Peng Zhou

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Peng Zhou

CV (pdf, updated 2022-12-04)

Research Interests

Homological Mirror Symmetry, Geometric Representation Theory, Microlocal Sheaf theory, and Semi-Classical Analysis

Positions

  • 2022.7-2023.6, postdoc at UC Berkeley. Mentor: Mina Aganagic
  • 2019.8-2022.6, Morrey Assistant Professor at UC Berkeley. Mentor: Vivek Shende
  • 2017.9-2019.8, postdoc at IHES. Mentor: Maxim Kontsevich.

Education

  • 2012-2017, Northwestern Univeristy
    • Ph.D. Mathematics. Advisor: Eric Zaslow
    • Thesis: From Fukaya-Seidel Category to Constructible Sheaves
  • 2006-2012, Univeristy of Wisconsin-Madison
    • Ph.D. Physics (cosmology). Advisor: Daniel Chung
    • Thesis: Gravitational Fermion Production during Inflation.
  • 2002-2006, Peking University
    • B.S., Physics major, Math mino

Publication

Homological Mirror Symmetry

  1. Twisted polytope sheaves and coherent–constructible correspondence for toric varieties. Selecta Mathematica, 25(1):1–23, 2019
  2. Lagrangian skeleta of hypersurfaces in $(\C^*)^n$. Selecta Mathematica, 26(2):1–33, 2020
  3. Sheaf quantization of Legendrian isotopy. (accepted by Compositio of Math) 2018
  4. Variation of GIT and variation of Lagrangian skeletons II: Quasi-symmetric case. (with Jesse Huang) Advances in Mathematics, Volume 408, Part A, 2022, 108597

preprints

  1. GKZ discriminant and Multiplicities. (with Jesse Huang) arXiv:2206.14778, 2022
  2. Gamma II for toric varieties from integrals on T-dual branes and homological mirror symmetry. arXiv:1903.05300, 2019
  3. Variation of GIT and variation of Lagrangian skeletons I: flip and flop. arXiv:2011.03719, 2020

Microlocal Analysis

  1. Interface asymptotics of partial Bergman kernels on S1-symmetric K ̈ahler manifolds (with Steve Zelditch) Journal of Symplectic Geometry, 17(3):793–856, 2019
  2. Central limit theorem for spectral partial Bergman kernels. (with Steve Zelditch) Geometry & Topology, 23(4):1961–2004, 2019
  3. Central limit theorem for toric Kahler manifolds. (with Steve Zelditch) Pure and Applied Mathematics Quarterly, 17(3):843–864, 2021
  4. Interface asymptotics of Partial Bergman kernels around a critical level. (with Steve Zelditch) Arkiv for Matematik, 57(2):471–492, 2019
  5. Pointwise Weyl law for partial Bergman kernels. (with Steve Zelditch) In Algebraic and analytic microlocal analysis, pages 589–634. Springer, 2018
  6. Nodal sets of random eigenfunctions for the isotropic harmonic oscillator. (with Boris Hanin, Steve Zelditch) International Mathematics Research Notices, 2015(13):4813–4839, 2015
  7. Scaling of harmonic oscillator eigenfunctions and their nodal sets around the caustic. (with Boris Hanin, Steve Zelditch) Communications in Mathematical Physics, 350(3):1147–1183, 2017

Log D-modules and applications

  1. Log D-modules and index theorems. (with Lei Wu) In Forum of Mathematics, Sigma, volume 9. Cambridge University Press, 2021
  2. Zero loci of Bernstein–Sato ideals. (with Nero Budur, Robin van der Veer, Lei Wu) Inventiones mathematicae, 225(1):45–72, 2021
  3. Zero loci of Bernstein-Sato ideals-II. (with Nero Budur, Robin van der Veer, Lei Wu) Selecta Mathematica, 27(3):1–30, 2021

Journals Refereed

  • Advances in Mathematics
  • Communications in Mathematical Physics
  • Tunisian Journal of Mathematics
  • Pure and Applied Math Quarterly
  • Journal of Differential Geometry
  • Journal of Topology
  • Communications in Analysis and Geometry

Teaching Experience

As an instructor in UC Berkeley

  • Introduction to Real Analysis (Math 104)
  • Mathematical Tools in Physical Science (Math 121A, 121B)
  • Introduction to Complex Analysis (Math 185)
  • Introduction to Differential Geometry (Math 214)
  • Linear Algebra (Math 54)

As a TA in Northwestern University

  • (Graduate) Real Analysis
  • (Graduate) Probability
  • Probability and stochastic process,
  • Dynamical System
  • Linear Algebra
  • Linear Optimization

Directed Reading Projects

I advised a few undergrads reading projects in UC Berkeley.

  • 2022 Fall: Cohomology of Flag varieties
  • 2022 Summer: Differentiable Manifold
  • 2022 Spring: Introduction to Group and Representation theory
  • 2021 Summer: Random Matrix Theory.
  • 2021 Summer: Differentiable Manifold.

Awards

  • 2017 Best Thesis Award. By Northwestern Mathematics Department.
  • 2015-16 Gelfand Award (for contribution to the math department). By Northwestern Mathematics

Department.

  • 2015-16 Mathematics Department Graduate Teaching Assistant Award.
  • 2013-14 Department Nomination for Presidential Fellowship
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