TL;DR
This paper introduces modular and quasi-modular forms, exploring their mathematical properties and applications in physics and enumerative geometry, providing foundational knowledge for further research.
Contribution
It presents a comprehensive introduction to modular and quasi-modular forms, emphasizing their connections to physics and enumerative problems, which is a novel synthesis for the field.
Findings
Modular forms related to PSL2Z are characterized.
Quasi-modular forms and their applications are discussed.
Connections between modular forms and physics are explored.
Abstract
We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes are based on a lecture given at the Field's institute during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics.
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