Summary

New mathematical structures and inequalities: from interpolation techniques to modular forms

The MINIMOD project is focused on the development of new mathematical structures and inequalities through three work packages. In RP1, generalizations of Hardy's and Jensen's inequalities are investigated using interpolation polynomials and Green's functions, which expands the boundaries of classical functional analysis. RP2 brings innovative generalizations of the Jensen–McShane inequality and their application to special sequences such as Fibonacci, along with the development of Diaz–Metcalf and Petrović type variants. In RP3, the focus is on geometric structures, especially Cayley–Klein projective planes, and their connection with modular forms and number theory.