Introduction to computer-algebraic analysis

Luogo:  Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
Ore 9:00

• Relatore: Viktor Levandovskyy (RWTH Aachen University)

Abstract:
Algebraic Analysis has been coined by the Japanese group led by Mikio Sato in the 1950's
In recent years many constructions of Algebraic Analysis have been approached from the computer-algebraic point of view, with algorithms and their implementations. Extension of such an interaction from linear differential operators to linear difference, q-difference and q-differential operators (to name a few) we call Computer-Algebraic Analysis. The major object of study are systems of linear functional equations, their properties, solutions (including those in terms of generalized functions) and behaviour. Modern techniques of the ring theory, such as Gel'fand-Kirillov dimension and Ore localization as well as methods of homological algebra such as the equidimensional filtration have been recently turned into algorithms with the help of computer algebra, where  noncommutative Groebner bases play a prominent role. We will show the merits of these emerged techniques and discuss their applicability to concrete problems with the help of available implementations.

Referente: Massimiliano Sala