Linear Recurrent Relations, Linear ODEs and Generalized Pieri's Formulas

• Grant number: 15/04513-8
• Support Opportunities: Scholarships abroad - Research
• Effective date (Start): September 01, 2015
• Effective date (End): February 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Parham Salehyan
• Grantee: Parham Salehyan
• Host Investigator: Letterio Gatto
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Research place: Politecnico di Torino, Italy

Abstract

Within the last twenty years, Wronskians have been revealed to be mathematical objects of very much great interest, in spite of their seemingly innocent and natural definition. The main reason is that they are a common tool to solve and/or to interpret classes of problems in many different areas of mathematics, going from the elementary theory of (systems of) ordinary differential equations (ODEs in the following) to the enumerative geometry of curves, to the study of the intersection theory on the moduli space of curves, from the real and complex Schubert calculus to the theory of symmetric functions. The main purpose of the present project is toestablishes the several bridges existing among these different disciplines within an interdisciplinary framework, in order to obtain new mathematical results.