Computational Differential and Difference Algebra and its Applications
Special Session at the 26th International Conference on
Applications of Computer Algebra (July 23-27, 2021, online)
Organizers:
Roberto La Scala (Bari, Italy)
Alexander Levin (Washington D.C., USA)
Daniel Robertz (Plymouth, UK)
This session is devoted to the memory of Vladimir P. Gerdt who made outstanding contributions to the fields of symbolic computation, differential and difference algebra, and applications of computational algebraic methods in physics. He was also an organizer of numerous conferences and sessions on computer algebra and its applications including a number of ACA conferences, a member of the JSC editorial board since its foundation in 1985, and a member of editorial boards of several other research journals.
Schedule (in MATRIS-1, time zone CEST):
Friday, July 23, 2021
18:30 Roberto La Scala (slides)
19:00 Raffaele Vitolo (slides)
19:30 V. V. Bavula
20:00 Alexander Levin (slides)
20:30 Omar Leon Sanchez (slides)
21:00 Carlos E. Arreche (slides)
Sunday, July 25, 2021
18:30 Yunnan Li (slides)
19:00 Richard Gustavson (slides)
19:30 Li Guo (slides)
20:00 Thomas Dreyfus (slides)
20:30 Michael Wibmer (slides)
Talks:
Carlos E. Arreche, Yi Zhang, Mahler residues and telescopers for rational functions
V. V. Bavula, Simplicity criteria for rings of differential operators in arbitrary characteristic
Boris Adamczewski, Thomas Dreyfus, Charlotte Hardouin, Michael Wibmer, Algebraic independence between special functions
Li Guo, Richard Gustavson, Yunnan Li, An algebraic formulation of integral equations
Li Guo, Richard Gustavson, Yunnan Li, Operator Linearity of Volterra Integral Equations
Roberto La Scala, Ciphers and Difference Algebra
Alexander Levin, A New Type of Difference Dimension Polynomials
Li Guo, Yunnan Li, Construction of free differential algebras by extending Gröbner-Shirshov bases
Omar Leon Sanchez, A division algorithm for Poisson algebras of graded Lie algebras
Raffaele Vitolo, Weakly nonlocal Poisson brackets: algorithms and symbolic computation
Michael Wibmer, On the computation of the dimension of systems of algebraic difference equations
Objectives:
Algebraic differential and difference equations and systems of such equations arise in many areas of mathematics, natural sciences and engineering. One can say that difference equations relate to differential equations as discrete mathematics relates to continuous mathematics. Differential and difference computer algebra concerns the study of systems of differential and difference equations in a constructive way that extends methods and algorithms of commutative algebra and algebraic geometry. The main goal of the session is to consider actual computational problems in differential and difference algebra to explore new constructive ideas and approaches oriented toward various applications.
Topics of the session include, but are not limited to:
Systems of Differential, Difference and Difference-Differential Algebraic Equations
Differential and Difference Gröbner (Standard) and Involutive Bases
Differential and Difference Characteristic Sets
Triangular Decompositions of Differential and Difference Systems
Differential and Difference Elimination
Algorithmic Generation of Finite Difference Approximations to PDEs
Consistency and Stability Analysis of Finite Difference Approximations
Dimension Characteristics of Differential and Difference Algebraic Structures
Software Packages for Differential and Difference Algebra
Difference Equations over Finite Fields and their Applications
Submissions:
If you are interested in giving a presentation at this session, please email an abstract to one of the organizers (including both the LaTeX source and a compiled PDF version) by May 31, 2021. We suggest that abstracts will be 1-2 pages, with some references. Detailed information about the conference and a LaTeX template for abstracts will be posted at the ACA 2021 web page.