Publications
An LLM–CAS framework for proving asymptotic inequalities
We build an LLM+CAS framework that proves research‑level asymptotic inequalities. Using it, we resolve multiple questions from MathOverflow and other research forums. This answers a question posed by Terence Tao. We are grateful for Terence's support for our project, including his highlighting of our tool here.
Elementary symmetric polynomials under the fixed point measure
We prove a surprising inhomogeneous inequality for symmetric polynomials, fully confirming a conjecture of Bhargav Narayanan. The result advances the program of obtaining sharp unconditional lower bounds on the permanent of a matrix.
Computing renormalized curvature integrals on Poincaré–Einstein manifolds
We describe a general procedure for constructing renormalized curvature integrals on Poincaré–Einstein manifolds.
Ambient metric for manifolds with density and the Ricci flow
We construct fully non‑linear analogues of Perelman’s W‑functional that are monotone along the Ricci flow, and stationary only for shrinking Ricci solitons. We do so by constructing a Fefferman–Graham ambient metric for manifolds with density.
The weighted ambient metric
We construct the Fefferman–Graham ambient metric for smooth metric measure spaces.
GJMS operators of smooth metric measure spaces
We construct GJMS operators for smooth metric measure spaces, and prove several properties.
Weighted renormalized volume coefficients
We construct renormalized volume coefficients for smooth metric measure spaces and prove several key properties.