Notes and other resources

NOTES:

• How to give a good math talk

A long list of concrete tips I put together on (my subjective views on) how to give a good talk. These were the main notes for the graduate professional skills class I taught in 2022 at Johns Hopkins. 

• An introduction to locally finitely presentable categories

Notes of my attempt to understand the concept. Contains an introduction, examples, and different characterizations.

• Loop spaces and Operads (written in preparation for my A-Exam)

This document serves as an introduction to operads and their algebras, along with basic examples. We review the theory necessary to show May’s recognition principle for loop spaces, and then, following Berger and Moerdijk, present a model structure on the category of operads which allows us to show that every loop space can be rectified to a topological monoid.

SOME FUN TALKS I'VE GIVEN (not updated anymore):

• Here you can find a short video I made when I was a PhD student going on the job market. I summarize my research interests and the projects I'd completed as of October 2020 .

• An introduction to algebraic K-theory

Notes for my (chalkboard) presentation at Cornell's Topology Festival.

• Detecting algebraic categories with an internal Hom

Notes for my (chalkboard) presentation at the International Category Theory Conference 2017 as part of the Kan Extension Seminar II.

• Category theory in action

Notes for my (whiteboard) presentation at the 43rd Annual New York Regional Graduate Mathematics Conference, a general audience expository talk showing a case where category theory brings something new to the table.

• Applying category theory to real life (for real)

Slides for my talk at Cornell's Olivetti Club, about how we can use category theory to model chemical reaction networks.

• Infinity-cosmoi and their homotopy 2-categories

Notes for my presentation at the 2018 MIT Talbot Workshop: Model intependent theory of infinity-categories.

OTHER THINGS:

• Algebra valued functors in general and tensor products in particular 

A guest post on the n-Category Cafe, written as part of my participation in the Kan Extension Seminar II.

• Dynamical systems and their steady states

A guest post on the n-Category Cafe, written as part of my participation in the Applied Category Theory School.

• Infinity and Paradoxes

Problem sets + teaching notes written for the session I led of Cornell's Math Explorer's Club -- a two day, fun activity that introduces new math concepts to high school students.