
  • William Sit, CCNY
    Revisiting Term-Rewriting in Algebra (02/13/2015)
    Basics of Dimension in Differential Algebra (02/22/2013)
    Anomaly of Intersections in Differential Algebra (02/10/2012)
    Differential Algebraic Subgroups of SL(2) (11/19/2010 and 12/17/2010)
    Algebraic Constraints on Initial Values of Differential Equations (05/08/2009, Joint work with F. Leon Pritchard)
    Enumeration of Rota-Baxter and differential Rota-Baxter words  (02/29/2008 and 03/07/2007, joint work with Li Guo)
    Computations and some open problems  (4/28/2006)
    Introduction to computational differential algebra, I & II  (Fall 2005)
  • Varadharaj Ravi Srinivasan, University of Oklahoma
    On Certain Towers of Extensions by Antiderivatives (09/26/2008)
  • Michael Tepper, The Graduate Center
    Height functions, Part 2  (2/10/2006)
    Height functions, Part 1  (2/3/2006)
  • Michael Wibmer, RWTH Aachen University, Germany
    Difference Algebraic Group (slides)  (03/06/15)
  • Noson Yanosky, The Graduate Center and Brooklyn College
    Galois Theory of Algorithms  (9/3/2010)

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    Last updated February 5, 2016