ICMS 2020 Session: Algebraic geometry through numerical computation

Speakers:

Click here for titles and abstracts

Daniele Agostini
Jose Rodriguez
Francesca Bianchi
Michael Burr
Netan Dogra
Jon Hauenstein
Nicolas Mascot
Maggie Regan
Frank Sottile
Simon Telen

Organizers:

Taylor Brysiewicz, tbrysiewicz@math.tamu.edu
Texas A&M University

Emre Can Sertöz, emresertoz@gmail.com
Max Planck Institute MiS

Date and place:

13-17 July 2020, Braunschweig/Germany
See also the main website for ICMS 2020

Abstract:

The range of applicability of numerical methods within algebraic geometry has been rapidly expanding over the past years. This session will concentrate on problems in the frontiers of algebraic geometry which are solved by (complex or p-adic) numerical computations.

Although developments in numerical methods themselves are frequently disseminated in mathematical forums, we shift the focus here and put the emphasis on applications of these methods to algebraic geometry. This session intends to demonstrate the power of numerical computation to algebraic geometers while promoting the work of geometers who develop algorithms and software for numerical computation.

Topics (including, but not limited to):

Monodromy computations
Evaluating and using theta functions in geometry
Numerical methods in Hodge theory
Periods of Riemann surfaces
Pursuit of rigor in numerical polynomial solving
Numerical integration of differential equations arising from geometry
Applications of p-adic numerical methods in algebraic geometry, e.g. to computation of zeta functions
Singularity analysis using floating point arithmetic

Publications

  • A short abstract will appear here and on the conference web page as soon as accepted.
  • An extended abstract may be submitted for the conference proceedings that will be distributed during the meeting.