USC Probability/Statistics Seminar, Wednesday, Sep 30, 2PM KAP 414
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Fatih Erdem Kızılkaya
Sep 30, 2026, 1:04:57 AMSep 30
to USC Theory Group, usc-t...@googlegroups.com, csth...@usc.edu, Steven Heilman
Hi all,
Steven Heilman, from the math department, thought the seminar below would be of interest to this mailing list.
---
This week the Probability and Statistics Seminar occurs Wednesday,
September 30, at 2:00PM in KAP 414.
A mathematics tea reception will take place afterwards at 3:00 PM in
the lounge. Details below
Sep 30: Alan Li and Rahul Saha (UT Austin)
New Bounds on the Grothendieck Constant via Long Horizon AI Assisted Research
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.
---
Best,
Fatih
Steven Heilman, from the math department, thought the seminar below would be of interest to this mailing list.
---
This week the Probability and Statistics Seminar occurs Wednesday,
September 30, at 2:00PM in KAP 414.
A mathematics tea reception will take place afterwards at 3:00 PM in
the lounge. Details below
Sep 30: Alan Li and Rahul Saha (UT Austin)
New Bounds on the Grothendieck Constant via Long Horizon AI Assisted Research
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.
---
Best,
Fatih
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