Maxim Braverman

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math.DG2026

The classical Weyl law for Schrödinger operators on complete Riemannian manifolds

Maxim Braverman, Xianzhe Dai, Junrong Yan

We establish a criterion for the validity of the classical (non-semiclassical) Weyl law for Schrödinger operators $H = Δ + V$ on complete Riemannian manifolds. In contrast to existin…

math.DG2025

A gluing formula for the $Z_{2}$ -valued index of odd symmetric operators

Maxim Braverman, Ahmad Reza Haj Saeedi Sadegh, Junrong Yan

We investigate Dirac-type operator $D$ on involutive manifolds with boundary with symmetry, which forces the index of $D$ to vanish. We study the secondary $Z_{2}$ -valued index of el…

math.DG2024

The Z_2-valued spectral flow of a symmetric family of Toeplitz operators

Maxim Braverman, Ahmad Reza Haj Saeedi Sadegh

We consider families $A (t)$ of self-adjoint operators with symmetry that causes the spectral flow of the family to vanish. We study the secondary $Z_{2}$ -valued spectral flo…

The classical Weyl law for Schrödinger operators on complete Riemannian manifolds

A gluing formula for the Z2​-valued index of odd symmetric operators

The Z_2-valued spectral flow of a symmetric family of Toeplitz operators

A gluing formula for the $Z_{2}$ -valued index of odd symmetric operators