George Stepaniants

Spectral isometries of unital $C^*$-algebras

This paper provides a human digestion of a proof of the spectral isometry conjecture for $C^*$-algebras found by GPT-6 Astra. We prove that every unital surjective complex-linear spectral isometry between unital $C^*$-algebras is a Jordan isomorphism. Without the assumption that the map preserves the identity, it is a...

SMAI-JCM SMAI Journal of Computational Mathematics Learning Memory And Material Dependent Constitutive Laws

A computer-assisted counterexample to the planar Berenstein conjecture

The Dirichlet endpoint considered here, the nonzero Neumann datum forces the harmonic source modes to remain, producing a coupled interior--boundary system involving the full zero-Dirichlet inverse and its Neumann trace, together with a separate sign-recovery problem.

A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures

A bounded simply connected noncircular domain of $\Omega$ with real-analytic Jordan boundary and a nonconstant function $u$ such that $u$ is a Neumann eigenfunction which is constant on the boundary, and $\Omega$ is a counterexample to Schiffer's conjecture.