Introduction to Higgs Bundles - Lecture 1

Explore the foundations of Higgs bundles in this introductory lecture from the Geometry, Groups and Dynamics (GGD) 2017 program. Delve into complex geometric interpretations, key definitions, and illustrative examples. Examine important propositions, including the Riemann-Hodge Theorem, and learn essential notation. Investigate claims related to Riemann surfaces and explore equivalence concepts. Follow the construction of mathematical objects and tackle exercises to reinforce understanding. Study the development of crucial maps and theorems, including uniqueness and existence proofs. Gain insights into fundamental facts and proof strategies in this field. Conclude with an exploration of Abel's Theorem and participate in a Q&A session to clarify concepts.

Geometry, Groups and Dynamics GGD - 2017
Mini course 2: Introduction to Higgs bundles Lecture - 01
Interpret object in a complex geometric situation
Definition
Example
Proposition
Riemann - Hodge Theorem
Notation
Claim
Riemann surface
Equivalent
Construction of 3
Exercise
Construction of a map
Theorem
Uniqueness
Existence
Facts
Idea of the proof
Theorem Abel
Q&A