13 citations · 29 across the 9 of their papers we have counts for
11 papers
On vector-valued multisymplectic forms
Tatyana Barron, Kai Boisvert, Noah Vale
We obtain a standard local presentation for a vector-valued multisymplectic form on a smooth manifold, generalizing the known proof for polysymplectic forms. We show that vector-va…
Average entropy and asymptotics
Tatyana Barron, Manimugdha Saikia
We determine the asymptotics of the expected value of entanglement entropy in , where and are the spaces of holomorphic se…
Coherent states and entropy
Tatyana Barron, Alexander Kazachek
Let , , be the Hilbert spaces of geometric quantization on a Kähler manifold . With two points in we associate a Bell-type state $b_k \in H_k\otimes…
Entanglement and products
Tatyana Barron, Noah Wheatley
We consider a sequence of quantum states, , associated with a submanifold of product of two integral compact Kähler manifolds. We show that, when is a product submanif…
The twistor space of and Berezin-Toeplitz operators
T. Barron, A. Tomberg
A hyperkähler manifold has a family of induced complex structures indexed by a two-dimensional sphere . The twistor space of is a complex manifold…
Closed geodesics and pluricanonical sections on ball quotients
Tatyana Barron
We obtain asymptotics of sequences of the holomorphic sections of the pluricanonical bundles on ball quotients associated to closed geodesics. A nonvanishing result follows.
Kähler quantization and entanglement
Tatyana Barron, Timothy Pollock
For a very ample line bundle L on a compact connected complex manifold X, with a real structure, we discuss entanglement properties of certain sequences of vectors in tensor produc…
On vector-valued automorphic forms on bounded symmetric domains
Nadia Alluhaibi, Tatyana Barron
We prove a spanning result for vector-valued Poincaré series on a bounded symmetric domain. We associate a sequence of holomorphic automorphic forms to a submanifold of the domain.…
Berezin-Toeplitz quantization, hyperkähler manifolds, and multisymplectic manifolds
Tatyana Barron, Baran Serajelahi
We suggest a way to quantize, using Berezin-Toeplitz quantization, a compact hyperkahler manifold (equipped with a natural 3-plectic form), or a compact integral Kahler manifold of…
On varieties of Lie algebras of maximal class
Tatyana Barron, Dmitry Kerner, Marina Tvalavadze
We study complex projective varieties that parametrize (finite-dimensional) filiform Lie algebras over C, using equations derived by Millionshchikov. In the infinite-dimensional ca…
Semi-classical properties of Berezin--Toeplitz operators with $\cC^k$--\,symbol
Tatyana Barron, Xiaonan Ma, George Marinescu +1
We obtain the semi-classical expansion of the kernels and traces of Toeplitz operators with $\cC^k$--\,symbol on a symplectic manifold. We also give a semi-classical estimate of th…