Thu, February 26, 2026
1:50 pm - 2:45 pm
Math Tower (MW) 154
Yifan Jing
The Ohio State University
Title
Sharp quantitative stability in Hilbert spaces
Abstract
Grothendieck compactness criterion, and the stability theory from model theory, show that the inner product on the unit ball over Hilbert spaces is stable. We study this phenomenon quantitatively. We prove that the inner product is $(k,\epsilon)$-stable for all $k\geq \exp(\pi/\epsilon)$, and it is not $(k,\epsilon)$-stable for $k\leq \exp(\log 2/\epsilon)$, showing that the growth is necessarily exponential in $1/\epsilon$. This answers a question of Conant. We also analyze how stability scales under nonlinear connectives applied to the inner product, and general binary formulas over Hilbert spaces expanded by unitary or normal operators.