Notes
Have a look to some of my notes! Hopefully you might find something useful here.
I'm collecting a list of forgetful facts in topology - though perhaps I am the forgetful one.
I'm also collecting a list of terminology regarding the zoo of monoidal/abelian/tensor/modular/... categories.
Some ongoing notes on Representation Theory.
Knot Theory
Heegaard-Floer homology, based on a lecture series by J. Hom at IAS | PCMI 2019.
Example-driven introduction to Python, based on the course "Using Pyhton for Research" at HarvardX.
A note on the equivalence between the classical Kauffman braket and Khovanov's modification.
Algebraic Topology
Introduction to chromatic homotopy theory, based on a talk by J. Lurie
Lecture notes (English)
These notes were taken during my Master's degree at UU (though some courses took place somewhere else). Use them (at your own risk!) preferably for a reminder - they lack proofs!
Commutative Algebra, Autumn 2018 (VU)
Differential Geometry, Autumn 2018 (UU)
Lie Groups and Algebras, Spring 2018 (UvA)
Topological K-Theory, Spring 2018 (UU)
Algebraic Topology II, Spring 2018 (UU)
Algebraic Topology I, Autumn 2017 (UU)
Poisson Geometry, Autumn 2017 (UU)
Advanced Hamiltonian Mechanics, Autumn 2017 (VU)
Lecture notes (Spanish)
Estos apuntes fueron tomados durante mi carrera de matemáticas en la UEx. Úsalos (bajo tu resposabilidad!) preferiblemente para un repaso - no tienen demostaciones.
Teoría de Números, Primavera 2017 (UEx)
Geometría Riemanniana, Primavera 2017 (UEx).
Analisis Funcional, Primavera 2017 (UEx)
Ecuaciones en Derivadas Parciales, Primavera 2017 (UEx)
Estadística Matemática, Otoño 2016 (UEx)
Topología Algebraica, Otoño 2016 (UEx)
Sistemas Dinámicos, Otoño 2016 (UEx)
Análisis Numérico II, Otoño 2016 (UEx)
Probabilidad, Primavera 2016 (UEx)
Geometría Algebraica, Primavera 2016 (UEx)
Geometría Diferencial II, Primavera 2016 (UEx)
Geometría Diferencial I, Otoño 2015 (UEx)
Teoría de la Medida, Otoño 2015 (UEx)
Análisis Numérico I, Otoño 2015 (UEx)
Ecuaciones Diferenciales, Otoño 2015 (UEx)
Teoría de Galois, Otoño 2015 (UEx)
Topología General, Primavera 2015 (UEx)
Análisis II, Primavera 2015 (UEx)
Geometría II, Primavera 2015 (UEx)
Geometría I, Otoño 2014 (UEx)
Análisis I, Otoño 2014 (UEx)
Programación Lineal, Otoño 2014 (UEx)
Álgebra Conmutativa, Otoño 2014 (UEx)
Recommended notes by other authors
Notes for a Degree in Mathematics, by J.A. Navarro.
A Concise Course in Algebraic Topology, by J.P. May.
Lecture Notes in Algebraic Topology, by J.F. Davis & P. Kirk.
Algebraic Topology, by A. Hatcher. See also his Chapter 5 on Spectral Sequences.
Category Theory in Context, by E. Riehl.
Lectures on the Triangulation Conjecture, by C. Manolescu.
Álgebra Conmutativa Básica, by J.A. Navarro.
Apuntes de Ecuaciones Diferenciales, by R. Faro.
Galois Categories, by A. Cadoret.
A Geometric Introduction to K-theory, by D. Dugger.
On the Classification of Topological Field Theories, by J. Lurie.
Introduction to symbolic computation (SAGE), by J. Verschelde.
Plenty of expository papers by Keith Conrad.
Notes on principal bundles and classifying spaces, by S. Mitchell.
A short introduction to mapping class groups, by G. Massyuyeau.
The category of CGWH spaces, by N.P. Strickland.
The Arf-Kervaire invariant problem in algebraic topology: an introduction, by Hill, Hopkins & Ravenel.
Plenty of lecture notes on homotopy theory by Javier Gutiérrez.
Bordism: old and new, by D. Freed.
Oriented cobordism: calculation and application, by A. Kupers.
Lecture notes on Topology of Manifolds, by J. Francis.
Piecewise linear structures on topological manifolds, by Y. Rudyak.
Milnor's construction of exotic 7-spheres, by R. McEnroe
An introduction to 3-manifolds and their fundamental groups, by S. Frield.
Notes on Lie Algebras, by Kevin McGerty.