Research

Below is a list of my research papers.

Machine Learning

  1. Dataset Distillation with Infinitely Wide Convolutional Networks (with R. Novak, L. Xiao, and J. Lee). arxiv:2107.13034 (accepted to NeurIPS 2021)
  2. Dataset Meta-Learning from Kernel Ridge-Regression (with Z. Chen and J. Lee).  arxiv:2011.00050 (International Conference on Learning Representations 2021)

Quantum Field Theory

  1. Stochastic Feynman rules for Yang-Mills theory on the plane.  arxiv:1607.07463
  2. Wilson loop area law for 2D Yang-Mills in generalized axial gauge. arxiv:1601.04726
  3. Quantum Yang-Mills theory in two dimensions: Exact versus perturbative. arxiv:1508.06305
  4. The perturbative approach to path integrals: A succinct mathematical treatment.
    J. Math. Phys. 57, 092301 (2016)  arxiv:1505.04809
  5. Quantization of the nonlinear sigma model revisited.
    J. Math. Phys. 57 082301 (2016) arxiv:1408.4466

Gauge Theory

  1. Lagrangian correspondences and Donaldson’s TQFT construction of the Seiberg-Witten invariants of 3-manifolds.
    Algebraic & Geometric Topology. 14 (2014) 863–923. arxiv:1111.3672
  2. The Seiberg-Witten equations on manifolds with boundary II: Lagrangian boundary conditions for a Floer theory.
    Comm. Anal. & Geom. 26 (2018), no. 1, 113–216. arxiv:1008.2017
  3. The Seiberg-Witten equations on manifolds with boundary I: The space of monopoles and their boundary values.
    Comm. Anal. & Geom. 20 (2012), no. 3, 565–676. arxiv:1008.2013

Miscellaneous

  1. Anisotropic function spaces and elliptic boundary value problems.
    Mathematische Nachrichten. 285 (2012), no. 5-6, 687-706. arxiv:1010.4046
  2. A lower bound on the radius of analyticity of a power series in a real Banach space.
    Studia Math. 191 (2009), 171–179. pdf
  3. On discrete features of the wave equation in singular pp-wave backgrounds (with O. Evnin).
    JHEP 09 (2008) 105–115. arXiv:0806.3057
  4. Positive Lyapunov exponents for a class of ergodic orthogonal polynomials on the unit circle.
    J. Math. Anal. Appl. 327 (2007), no. 2, 977–990. pdf

PhD Thesis (2011): The Seiberg-Witten Equations on Manifolds with Boundary  pdf