5 citations · 15 across the 13 of their papers we have counts for
16 papers
Berezin-Toeplitz Quantization of non-compact manifolds
Louis Ioos, Wen Lu, Xiaonan Ma +1
We develop Berezin-Toeplitz quantization in a non-compact complex geometric setting. Let be a Hermitian manifold, a positive holomorphic line bundle, and $(E,h^E)…
Bergman kernels and Poincaré series
Louis Ioos, Wen Lu, Xiaonan Ma +1
We show that the Bergman kernel of a finite-volume quotient of a Hermitian manifold with bounded geometry by a discrete group of its isometries is the same as t…
Partial Bergman kernels and determinantal point processes on Kähler manifolds
Louis Ioos
We compute the full off-diagonal asymptotics of the equivariant and partial Bergman kernels associated with a circle action on a prequantized Kähler manifold with bounded geometry…
Asymptotics of unitary matrix elements in canonical bases
Louis Ioos
We compute the asymptotics of matrix elements in the Gelfand-Zetlin bases of irreducible representations of the unitary group as the highest weight goes to infinity, in terms of th…
A Riemann-Roch formula for singular reductions by circle actions
Benjamin Delarue, Louis Ioos, Pablo Ramacher
We compute a Hirzebruch-Riemann-Roch type formula for the invariant Riemann-Roch number of a quantizable Hamiltonian -manifold $(M,ω,\J)$, allowing to be a singular value…
Quantization of symplectic fibrations and canonical metrics
Louis Ioos, Leonid Polterovich
We relate Berezin-Toeplitz quantization of higher rank vector bundles to quantum-classical hybrid systems and quantization in stages of symplectic fibrations. We apply this picture…
Balanced metrics for Kähler-Ricci solitons and quantized Futaki invariants
Louis Ioos
We show that a Kähler-Ricci soliton on a Fano manifold can always be smoothly approximated by a sequence of relative anticanonically balanced metrics, also called quantized Kähler-…
Anticanonically balanced metrics on Fano manifolds
Louis Ioos
We show that if a Fano manifold has discrete automorphism group and admits a polarized Kähler-Einstein metric, then there exists a sequence of anticanonically balanced metrics conv…
Almost representations of algebras and quantization
Louis Ioos, David Kazhdan, Leonid Polterovich
We introduce the notion of almost representations of Lie algebras and quantum tori, and establish an Ulam-stability type phenomenon: every irreducible almost representation is clos…
Berezin-Toeplitz quantization and the least unsharpness principle
Louis Ioos, David Kazhdan, Leonid Polterovich
We show that compatible almost-complex structures on symplectic manifolds correspond to optimal quantizations.
Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula
Louis Ioos
We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized s…
Spectral aspects of the Berezin transform
Louis Ioos, Victoria Kaminker, Leonid Polterovich +1
We discuss the Berezin transform, a Markov operator associated to positive operator valued measures (POVMs), in a number of contexts including the Berezin-Toeplitz quantization, Do…
Geometric quantization of symplectic maps and Witten's asymptotic conjecture
Louis Ioos
We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the spaces of holomorphic sections of a prequantizing line bundle over compact Kähler manifolds under d…
Quantization and isotropic submanifolds
Louis Ioos
We introduce the notion of an isotropic quantum state associated with a Bohr-Sommerfeld manifold in the context of Berezin-Toeplitz quantization of general prequantized symplectic…
Berezin-Toeplitz quantization for eigenstates of the Bochner-Laplacian on symplectic manifolds
Louis Ioos, Wen Lu, Xiaonan Ma +1
We study the Berezin-Toeplitz quantization using as quantum space the space of eigenstates of the renormalized Bochner Laplacian corresponding to eigenvalues localized near the ori…
On the composition of Berezin-Toeplitz operators on symplectic manifolds
Louis Ioos
We compute the second coefficient of the composition of two Berezin-Toeplitz operators associated with the Dirac operator on a symplectic manifold, making use of th…