Earlier today, I gave two talks at the PittĀ 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.