SS4 - Computational Differential and Difference Algebra and Their Applications
Objectives:
Algebraic differential and difference equations and systems of such equations arise in many areas of mathematics and in a wide range of subject areas including physics, biology, chemistry, economics, and engineering. 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 discuss recent developments in computational methods of differential and difference algebra, as well as to explore new ideas and approaches oriented toward various applications of these methods.
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
- Difference Equations over Finite Fields and Their Applications
- Software Packages for Differential and Difference Algebra
- Applications of Differential and Difference Algebra in the Sciences
Session organizers
Talks
| Jing Yang - Subresultants of Several Ore Polynomials |
| Raffaele Vitolo - Reduce package for Differential Operators in Mathematical Physics and Theoretical PhysicsA |
| Bo Huang - Integrability and Linearizability of a Family of Three-Dimensional Polynomial Systems |
| Alexander Levin - Gröbner type Bases with Respect to the Effective Order and Bivariate Dimension Polynomials of Difference Modules |
| Roberto La Scala - Stream cipher over Finite Fields: A Difference Algebra Approach |
| Thierry Combot - Symbolic integration on a planar differential foliation |
| Volodymyr Bavula - Affirmative answer to the Question of Leroy and Matczuk on injectivity of endomorphisms of semiprime left Noetherian rings with large images |