An online session of the Algebra and Logic Seminar will be held on March 11, 2022 (Friday) at 2:00 pm (UTC+2).

A talk on:

Multi-summation in difference rings and applications

will be delivered by Carsten Schneider (Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria).

Abstract. Symbolic summation in difference fields started with Karr’s summation algorithm (1981) which can be considered as the discrete version of Risch’s indefinite integration algorithm in differential fields. In the last 20 years this approach has been generalized and enhanced to a constructive summation theory of difference rings.
In general, one can represent algorithmically any expression in terms of indefinite nested sums defined over hypergeometric products in such rings. As a crucial by-product one obtains optimal representations where the arising sums and products are algebraically independent among each other. In particular, difference ring algorithms have been developed that enable one to simplify certain classes of definite multi-sums to expressions in terms of indefinite nested sums defined over hypergeometric products.
Within this machinery one can apply Zeilberger’s creative telescoping paradigm in order to compute linear recurrences for definite multi-sums and one can find all solutions of linear recurrences that can be expressed in terms of indefinite nested sums and products. In this talk we will present this algorithmic difference ring theory for symbolic summation implemented in the summation package Sigma and will illustrate its potential by non-trivial applications coming, e.g., from combinatorics and elementary particle physics.

The seminar will be held via Zoom and anyone can join at:

https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09

Topic: Онлайн семинар на секция “Алгебра и логика”
Time: Mar 11, 2022 02:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647

Algebra and Logic Department, IMI-BAS
http://www.math.bas.bg/algebra/seminarAiL/
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