Available here (Spanish with English Preface)
Note: Although the main text is in Spanish, I have included an English preface containing a translation of the introduction and a guide to the chapters.
My bachelor's thesis is a monograph on nuclear C*-algebras. A C*-algebra is nuclear if it has a unique tensor product with any C*-algebra. The Choi-Effros-Kirchberg Theorem proves this extrinsic definition equivalent to the CPAP (approximation by finite-dimensional algebras via completely positive maps).
This text builds the theory of tensor products and completely positive approximations, offering a self-contained exposition that culminates in a detailed proof of the Choi-Effros-Kirchberg Theorem.
Ongoing lecture notes based on Gregor Weingart’s course on Index Theory, aiming for a proof of the Atiyah-Singer Index Theorem. The draft covers complex manifolds, differential operators, formal adjoints and Clifford algebras.
Note: This is a work in progress and may contain typos.