Differential Square-Zero Extensions and Picard-Vessiot Theory (05/06/2017, AMS Special Session)

Ax-Schanuel and Strong Minimality (10/13/2017)

Continuous Dynamic Systems and Computation (03/12/2010)

The Wild Behavior of Truncation in Hahn Fields (05/05/2017)

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)

Rooks, Recurrences and Residues (10/19/2012), Joint work with Manuel Kauers (RISC) and Michael F. Singer (NCSU)

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)

A brief introduction to schemes  (12/16/2005)

Evaluation of the Strength of Systems of Partial Differential and Difference Equations via Differential and Difference Dimension Polynomials  (02/03/2012)

Picard-Vessiot extensions over number fields  (Diplomarbeit)

Indecomposability  (11/16/2012)
A Note on Canonical Bases in Partial Differential Fields (11/16/2012)

Differential and Difference Chow Form, Sparse Resultant, and Toric Variety (10/02/2015)
Characteristic Set and Resolvent for Difference Polynomial Systems  (5/6/2006)

Integro-Differential Algebras on Combinatorial Species (09/11/2015)

A bound for the order of derivatives in the Rosenfeld-Gröbner Algorithm  (3/18/2006)

Order Bounds for the Rosenfeld-Gröbner Algorithm  (02/05/2016)

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)

Differential Brauer Group  (05/06/2017 AMS Special Session)
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)

Rational and algebraic invariants of a group action  (12/16/2006)
Symbolic computation for overdetermined systems of nonlinear differential equations  (12/15/2006)

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)

On the Nature of the Generating Series of Random Walks in the Quarter Plane  (05/07/2017 AMS Special Session)
A Density Theorem for Parameterized Differential Galois Theory  (01/31/2014)

Representations of an Algebra of Quantum Differential Operators  (10/04/2016)
Generic Base Algebras and Universal Comodule Algebras for Some Finite Dimensional Hopf Algebras (12/13/2013)
On the Quantum Torus  (04/28/2012)

The infinite Quaternion group Q 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)

Algebraic Theory of Integrable Systems (05/16/2014)

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)

Runge-Kutta Methods From an Algebraic Point of View (05/06/2016)

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)

Analytic Theory of Difference Equations with Rational Coefficients (03/01/2013)

Dimension Quasi-polynomials of Inversive Difference Field Extensions with Weighted Translations  (05/07/2017 AMS Special Session) Differential Dimension Polynomials  (10/22/2005)

Sparse Differential Resultant for Laurent Differential Polynomials  (11/11/11)
Differential Chow Form   (11/18/11)

Lie Pseudogroups and Differential Galois Theory  (Posted 04/20/2010)

The Logical Complexity of Schanuel's Conjecture and Exponential Derivations  (05/06/2017, AMS Special Session)
Embedding Differential Algebraic Groups in Algebraic Groups  (05/01/2009, expanded version)
Embedding Differential Algebraic Groups in Algebraic Groups  (02/20/2009)

Difference Algebraic Geometry in/for Hrushovski's Frobenius Paper  (10/04/2013)

A generalization of Rosenfeld's Lemma  (10/22/2005)
Coherence and prime decomposition  (10/21/2005)

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)

Algebras of Differential Invariants (02/23/2018))

Standard Differential Bases  (4/7/2006)

Jacobi Algebras, in-between Poisson, Differential, and Lie Algebras  (05/15/2015)

Bezout-type Theorems for Differential Fields  (03/20/2015)

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)

Sparse Resultant Forumulas for Differential Polynomials  (7/7/2014)

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)

D-fields as a Common Formalism for Difference and Differential Algebra (10/18/2013)

Algebraic Group Representation, and Related Topics (11/6/2009)

Identifiability of Linear Compartment Models: The Singular Locus (03/02/2018)

Nonstandard Methods for Bounds in Differential Polynomial Rings  (05/06/2017 Reprint, J. Alg. 2012)
Mining Effective Information from Nonconstructive Proofs in Differential Algebra  (05/06/2017 AMS Special Session)
Identifying Complete Differential Varieties  (03/09/2012)
A Differential Algebra Sampler  (04/24/2015)

Differential Groups and the Gamma Function  (12/12/2008)
Arithmetic Finite Automata, Automatic Sets, and Difference Equations  (10/03/2016)

What Initial Values Guarantee Existence and Uniqueness in Algebraic Differential Systems? (03/16/2018)
Rota-Baxter Type Operators, Rewriting Systems, and Gröbner-Shirshov Bases, Part II (12/09/2016)
Rota-Baxter Type Operators, Rewriting Systems, and Gröbner-Shirshov Bases, Part I (12/02/2016)
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)

On Certain Towers of Extensions by Antiderivatives (09/26/2008)

Height functions, Part 2  (2/10/2006)
Height functions, Part 1  (2/3/2006)

Computing Algebraic and Rational General Solutions of First Order Algebraic ODEs  (4/1/2006)

Constructive Bounds from Ultraproducts and Noetherianity (2/19/2016)

Group Foliation of Finite Difference Equations Using Equivariant Moving Frames (03/23/2018)

Difference Algebraic Group (slides)  (03/06/15)

Galois Theory of Algorithms  (9/3/2010)