YuTung Yau

activity

20212026

collaborators

11 papers

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.SG2026

Brane quantization of $A_{n}$ -resolutions

Yat-Hin Suen, Yutung Yau

We extend the study of brane quantization via SYZ mirror symmetry to the setting of singular fibers, building on recent joint work with Chan, Leung, and Li in the semi-flat case. W…

math.DG2026

Brane quantization and SYZ mirror symmetry

Kwokwai Chan, Naichung Conan Leung, Qin Li +2

Coisotropic A-branes were introduced by Kapustin--Orlov to enlarge the Fukaya category of a symplectic manifold in a way that aligns with predictions from homological mirror symmet…

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.DG2025

Quantization of Kähler manifolds via differential operators

Kwokwai Chan, Naichung Conan Leung, Qin Li +1

In this paper, we study the quantization of classical observables (i.e., functions) on a Kähler manifold $X$ as differential operators acting on holomorphic sections of tensor powe…

math.SG2025

Quantization commutes with reduction for coisotropic A-branes

Naichung Conan Leung, Ying Xie, Yutung Yau

On a Hamiltonian $G$ -manifold $X$ , we define the notion of $G$ -invariance of coisotropic A-branes $B$ . Under neat assumptions, we give a Marsden-Weinstein-Meyer type construction o…

math.SG2024

Categorical quantization on Kähler manifolds

YuTung Yau

Generalizing deformation quantizations with separation of variables of a Kähler manifold $M$ , we adopt Fedosov's gluing argument to construct a category $DQ$ , enriched ove…

math.SG2024

Quantization of Kähler Manifolds via Brane Quantization

YuTung Yau

In their physical proposal for quantization [20], Gukov-Witten suggested that, given a symplectic manifold $M$ with a complexification $X$ , the A-model morphism spaces $\operatorna…

math.SG2023

Hidden Sp(1)-Symmetry and Brane Quantization on HyperKähler manifolds

NaiChung Conan Leung, YuTung Yau

For a fixed prequantum line bundle $L$ over a hyperKähler manifold $X$ , we find a natural $Sp (1)$ -action on $Ω^{*} (X, L)$ intertwining a twistor family of $\operatorna…

math.SG2021

Berezin-Toeplitz Quantization in Real Polarizations with Toric Singularities

NaiChung Conan Leung, YuTung Yau

On a compact Kähler manifold $X$ , Toeplitz operators determine a deformation quantization $(C^{\infty} (X, C) [[ℏ]], ⋆)$ with separation of variables [1…

math.SG2021

Deformation quantization via Toeplitz operators on geometric quantization in real polarizations

Naichung Conan Leung, Yutung Yau

In this paper, we study quantization on a compact integral symplectic manifold $X$ with transversal real polarizations. In the case of complex polarizations, namely $X$ is Kähler e…

Limits of quantization from mixed to real polarizations on toric varieties

Brane quantization of An​-resolutions

Brane quantization and SYZ mirror symmetry

Quantization in polarization via transverse Poincaré-Birkhoff-Witt theorem

Quantization of Kähler manifolds via differential operators

Quantization commutes with reduction for coisotropic A-branes

Categorical quantization on Kähler manifolds

Quantization of Kähler Manifolds via Brane Quantization

Hidden Sp(1)-Symmetry and Brane Quantization on HyperKähler manifolds

Berezin-Toeplitz Quantization in Real Polarizations with Toric Singularities

Deformation quantization via Toeplitz operators on geometric quantization in real polarizations

Brane quantization of $A_{n}$ -resolutions