The ACSV Project
Analytic Combinatorics in Several Variables (ACSV) is an emerging field of combinatorics that develops tools for the asymptotic analysis of multivariate generating functions and discrete structures with parameters. ACSV is inherently interdisciplinary, adapting and extending results in complex analysis in one and several variables, the asymptotics of integrals, topology, algebraic geometry, and symbolic computation. These results are explicit enough to be implemented in computer algebra software, and powerful enough to cover a vast range of applications from mathematics, computer science, and the natural sciences.
This website collects updating lists of references forming the core theory of ACSV, applications of ACSV, and software for ACSV, and hosts the webpage for the textbook Analytic Combinatorics in Several Variables (2nd Edition) by R. Pemantle, M. C. Wilson, and S. Melczer.
Events related to the project
The American Institute of Mathematics (AIM) held a workshop Analytic Combinatorics in Several Variables in April 2022.
The AMS Joint Math Meeting had a Special Session on Combinatorial Applications of Computational Geometry and Algebraic Topology (based on research from the MRC) in April 2022.
There was an AMS Mathematics Research Community (MRC) Combinatorial Applications of Computational Topology and Algebraic Geometry on ACSV, including a workshop in the summer of 2021
Contributors to the project
Since its beginnings in early 2000s papers by Pemantle and Wilson, there have been many authors contributing to the theory of ACSV, including Yuliy Baryshnikov, Timothy DeVries, Stephen Gillen, Torin Greenwood, Joris van der Hoeven, Manuel Lladser, Stephen Melczer, Marni Mishna, Robin Pemantle, Alexander Raichev, Bruno Salvy, and Mark C. Wilson.
See the publication list for more information.