Dan Wang

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20242026

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math.SG2026

Limits of quantization from mixed to real polarizations on toric varieties

Dan Wang, Yutung Yau

Let $(M, ω, J)$ be a $2 n$ -dimensional toric variety determined by a Delzant polytope $P$ , whose $T^{n}$ -symmetry determines a real polarization $P_{R}$ . Let $K \…

math.SG2025

Quantization in polarization via transverse Poincaré-Birkhoff-Witt theorem

Dan Wang, Yutung Yau

We construct, for every prequantizable symplectic manifold $(M, ω, L)$ equipped with a nonsingular polarization, a deformation quantization $(C_{M}^{\infty} [[ℏ]], ⋆)$ together wit…

math.SG2024

A new look at unitarity in quantization commutes with reduction for toric manifolds

José M. Mourão, João P. Nunes, Augusto Pereira +1

For a symplectic manifold $M$ with the Hamiltonian action of a compact Lie group $G$ , we give a new perspective on the problem of unitarity in the quantization commutes with reduct…

math.SG2024

Quantum spaces associated to mixed polarizations and their limiting behavior on toric varieties

Dan Wang

Let $(X, ω, J)$ be a toric variety of dimension $2 n$ determined by a Delzant polytope $P$ . As indicated in [40], $X$ admits a natural mixed polarization $P_{k}$ , induced…