微局部分析及其应用方向博士职位
PhD Studentship: Microlocal analysis and its applications in quantum resonances, partial differential equations with analytic or Gevrey regularity, and several complex variables
原帖优先：申请材料、截止时间与资格以原帖和学校官方说明为准。
AI 中文速览
- 研究内容
- 微局部分析及其在量子谐振、偏微分方程和复变函数中的应用
- 申请条件
- 原文未说明
- 待遇
- 奖学金包括学费、培训支持和标准工资的津贴，持续3-3.5年
- 申请方式
- 原文未说明
- 材料清单
- 原文未说明
由 @cf/meta/llama-3.3-70b-instruct-fp8-fast 生成，博士岗判定置信度 100%。
结构化信息
- 截止
- （Europe/London） 剩 14 天
- 学科
- 数学
- 合同类型
- 雇佣合同
- 原帖发布
- 本站收录
- 内容更新
- 导师
- Haoren Xiong
- 来源
- jobs.ac.uk（英国博士项目及学术招聘） · 最近核对 2026-10-07
判定依据（原文摘录）
- is_phd
PhD Studentship
原文
Microlocal analysis explores the classical/quantum correspondence in partial differential equations (PDEs). For example, the concept of symbol quantisation in the theory of pseudodifferential operators links classical observables (functions on phase space) with quantum operators. Microlocal analysis also provides essential tools to rigorously define, compute, and analyse resonances, which describe the oscillation and decay of waves in systems where energy can escape to infinity, replacing eigenvalues and eigenfunction expansions in non-compact domains.
The consideration of analytic or Gevrey regularity in the study of PDEs has attracted considerable attention in recent years. The aim of this project is to develop microlocal analysis techniques in analytic and Gevrey settings. The analytic scheme often yields exponentially accurate approximation or controls in PDEs. Gevrey regularity allows one to go beyond the smooth theory and obtain quantitative remainder estimates, while retaining useful tools such as cutoffs and partitions of unity that are unavailable in the analytic setting. We expect to apply these techniques to geometry, quantum mechanics, and other fields in mathematical physics.
The project will be supervised by Dr Haoren Xiong ( h.xiong@bham.ac.uk ).
Funding notes: Funding is available through the School of Mathematics for a suitably strong candidate. The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years.
Candidates are encouraged to make an informal inquiry with Dr Haoren Xiong.
References: Xiong, H., Pseudodifferential operators with formal Gevrey symbols and symbolic calculus, arXiv: 2603.07693.
Xiong, H., Boundary spectral estimates for semiclassical Gevrey operators. J. Spectr. Theory 15 (2025), no. 4, pp. 1503–1522.
Xiong, H. and Xu, H., Semiclassical asymptotics for Bergman projections with Gevrey weights, arXiv: 2403.14157.
Xiong, H., Generic simplicity of resonances in obstacle scattering, Trans. Amer. Math. Soc. 376 (2023), 4301-4319.