Short expository notes on various mathematical topics

Table of Contents

Short stories about category or homotopy theory

Miscellaneous mathematical short stories

Longer expository articles

A Whirlwind Tour of the World of (∞,1)-categories (PDF).

I am (still planning to finish) writing rough lecture notes for a course I taught on the fundamental groupoid. The section on the van Kampen theorem is done (PDF).

I wrote my minor thesis2 on the iteration of rational maps on the Riemann sphere. It includes fairly complete proofs of Sullivan’s No Wandering Domains theorem and the classification of the periodic Fatou components and is, I hope, fairly light reading —and is also available in PDF.

Artículos expositorios en español


No link needed because the whole story fit into the title!


This an excellent program requirement: a chance to make a fool of yourself in writing by producing an exposition of a topic outside your field of expertise in a limited amount of time. I loved it! All math departments should have this.

Omar Antolín Camarena