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.

Upcoming talks

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, respectively. 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).
Video

October 4, Anand Pillay, University of Notre Dame
TBA

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October 11, Yi Zhou, Florida State University
TBA

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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.

October 25, Fabian Immler, Carnegie Mellon University
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November 1, Carsten Schneider, Johannes Kepler University
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November 8, Léo Jimenez, University of Notre Dame
TBA

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November 15, Jonathan Kirby, University of East Anglia
TBA (remote presentation)

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December 6, Sam Coogan, Georgia Tech
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December 13, Yi Zhang, University of Texas at Dallas
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January 31, Amir Ali Ahmadi, Princeton University
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February 21, Patrick Speissegger, McMaster University
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March 27, Marisa Eisenberg, University of Michigan
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April 3, Gareth Jones, University of Manchester
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