Kolchin Seminar in Differential Algebra
Fall 2019 and Spring 2020
All talks take place at the CUNY Graduate Center, 10:15-11:30 am, in Room 5382 unless something else is specified.
The seminar activities are partially supported by the National Science Foundation.
Talks of the Spring 2019 semester are available here.
Talks of the Fall 2018 semester are available here.
Talks of the Spring 2018 semester are available here.
For earlier seminars, see the old webpage.
September 13, Daniel Robertz, University of Plymouth
Algorithmic Approach to Strong Consistency Analysis of
Finite Difference Approximations to PDE Systems
The most common numerical method for solving partial
differential equations is the finite difference method.
Consistency of a finite difference scheme with a given
PDE is a basic requirement for this method.
Earlier work by V. P. Gerdt and the speaker introduced
the notion of strong consistency that takes into account
the differential ideal and the difference ideal associated
with the PDE system and the approximating difference system,
We present an algorithmic approach to strong consistency for
polynomially nonlinear PDE systems based on a new decomposition
technique for nonlinear partial difference systems that is
analogous to the differential Thomas decomposition. This is
joint work with Vladimir P. Gerdt (JINR, Dubna).
October 11, Yi Zhou, Florida State University
October 18, Omar Leon Sanchez, University of Manchester
Differentially large fields
Recall that a field K is large if it is existentially closed in the field of Laurent series K((t)). Examples of such fields are the complex, the real, and the p-adic numbers. This class of fields has been exploited significantly by F. Pop and others in inverse Galois-theoretic problems. In recent work with Tressl we introduced and explored a differential analogue of largeness, that we conveniently call “differentially large”. I will present some properties of such fields and characterise them using formal Laurent series and to even construct “natural” examples (which ultimately yield examples of DCFs and CODFs... acronyms that will be explained in the talk). Time permitting I will mention some applications to Parameterized PV theory.
November 8, Léo Jimenez, University of Notre Dame
Jonathan Kirby, University of East Anglia
TBA (remote presentation)
December 13, Yi Zhang, University of Texas at Dallas