Hello! I’m an incoming mathematics PhD student at the University of Pittsburgh supported by the K. Leroy Irvis Fellowship. I hope to become a mathematics professor in the future. I recently graduated from Yale, where I double majored in mathematics on the intensive track and ethnic studies. (You might know me as Luc Ta; that was my name prior to 2025.)

Below is a list of my publications. To read more about me, please refer to my CV or my bio. Both of these are also accessible via the navigation bar located at the top of this webpage, along with a few of my teaching resources and a catalog of my music.

Publications

Submitted Preprints

Enumeration of virtual quandles up to isomorphism. arXiv:2506.16536, 2025. 11 pages.

Graph quandles: Generalized Cayley graphs of racks and right quasigroups. arXiv:2506.04437, 2025. 19 pages.

Equivalences of racks, Legendrian racks, and symmetric racks. arXiv:2505.08090, 2025. 13 pages.

Generalized Legendrian racks: Classification, tensors, and knot coloring invariants. arXiv:2504.12671, 2025. 39 pages.
Bachelor’s thesis at Yale, advised by Sam Raskin.
(Presentation slides: Mellon Forum [nontechnical], HRUMC [technical], thesis defense [very technical].)

Constructions of and bounds on the toric mosaic number, with Kendall Heiney, Margaret Kipe, Samantha Pezzimenti, and Kaelyn Pontes. arXiv:2504.02265, 2025. 21 pages.

Accepted for Publication

Bounds on the mosaic number of Legendrian knots, with Margaret Kipe, Samantha Pezzimenti, Leif Schaumann, and Wing Hong Tony Wong. To appear in the Journal of Knot Theory and Its Ramifications. doi:10.1142/S0218216525500555, 2025. 47 pages. (Preprint available on arXiv.)
(Presentation slides: JMM.)

Editor-Reviewed Publications

Integer sequences A383144–A383146, A383828–A383831, and A385040–A385041 relating to racks and quandles. On-Line Encyclopedia of Integer Sequences (OEIS), 2025.

Integer sequences A375353–A375357, A375392, A375619, and A376155 relating to various topics in knot theory and combinatorics. On-Line Encyclopedia of Integer Sequences (OEIS), 2024.

Margaret Kipe, Samantha Pezzimenti, Leif Schaumann, Lực Ta, and Wing Hong Tony Wong. Integer sequences A374939, A374942–A374947, and A375354 relating to Legendrian knot mosaics. On-Line Encyclopedia of Integer Sequences (OEIS), 2024.

Giving a presentation on toric knot mosaics at UnKnot V