Dept. of Mathematics & Statistics, McMaster University
1280 Main Street West
Canada L8S 4K1
905-525-9140, ext. 27365
ResearchResearch Area: Model Theory, Differential and Difference Algebra
I am interested in the interaction of geometric stability theory (a branch of model theory) and differential (and difference) algebraic geometry. This includes the study of the geometric Galois theory associated to "logarithmic" differential equations. I am also interested in the study of the model theoretic properties of theories of fields with general types of (Hasse- Schmidt) operators.
"On parameterized differential Galois extensions" (with Joel Nagloo). To appear in the Journal of Pure and Applied Algebra.
"The model companion of differential fields with free operators" (with Rahim Moosa). To appear in the Journal of Symbolic Logic.
On bounds for the effective differential Nullstellensatz" (with Alexey Ovchinnikov). To appear in the Journal of Algebra.
"Effective uniform bounding in partial differential fields" (with James Freitag). To appear in Advances in Mathematics.
"On linear dependence over complete differential algebraic varieties" (with James Freitag and William Simmons). To appear in Communications in Algebra.
"Poisson algebras via model theory and differential algebraic geometry" (with Jason Bell, Stephane Launois and Rahim Moosa). To appear in the Journal of the EMS.
"On the model companion of partial differential fields with an automorphism". To appear in the Israel Journal of Mathematics.
"Relative d-groups and differential Galois theory in several derivations". To appear in Transactions of the AMS.
"Geometric axioms for differentially closed fields with several commuting derivations". Journal of Algebra. Vol. 362, pp.107-116, 2012. (Corrigendum, Vol. 382, pp.332-334, 2012)
"The Clifford-Fourier transform F_0 and monogenic extensions" (with Arnoldo Bezanilla). Advances in Applied Clifford Algebras. Vol. 21, Number 4, pp.757-772, 2010.
"Fundamental Theorem of Calculus" (with Garret Sobczyk). Advances in Applied Clifford Algebras. Vol. 21, Number 1, pp. 221-231, 2010.