Symbolic computation through the holonomic looking-glass

Speaker:
Date: 28/06/2021
Time: 09:00 - 09:50

Location: online via Zoom

ABSTRACT: Symbolic computation is an evolving research area at the interplay between mathematics and computer science, which has found applications in nearly all fields of science. A branch of symbolic computation that has established particularly many such connections, is the symbolic evaluation of integrals and sums. The holonomic systems approach comprises several methods for such tasks, that are based on implicit descriptions of the objects in terms of linear differential equations or recurrences. In this talk I will present some recent developments in this area and discuss several of its applications, such as: (1) the computation of diagonals of rational functions and the elimination of some potential counter-examples to Christol's conjecture about globally bounded series, (2) a systematic study of binomial determinants counting rhombus tilings via the Lindstroem-Gessel-Viennot theory of non-intersecting lattice paths, (3) ongoing work on the enumeration of off-diagonally symmetric alternating sign matrices of odd order.