6 papers
Computing renormalized curvature integrals on Poincaré-Einstein manifolds
Jeffrey S. Case, Ayush Khaitan, Yueh-Ju Lin +2
We describe a general procedure for computing renormalized curvature integrals on Poincaré-Einstein manifolds. In particular, we explain the connection between the Gauss-Bonnet-ty…
Local and global conformal invariants of submanifolds
Jeffrey S. Case, Ayush Khaitan, Yueh-Ju Lin +2
We develop methods for constructing and computing conformal invariants of submanifolds, with a particular emphasis on conformal submanifold scalars and conformally invariant integr…
Weighted GJMS operators on smooth metric measure spaces
Ayush Khaitan
We construct weighted GJMS operators on smooth metric measure spaces, and prove that they are formally self-adjoint. We also provide factorization formulas for them in the case of…
The weighted ambient metric for manifolds with density
Ayush Khaitan
We prove the existence and uniqueness of a weighted analogue of the Fefferman-Graham ambient metric for manifolds with density. We then show that this ambient metric forms the natu…
O-Forge: An LLM + Computer Algebra Framework for Asymptotic Analysis
Ayush Khaitan, Vijay Ganesh
Large language models have recently demonstrated advanced capabilities in solving IMO and Putnam problems; yet their role in research mathematics has remained fairly limited. The k…
Elementary symmetric polynomials under the fixed point measure
Ayush Khaitan, Ishan Mata, Bhargav Narayanan
We identify a surprising inequality satisfied by elementary symmetric polynomials under the action of the fixed point measure of a random permutation. Concretely, for any collectio…