Probability and Statistics Seminar: New Bounds on the Grothendieck Constant via Long Horizon AI Assisted Research

Event details Date: Wednesday, September 30, 2026 Time: 2:00 PM to 3:00 PM Location: Kaprielian Hall (KAP) - 414 - 3620 South Vermont Avenue, Los Angeles, CA 90089 Type: Lecture / Talk / Workshop Campus: University Park Campus Department: Mathematics About this event Alan Li and Rahul Saha, University of Texas, Austin Title: New Bounds on the Grothendieck Constant via Long Horizon AI Assisted Research Abstract: The Grothendieck constant (K_G) is a fundamental quantity measuring the worst-case gap between a particular class of integer quadratic optimization problem and its efficiently solvable semidefinite programming relaxation. It has found diverse applications in fields such as functional analysis, combinatorial optimization, theoretical computer science, and quantum information theory. Its value has remained open since its introduction by Alexander Grothendieck over 70 years ago, despite sustained interest from the mathematical community. Our work determines the tenths digit for the first time, proving (6π/11 < K_G < π/(2log(1+√2)) – 10⁻⁴). We will describe the technical details of these improvements, which relies on conceptually new approaches to both sides of the problem: new asymptotic rounding schemes for the upper bound, and a lower-bound method based on proving fundamental limitations of entire classes of rounding schemes rather than constructing individual hard instances. We will describe the AI research system we built, and the roles played by both AI and human researchers throughout the process. Finally, we will discuss what this experience suggests about the importance of human research judgement and the future of human-AI collaboration. Official event details: https://calendar.usc.edu/event/probability-and-statistics-seminar-new-bounds-on-the-grothendieck-constant-via-long-horizon-ai-assisted-research