Talks at Pitt ACOG seminar

Earlier today, I gave two talks at the Pitt Algebra, Combinatorics and Geometry seminar. The first was about my research, and the second was about the book. Their titles and abstracts are below.

Talk #1 title: Algebraic structures from dependent type theory

Abstract: There are many different notions of ‘model’ of dependent type theory, with each notion allowing us to view it in a different way. In recent work with Steve Awodey, we used the notion of a natural model to view dependent type theory through the lens of polynomial functors—this allowed us to identify a surprising monoid-like structure in the syntax of dependent type theory. This talk will be a high-level overview of our results and the ideas behind the proofs; I will assume basic knowledge of category theory but no knowledge of dependent type theory.

Talk #2 title: An infinite descent into pure mathematics

Abstract: A few years ago, I wrote a set of lecture notes for a course I was teaching over the summer. Various factors led to this evolving, almost by accident, into a fully fledged textbook. In this talk, I will discuss my experience of writing a textbook alongside doing my PhD research, with emphasis on the research-based pedagogical principles underlying its design.

Slides: available here.

Talk about formalisation at the GSS

Yesterday, I gave a talk at the CMU Graduate Student Seminar entitled Formalisation or: How I Learned to Stop Worrying and Love the Computer.

Abstract: What distinguishes mathematics from the empirical sciences is that we prove stuff with complete certainty. Ha, just kidding! If you look at the mathematical literature in a bit more detail, you’ll see a body of work littered with errors, omissions, disagreements, leaps of faith, appeals to intuition and duplicated efforts. In this talk, I will describe some ongoing efforts to use computers to help us overcome these problems, including work currently being done right here in our beloved Steel City. Prerequisites: nothing but an open mind and a hungry stomach.

Slides: available here.

Video recording: