Executive Summary : | This research project aims to study the relationship between the geometry of minimal surfaces in R³ and certain Euler-Ramanujan’s type identities. This project will be interdisciplinary, connecting two seemingly different areas of Mathematics: Number Theory and Differential Geometry. In the past, we have obtained some new non-trivial identities in the context of maximal surfaces (which are analogues of minimal surfaces in L³). However, what we have done till now is just one instance of such a relationship. In this project, we will explore such connections between minimal surfaces and Euler Ramanujan’s type identities. In fact, these identities are immediate consequences of a more general theorem ``Weierstrass Factorization theorem'' in complex analysis. So it will be interesting to explore the possibility of applying this factorization theorem in a similar way to construct new non-trivial complex identities. More precisely, the main objective of this project is to understand the geometry and symmetries of minimal surfaces by connecting them to some special number theoretic identities coming from the Weierstrass factorization theorem. |