tslil clingman

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.


my CV

I am a 5th year graduate student, my supervisor is Emily Riehl.

My interests are: formal category theory, higher categories, and homotopy type theory.

Today's day of the day is -- well, this joke requires javascript :(.

📧 tslil@jhu.edu
200 Krieger Hall, 3400 N. Charles Street, Baltimore, MD 21218
This website and its content is also available through IPFS via DNSLink at /ipns/tslil.xyz, or directly at /ipns/QmeGwomQyT5TtBfYAuA5KHr5XJEuiEvWAdhcapppUftVU5.



A sample of some of the formalisation work i have done in Homotopy Type Theory.


Here you can find some of the other 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 or talks. In no particular order,


William Kelso Morrill Award

In April of 2021 i was honoured to receive from my department the William Kelso Morill Award for Excellence in Mathematics. This award is given to the PhD candidate who “best displays the traits of William Kelso Morrill in his teaching, love of teaching, love of mathematics, and concern for students”.

I was nominated for this award by my students, one of whom wrote “Teaches and simplifies material very well. Takes the time to work with students and gives a lot of feedback on homework and portfolio. Grades within a reasonable timeframe and is easy to reach out to. Reaches out to struggling students. Overall caring person.”

Introduction to Proofs: Course development assistant

In Spring of 2019 Prof. Riehl and i designed and ran an introductory course for mathematics. The course was split into three components: a ‘standard’ introduction to proofs, an enquiry-based learning approach to metric spaces, and a discussion-format section on the notion of proof in mathematics.

The first third of the course used the structure of the book “How to Prove It” by Velleman, and had homework generated by Prof. Riehl and i, as well as some extracted from the book.

During the first third, for a change of perspective and so as to introduce notions of constructive mathematics, i lectured for a week on computer proof assistants. The class re-learnt propositional calculus through the use of the Coq computer proof assistant, as available online at Collacoq, and the goal was a modest reading comprehension of Coq code.

The script for these lectures, containing an introduction to type theory, Coq, and Collacoq – to the extent necessary for, and phrased within the broader of the course – as well as reading exercises, is available here.

In addition i created a written homework sheet, with feedback from Prof. Riehl, on constructive mathematics, available here.

In the second third of the course we switched to an IBL (enquiry-based learning) format and explored some of the early theory of metric spaces. Students completed the appropriate (portion of) the appropriate script before class and took it in turns to present their difficulties or successes with the material to one another. Here are the scripts i designed, with editing and input from Prof. Riehl. These are all made available under the terms of the Creative Commons Attribution-ShareAlike 4.0 International License.

Mentor in and organiser for the JHU Directed Reading Programme

I have been a mentor in the JHU Directed Reading Programme since its inception. The programme pairs undergraduate students with graduate students for one-on-one independent studies over the course of a semester.

Out of a desire to see the budding programme succeed, through 2018-2019 i helped organise the programme, and represented our then fledgling chapter at the 2018 Directed Reading Programme Network and Workshop at MIT.

I have mentored projects on the following topics: Fundamentals of General Topology, Braid Group Representations and Knot Invariants, Category Theory, and Homotopy Type Theory.

Abstracts of the projects may be found on the programme website.

ODE Autumn 2019/Spring 2021: Portfolios experiment

As head teaching assistant to Prof. Richard Brown – director of undergraduate studies –, in the usually calculation-homework-centric differential equations “service course”, i helped construct and orchestrate an experiment in student evaluation. Despite a class size of 175, we designed the course around semester-long digital portfolios: every week students were charged with creating ‘artefacts’ covering some minimum amount of content, and we were careful to leave this task open-ended.

The goal was to afford students the freedom to express, challenge, and reinforce their understanding in their terms, and in doing so emphasise a fundamental facet of mathematics: creativity. Initially most students produced text-based documents closely matching some of the example artefacts. However, with weekly small-group TA meetings focused solely on crafting these portfolio entries, students gained in confidence throughout the semester. They regularly created artefacts exceeding the minimum requirements, about topics they enjoyed, connections to other courses they had noticed, and work they were proud of. Moreover, the diversity in the style and medium of entries grew noticeably too.

Most importantly, we the TAs spent the semester emphasising the room and need for creativity in engaging with and doing mathematics. Ultimately the course was ranked the highest among all service courses by the students.

Calculus III & ODE: Head T.A. and WeBWorK admin.

In the Autumn of 2018 i was offered the role of Head Teaching Assistant for the Calculus III course at JHU. The instructor, Prof. Riehl, decided that the course should have an online homework component and so we settled on the WeBWorK platform.

During the course i was responsible for managing the online platform, exporting grades, and at times, programming new exercises for the students.

Owing to my experience in this position and my desire to see an online homework platform succeed, i was offered the same role for the course in the Autumn of 2019, though this time the instructor was Prof. Richard Brown, the director of undergraduate studies. I was offered the same role in Autumn of 2020 and Spring 2021, again with Prof. Richard Brown, but this time for the ODE course.

Introduction to Calculus: Sole instructor

In Autumn of 2017 i was offered the chance to run the introductory mathematics course designed to bridge high-school and university level mathematics. Although there was an assigned course text, the syllabus, homework, tests and exams, teaching, and marking were left entirely to me. Thus, i designed and ran the course.

Intersession Course: Primary Instructor

In January of 2017 several colleagues and i applied for, and were granted permission by the university to run an intersession course on recreational mathematics entitled “Recreational Mathematics for All”. We divided up the course into several, related topics and each co-organiser was given a few lectures to develop their topic. I lectured on secret sharing, building on the number theory that had gone before, and paving the way to the group theory that would come after. For evaluation the students submitted an elaboration of a topic that they had met during the course.

Cumulative experience as a teaching assistant

I have served as a Teaching Assistant in courses concerning: Real Analysis, Introductory Abstract Algebra, Linear Algebra, Differential Equations, The Calculus Sequence, and String Theory.

Notable Service




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


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Except where otherwise noted, content on this website is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.