How does one begin a website? What should be the first sentence to meet the reader's eyes? I have elected to circumvent this predicament by, careful readers may note, omitting the first sentence of this website entirely.

I am a 3

^{rd}year graduate student, my supervisor is Emily Riehl.My interests are:

formal category theory,higher categories, andhomotopy type theory.Today's day of the day is this joke requires javascript :(.

📧 tslil@jhu.edu

201 Krieger Hall, 3400 N. Charles Street, Baltimore, MD 21218

Here you can find some of the things i have written up. Usually this is because i thought they were interesting, sometimes the notes were intended to help me better understand things, and sometimes they represent a transcript of my explorations. In no particular order,

- A formalised proof that univalence implies function extensionality.
- Exploration of enriched base change, mates, and universal algebra i did in my first summer before JHU (before i knew about Lawvere theories and really much else).
- (Very incomplete!) Working notes i compiled as i learnt category theory, beginning from elementary definitions working up to a statement of homology at the level of Ab-categories, and many things besides.
- (more coming soon)

- Primary organiser of the 2019 Category Theory Octoberfest at JHU (TBA)
- Co-organiser of the JHU chapter of the Directed Reading Programme
- Organiser of Slideshow Karaoke for the Graduate Lunch Seminar at JHU

- 2019/02/19

*Polynomial functors, a degree of generality*

Johns Hopkins Category Theory Seminar - 2019/02/10

Audience of high-school students,*Fractions: ratio of two integers or universal machine?*

Johns Hopkins Mathematics Tournament - 2018/11/30

*Homotopy Type Theory, the confluence of logic and space*(slides)

University Seminar: Logic Across Disciplines, George Washington University - 2018/11/08

*What is an LCC?*

Johns Hopkins Category Theory Seminar - 2018/09/20

*Type Theory and Categories, the unbearable likeness of being*(slides)

Oral Speciality Exam, Johns Hopkins University - 2017/11/15 and 2017/12/05

*What do we mean when we say spectra?*and

*`Rings, Modules and Algebras in Infinite Loop Space Theory' at a glance*

Graduate Course: Topics in Algebraic Topology, Johns Hopkins University - 2017/11/30

*An Intuitive Description of Toposes, Toposes as a Description of Intuitionism*

University Seminar: Logic Across Disciplines, George Washington University - 2017/10/12

*All good things must come to an end*

Johns Hopkins Category Theory Seminar - 2017/04/09

*The calculus of fractions and homotopy theory*

Graduate Course: Algebraic Topology II, Johns Hopkins University - 2016/12/12

*A monad is just … (with an eye to universal algebra)*

Johns Hopkins Category Theory Seminar

- Spring 2019, Introduction to Proofs: Co-designer of course
- Mentored the following projects in the JHU Directed Reading Programme: Fundamentals of General Topology, Braid Group Representations and Knot Invariants, Category Theory, and Homotopy Type Theory.
- Autumn 2018, Calculus III: Head T.A. and ran WeBWorK for the course
- Autumn 2017, Introduction to Calculus: Primary instructor
- Linear Algebra, Differential Equations, and the Calculus sequence as a T.A.

- Vladimir Voevodsky Memorial Conference, IAS
- Category Theory Octoberfest 2018, CUNY
- Directed Reading Programme Network and Workshop 2018, MIT
- Category Theory Octoberfest 2017, CMU
- Category Theory 2017, UBC

What do i do when i'm not doing maths? A small catalogue of some of my endeavours