This talk surveys some recent advances, and software, in the field of analytic combinatorics. First, we examine how rigorous numeric analytic continuation of D-finite functions can be combined with a singularity analysis of generating functions to automatically give asymptotics — with explicit error bounds – for P-recursive sequences (satisfying linear recurrence relations with polynomial coefficients). This work, joint with Marc Mezzarobba and Ruiwen Dong, was recently used by Melczer and Mezzarobba to automatically prove solution uniqueness of the genus one « Canham model » predicting the shape of biomembranes like blood cells. Next, we exhibit the first rigorous software for the asymptotics of multivariate sequences with rational generating functions, using tools from the theory of analytic combinatorics in several variables. Such multivariate tools provide a promising approach to answering certain open problems about the decidability of P-recursive sequences. All software and source code is freely available on public repositories — and can even be run in the browser with no installation — and many examples will be given.
- This event has passed.
24 mars Vendredi
Stephen Melczer (Waterloo): Uniqueness of Biomembranes and Analytic Combinatorics in Several Variables
24 mars 2023, 13:30 - 24 mars 2023, 14:30
Date: mars 24
Time: 1:30 pm - 2:30 pm
Venue Name: PK-4323