Diffeological Generalized Formal Series: An Overview
Jean-Pierre Magnot
TL;DR
This paper reviews recent advances in the theory of generalized formal series within a diffeological geometric framework, aiming to enhance understanding of infinite-dimensional phenomena in mathematical physics and related fields.
Contribution
It introduces a diffeological approach to generalized formal series, providing new tools for infinite-dimensional analysis and applications in tensor structures and categorical gradings.
Findings
Development of a diffeological framework for formal series
Application to tensor structures and categorical gradings
Potential for new insights in mathematical physics
Abstract
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in mathematical physics, particularly in contexts where standard atlases and charts are insufficient. Applications to tensor structures and categorical gradings are discussed, and emerging applications are mentioned.
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