Nicholas F. Marshall

Research interests

About

• Assistant Professor at Oregon State
• NSF Postdoc at Princeton with Amit Singer
• PhD in applied math at Yale with Ronald Coifman and Stefan Steinerberger.
• Math genealogy project.
• Semester at Math in Moscow
• Undergrad in math at Clarkson with honors
• Grew up in Vermont where I learned to ski

Research

1. arXiv:2212.14288
   From the binomial reshuffling model to Poisson distribution of money
   with Fei Cao


2. arXiv:2210.17501
   Fast Principal Component Analysis for Cryo-EM Images
   with Oscar Mickelin, Yunpeng Shi and Amit Singer
   Biological Imaging (to appear)


3. arXiv:2207.13674
   Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions
   with Oscar Mickelin and Amit Singer
   SIAM Journal on Scientific Computing (to appear)


4. arXiv:2202.12224
   An optimal scheduled learning rate for a randomized Kaczmarz algorithm
   with Oscar Mickelin
   SIAM Journal on Matrix Analysis and Applications (to appear)


5. arXiv:2201.13386
   On a linearization of quadratic Wasserstein distance
   with Philip Greengard , Jeremy Hoskins and Amit Singer


6. arXiv:2107.14747
   A common variable minimax theorem for graphs
   with Ronald Coifman and Stefan Steinerberger
   Foundations of Computational Mathematics doi.org/10.1007/s10208-022-09558-8


7. arXiv:2101.07709
   Multi-target detection with rotations
   with Tamir Bendory, Ti-Yen Lan, Iris Rukshin, and Amit Singer
   Inverse Problems and Imaging doi.org/10.3934/ipi.2022046


8. arXiv:1910.10006
   Image recovery from rotational and translational invariants
   with Tamir Bendory, Ti-Yen Lan, and Amit Singer
   ICASSP doi.org/10.1109/ICASSP40776.2020.9053932


9. arXiv:1910.04201
   Randomized mixed Hölder function approximation in higher-dimensions
   Technical Report


10. arXiv:1907.03873
    A fast simple algorithm for computing the potential of charges on a line
    with Zydrunas Gimbutas and Vladimir Rokhlin
    Applied and Computational Harmonic Analysis doi.org/10.1016/j.acha.2020.06.002


11. arXiv:1902.06633
    A Cheeger inequality for graphs based on a reflection principle
    with Edward Gelernt, Diana Halikias, and Charles Kenney
    Involve doi.org/10.2140/involve.2020.13.475


12. arXiv:1810.00823
    Approximating mixed Hölder functions using random samples
    Annals of Applied Probability doi.org/10.1214/19-AAP1471


13. arXiv:1711.06711
    Manifold learning with bi-stochastic kernels
    with Ronald Coifman
    IMA Journal of Applied Mathematics doi.org/10.1093/imamat/hxy065


14. arXiv:1707.00682
    Stretching convex domains to capture many lattice points
    International Mathematics Research Notices doi.org/10.1093/imrn/rny102


15. arXiv:1706.04170
    Triangles capturing many lattice points
    with Stefan Steinerberger
    Mathematika doi.org/10.1112/S0025579318000219


16. arXiv:1704.02962
    The Stability of the First Neumann Laplacian Eigenfunction Under Domain Deformations and Applications
    Applied and Computational Harmonic Analysis doi.org/10.1016/j.acha.2019.05.001


17. arXiv:1608.03628
    Time Coupled Diffusion Maps
    with Matthew Hirn
    Applied and Computational Harmonic Analysis doi.org/10.1016/j.acha.2017.11.003


18. arXiv:1607.05235
    Extracting Geography from Trade Data
    with Yuke Li, Tianhao Wu, and Stefan Steinerberger
    Physica A doi.org/10.1016/j.physa.2017.01.037

Notes

Some short notes on various topics

• some-math-for-numerics.pdf
  Introductory note about some key mathematical ideas for used in numerical methods including:
  asymptotic series, Richardson extrapolation, contraction mapping, and simple iteration.


• stirlings-approximation.pdf
  Elementary proof of Stirling's approximation up to constant using:
  concave functions, trapezoid rule, midpoint rule
  


• euler-maclaurin.pdf
  Informal and precise statements of Euler-Maclaurin formula with preliminaries about:
  asymptotic series, Richardson extrapolation, Taylor's theorem, Trapezoid rule
  


• gaussian-quadrature.pdf
  Introduction to Gaussian quadrature including discussion of:
  Legendre polynomials, Gaussian quadrature remainder formula, numerical example
  


• chebyshev-interpolation.pdf
  Introduction to polynomial interpolation focusing on:
  polynomial interpolation remainder formula, Chebyshev polynomials, Chebyshev nodes
  
  
• de-moivre-thm.pdf
  Sketch of de Moivre's central limit theorem involving:
  Binomial distribution, Stirling's formula, Reimann sum

Mentoring

• Summer undergraduate research 2020
  
  • I mentored Xiaorun Wu at Princeton
  • Paper: arXiv:2009.03208 (Journal of Number Theory)
• Summer undergraduate research 2018
  • I mentored a SUMRY group at Yale
  • Paper: arXiv:1902.06633 (Involve)

Teaching

• Fall 2023
  • Probability Theory, MTH 664, Oregon State University
• Spring 2023
  • Advanced Calculus II, MTH 312, Oregon State University
  • Probability III, MTH 465/565, Oregon State University
• Winter 2023
  • Probability II, MTH 464/564, Oregon State University
• Fall 2021
  • Numerical methods, MAT 321/APC 321, Princeton University
• Fall 2020
  • Numerical methods, MAT 321/APC 321, Princeton University
• Spring 2021
  • Linear Algebra with Applications, MAT 202, Princeton University
• Fall 2018
  • Calculus II, MATH 115, Yale University