Welcome to my website! I’m a 6th year PhD student in Mathematics at UNC – Chapel Hill, where my advisor is David Rose. I received a B.S. in Mathematics and a B.A. in Physics from Rice University in 2019. I’m interested in categorification, quantum link invariants, and low-dimensional topology. My CV is here.
My office is Phillips Hall 362. My email address is lconners [at] live [dot] unc [dot] edu.
My research is currently supported by funding awarded to David Rose by NSF CAREER Grant DMS-2144463 and Simons Foundation Collaboration Grant 523992. I was recently supported by UNC’s Summer Graduate Research Fellowship.
News
I was awarded the 2024 International Congress of Chinese Mathematicians (ICCM) Graduate Thesis Award (GTA) Silver Award for my paper Row-Column Mirror Symmetry for Colored Torus Knot Homology. Thank you to the ICCM for this honor!
Research
- Row-Column Mirror Symmetry for Colored Torus Knot Homology. Selecta Mathematica, 30 (2024), no. 97
- Fray functors and equivalence of colored HOMFLYPT homologies. Submitted for publication.
Software
Among the results in the two papers above is a method for computing various models of colored HOMFLYPT homology of positive torus knots. I’ve written a program that implements this method, which you can find on my GitHub page here.
If you find this program helpful or wish to report bugs or suggest improvements, please email me!
Teaching and Mentoring
I’ve taught the following courses at UNC:
- Summer 2022 – Math 347 (Linear Algebra)
- Spring 2022 – MATH 381 (Discrete Mathematics)
- Fall 2021 – MATH 383 (Differential Equations)
- Summer 2021 – MATH 232 (Calculus II)
- Spring 2021 – MATH 117 (Aspects of Finite Mathematics)
From 2021 to 2023, I also helped organize UNC’s Directed Reading Program.
Upcoming (and recent) Seminars and Travel
- 2025 Simons Collaboration on New Structures in Low-Dimensional Topology Annual Meeting, New York, NY, March 27-28, 2025
- International Congress of Chinese Mathematicians, Shanghai, China, January 3-6, 2025
- Geometry/Topology Seminar, Virginia Tech, October 15, 2024
- Graduate Math Association seminar, UNC-Chapel Hill, August 26, 2024
- WARTHOG 2024, University of Oregon, July 22-26, 2024
- New Structures in Low-Dimensional Topology Summer School, Rényi Institute (Budapest, Hungary), July 1-5, 2024
- Algebra and Discrete Mathematics Seminar, UC Davis, April 23, 2024
- Triangle Area Graduate Mathematics Conference (TAGMaC), UNC-Chapel Hill, March 23, 2024
- Quantum Structures in Lie Theory, University of Virginia, March 1-3, 2024
- Geometry and Topology Seminar, MIT, February 26, 2024
- Geometric Methods in Representation Theory Seminar, UNC-Chapel Hill, February 9, 2024
Come say hello if you see me! Feel free to email me if you would like me to come speak in your seminar series (or if you would like to go hiking before or after an upcoming conference).
I frequently speak at UNC’s Graduate Math Association seminar and jGMRT.
Personal
My wife, Emma Crawford, is also a mathematician working in Natalie Stanley’s lab at UNC. You can find her work on bioRxiv here.
I served on the Executive Board of UNC’s Graduate and Professional Student Government in AY 2023-2024.
In a past life, I played trumpet in the jazz fusion combo Steve Cox’s Beard. You can find our music on SoundCloud, Spotify, and Apple Music. I also played in Five Foot Five (before they recorded this album), Colts Drum and Bugle Corps, and The Cavaliers Drum and Bugle Corps.