MATH 597 (Fall 2026): Reading Group on the Mathematics of AI and LLMs

A synthograph of an astronaut riding a horse created in HuggingFace Space with Stable
Diffusion 3.5 Large. Prompt is: a photograph of an astronaut riding a horse. Picture taken from Wikimedia Commons.

Organizers: Gabriel Provencher Langlois, Richard Sowers, and Ryoko Sakura-Emi Kitadai Toller.

Description: This reading group will examine topics in the mathematics of artificial intelligence (AI), deep learning (DL), and foundation models, including large language models (LLMs). The readings will be selected from cutting-edge works displaying several facets of recent and emerging research in the mathematics of AI. The reading group will also be an opportunity for students to practice presenting research to a general audience, critically evaluate a paper students find interesting, and outline potential avenues of original research.

Time and location: Tuesdays, 2:30PM-3:30PM. The first meeting will be on Tuesday, August 25th.

Audience: This reading group is intended primarily for MS and PhD students in mathematics. Advanced undergraduate students and PhD students outside mathematics with sufficient background may be considered if sufficient space allows.

Assessment: Students who register will select one paper and 1) prepare a 2-3 page summary of it; 2) present the paper to the group (~20 minute presentation); and 3) discuss/respond to students’ questions. In addition, students will be expected to read all papers and formulate 1 or 2 questions to the presenter(s) in advance. Finally, students will write a final report (either a research proposal, a summary of the discussions, or a report of independent research), due at the end of the semester. Grading is satisfactory/unsatisfactory.

Registration: Please contact me at gp42[at][illinois][dot][edu] as soon as possible. Start your email with the header [MATH 597] to make it easier for me. Thank you!

Reading group schedule.

  • Week 1 (August 25th): Introduction, logistics, reading list, informal discussion.
  • Week 2 (September 1st): Paper presentation by Ryoko.
  • Week 3 (September 8th): Gabriel will talk about how he uses AI and LLMs in his day-to-day work.
  • Week 4 and on: Paper presentations by the students.
  • Around Week 12 (circa mid to late November): Final report is due.

Reading list

TBA. Tentatively, the readings will be shared on an external Google Drive.

Other materials (mathematics and AI)

Other materials (miscellaneous)

  • TBC.