Summary

The MINIMOD project investigates contemporary problems in mathematical analysis, the theory of inequalities, and geometry through three interconnected work packages. Work Package 1 (WP1) focuses on developing new generalizations of classical inequalities using interpolation methods, with particular emphasis on the Lidstone interpolation polynomial and Green's functions. The goal is to derive new functional expressions applicable to broader classes of functions and measure spaces. WP2 introduces modern approaches in convex analysis by generalizing the Jensen–McShane inequality and applying these results to special sequences, such as the Fibonacci sequence. Specifically, new variants of the Diaz–Metcalf and Petrović inequalities for functions of two variables are being developed. WP3 focuses on geometric structures—particularly Cayley–Klein planes—and their connection to modular forms.

The project incorporates computational modeling tools and a digital database of results accessible in accordance with open science principles. Collaboration with other universities and the IT sector is planned, particularly in the field of cybersecurity. The project contributes to theoretical advancement, digital transformation, and the education of early-career researchers.