Leading edge research in many pure and applied disciplines requires the knowledge of the classical theory of differential algebra together with a modern symbolic computation approach. This approach is relevant in the treatment of differential equations by means of symbolic computation, which today is one of the leading lines of research in computational algebra, and constitutes the framework of this project. The main goal of this project is to investigate new techniques in differential and noncommutative algebra to devolop spectral Pircard-Vessiot Theory, applied to the study of integrable hierarchies and related problems.

GOALS

• Goal A: Spectral Picard-Vessiot Theory 

• Goal B: Integrable hierarchies and recursion operators 

• Goal C: Development of differential elimination tools and implementation

ACTIVITIES AND RESOURCES

• Publications

• Conferences

• Software

• Meetings

• Computational Resources (ADAI computer)

RESEARCH TEAM

• Sonia L. Rueda. Universidad Politécnica de Madrid (IP)

• María Ángeles Zurro. Universidad Autónoma de Madrid (IP)

• Rafael Hernández Heredero. Universidad Politécnica de Madrid

• Rafael Delgado . Universidad Politécnica de Madrid

• Antonio Jiménez Pástor. Universidad Politécnica de Madrid 

FUNDING

• September 2022 to August 2025 , grant PID2021-124473NB-I00,  from the Spanish MCIN/AEI /10.13039/501100011033 and by FEDER, UE.

• UPM. Programa Propio de I+D+i 2022, Convocatoria de ayudas para la cofinanciación de infraestructuras de I+D+i de la UPM.