Scholars@Duke

• Background
• 

  Education, Training, & Certifications

  • Ph.D., University of California - Los Angeles 2016
• 

  Previous Appointments & Affiliations

  • Scholar in Residence of Mathematics, Mathematics, Trinity College of Arts & Sciences 2020
• 

  Academic Positions Outside Duke

  • Research Member, Mathematical Sciences Research Institute. 2021
  • NSF Postdoctoral Scholar, Stanford University. 2019
  • Stein Fellow, Stanford University. 2019 - 2020
  • NSF Assistant Adjunct Professor, University of California, Los Angeles. 2017 - 2018
  • NSF Postdoctoral Scholar, Stanford University. 2016 - 2017
• Recognition
• 

  Awards & Honors

  • New Researcher Award, honorable mention. Bernoulli Society. 2019
• Expertise
• 

  Subject Headings

  • Additive combinatorics
  • Extremal combinatorics
  • Functional analysis
  • Graph theory
  • Large deviations
  • Mathematical physics
  • Partial differential equations
  • Probability theory and stochastic processes
  • Random graphs
  • Random matrices
  • Statistical physics
• Research
• 

  Selected Grants

  • RTG: Training Tomorrow's Workforce in Analysis and Applications awarded by  National Science Foundation 2021 - 2026
  • Large Deviations and Extremes for Random Matrices, Tensors, and Fields awarded by  National Science Foundation 2022 - 2025
• 

  Fellowships, Supported Research, & Other Grants

  • Stein Fellowship awarded by Department of Statistics, Stanford University 2019 - 2020
  • NSF Postdoctoral Research Fellowship awarded by National Science Foundation 2016 - 2019
• 

  External Relationships

  • F. Hoffmann-La Roche Ltd
• Publications & Artistic Works
• 

  Selected Publications

  • Academic Articles

    • Cook, N. A., et al. “Universality of Poisson Limits for Moduli of Roots of Kac Polynomials.” International Mathematics Research Notices, vol. 2023, no. 8, Apr. 2023, pp. 6648–90. Scopus, doi:10.1093/imrn/rnac021.
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    • Cook, N., et al. “Non-Hermitian Random Matrices with a Variance Profile (II): Properties and Examples.” Journal of Theoretical Probability, vol. 35, no. 4, Dec. 2022, pp. 2343–82. Scopus, doi:10.1007/s10959-021-01140-2.
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    • Cook, N. A., et al. “Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices.” Annales De L’Institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 4, Nov. 2022, pp. 2284–320. Scopus, doi:10.1214/21-AIHP1225.
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    • Cook, Nicholas A., et al. Universality of Poisson limits for moduli of roots of Kac polynomials. May 2021.
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    • Cook, Nicholas A., et al. Regularity method and large deviation principles for the Erdős--Rényi hypergraph. Feb. 2021.
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    • Cook, Nicholas A., and Hoi H. Nguyen. Universality of the minimum modulus for random trigonometric polynomials. Jan. 2021.
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    • Cook, N. A., and H. H. Nguyen. “Universality of the minimum modulus for random trigonometric polynomials.” Discrete Analysis, vol. 2021, Jan. 2021. Scopus, doi:10.19086/da.28985.
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    • Cook, N., and A. Dembo. “Large deviations of subgraph counts for sparse Erdős–Rényi graphs.” Advances in Mathematics, vol. 373, Oct. 2020. Scopus, doi:10.1016/j.aim.2020.107289.
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    • Cook, N., and O. Zeitouni. “Maximum of the Characteristic Polynomial for a Random Permutation Matrix.” Communications on Pure and Applied Mathematics, vol. 73, no. 8, Aug. 2020, pp. 1660–731. Scopus, doi:10.1002/cpa.21899.
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    • Cook, N. “The Circular Law for random regular digraphs.” Annales De L’Institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 4, Jan. 2019, pp. 2111–67. Scopus, doi:10.1214/18-AIHP943.
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    • Cook, N. “Lower bounds for the smallest singular value of structured random matrices.” Annals of Probability, vol. 46, no. 6, Nov. 2018, pp. 3442–500. Scopus, doi:10.1214/17-AOP1251.
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    • Basak, A., et al. “Circular law for the sum of random permutation matrices.” Electronic Journal of Probability, vol. 23, Jan. 2018. Scopus, doi:10.1214/18-EJP162.
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    • Cook, N., et al. “Non-hermitian random matrices with a variance profile (I): Deterministic equivalents and limiting ESDs.” Electronic Journal of Probability, vol. 23, Jan. 2018. Scopus, doi:10.1214/18-EJP230.
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    • Cook, Nicholas, et al. “Size biased couplings and the spectral gap for random regular graphs.” The Annals of Probability, vol. 46, no. 1, Institute of Mathematical Statistics, Jan. 2018. Crossref, doi:10.1214/17-aop1180.
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    • Cook, N. “The circular law for random regular digraphs with random edge weights.” Random Matrices: Theory and Application, vol. 6, no. 3, July 2017. Scopus, doi:10.1142/S2010326317500125.
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    • Cook, N. A. “On the singularity of adjacency matrices for random regular digraphs.” Probability Theory and Related Fields, vol. 167, no. 1–2, Feb. 2017, pp. 143–200. Scopus, doi:10.1007/s00440-015-0679-8.
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    • Cook, N. A. “Discrepancy properties for random regular digraphs.” Random Structures and Algorithms, vol. 50, no. 1, Jan. 2017, pp. 23–58. Scopus, doi:10.1002/rsa.20643.
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    • Cook, Nicholas A., et al. Non-Hermitian random matrices with a variance profile (I): Deterministic equivalents and limiting ESDs. Dec. 2016.
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    • Cook, Nicholas A. Dense random regular digraphs: singularity of the adjacency matrix. Mar. 2014.
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    • Cook, Nicholas A., et al. “Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices (Accepted).” To Appear in Annales De L’Institut Henri Poincaré (B) Probabilités Et Statistiques.
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  • Preprints

    • Cook, Nicholas A., et al. Full large deviation principles for the largest eigenvalue of sub-Gaussian Wigner matrices. 28 Feb. 2023.
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    • Cook, Nicholas A., and Amir Dembo. Typical structure of sparse exponential random graph models. 12 Aug. 2022.
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• Teaching & Mentoring
• 

  Recent Courses

  • MATH 340: Advanced Introduction to Probability 2023
  • MATH 641: Probability 2023
  • MATH 740: Advanced Introduction to Probability 2023
  • STA 231: Advanced Introduction to Probability 2023
  • MATH 340: Advanced Introduction to Probability 2022
  • MATH 740: Advanced Introduction to Probability 2022
  • MATH 790-90: Minicourse in Advanced Topics 2022
  • STA 231: Advanced Introduction to Probability 2022
  • MATH 641: Probability 2021
• 

  Advising & Mentoring

  • Haotian Gu, PhD, Duke, 2021-present
    
    Mentored 3 Duke undergraduate students in a DOMath research project on "Structure and stability for Brascamp–Lieb inequalities", Summer 2022.
    
    Pengda Liu, undergraduate honors thesis, Stanford, 2019-2020.
• 

  Teaching Activities

  • In Summer 2022 I gave a 5-lecture course on "Geometric Methods in Random Matrix Theory" at the University of Michigan Random Matrix Theory Summer School .  
    
    In Summer 2022 I led a project for the Duke math department's DoMath summer undergraduate research program.
• Scholarly, Clinical, & Service Activities
• 

  Presentations & Appearances

  • Structure and stability for sparse exponential random graphs. Conference on Random Matrix Theory and Numerical Linear Algebra. June 24, 2022  2022
  • Geometric Methods in Random Matrix Theory. Random Matrix Theory Summer School. June 2022  2022
  • Structure and stability for sparse exponential random graphs. Southeastern Probability Conference (SEPC). May 2022  2022
  • Structure and stability for sparse exponential random graphs. Probability Seminar. Cornell University Math Dept.. April 2022  2022
  • Structure and stability for sparse exponential random graphs. Probability Seminar. Lehigh, Northwestern, UMN. April 2022  2022
  • Large deviations and the regularity method for sparse random hypergraphs. Probability Seminar. Centre de recherches mathématiques. December 1, 2021  2021
  • Universalidad en los extremos de polinomios aleatorios (in Spanish). Seminario de Probabilidad Hispanohablante. November 22, 2021  2021
  • Large deviations and regularity method for sparse random hypergraphs. Probability and Combinatorics Seminar. Ohio State University. October 7, 2021  2021
  • Large deviations and regularity method for sparse random hypergraphs. Probability Seminar. MIT. October 4, 2021  2021
  • Large deviations and the regularity method for the Erdős–Rényi (hyper)graph. Probability Seminar. University of California, Berkeley. September 29, 2021  2021
  • Large deviations and the regularity method for the Erdős–Rényi (hyper)graph. One World Probability Seminar. June 17, 2021  2021
  • Regularity method and large deviation principles for the Erdős–Rényi hypergraph. Combinatorics seminar. University of Warwick. June 11, 2021  2021
  • Universality for the min-modulus of random trigonometric polynomials. Probability Seminar. University of Chicago. April 2, 2021  2021
  • Universality for the minimum modulus of random trigonometric polynomials. Probability and Analysis Webinar. March 1, 2021  2021
  • Universality for the minimum modulus of random trigonometric polynomials. Probability Seminar. City University of New York. February 23, 2021  2021
  • Universality for the minimum modulus of random trigonometric polynomials. Probability Seminar. University of Southern California. February 19, 2021  2021
  • Universality for the minimum modulus of random trigonometric polynomials. Probability Seminar. Duke University. February 18, 2021  2021
  • Universality for the minimum modulus of random trigonometric polynomials. Probability and the City Seminar. Columbia University & Courant Institute. January 22, 2021  2021
  • The minimum modulus for random trigonometric polynomials. Probability seminar. University of British Columbia. November 2020  2020
  • Branching Brownian motion and the road-field model. Probability seminar. University of California, Berkeley. May 2020  2020
  • A branching Brownian motion perspective on the Road-Field Model. Applied Mathematics Seminar. Stanford University. February 2020  2020
  • Sparse exponential random graphs. Centre International de Rencontres Mathématiques. January 2020  2020
  • Convergence to Brown’s spectral measure for polynomials in Ginibre matrices. Latin American Congress of Probability and Mathematical Statistics. December 2019  2019
  • Large Deviations for Sparse Erdos–Renyi Graphs. Advances in Asymptotic Probability in Honor of Amir Dembo's 60th Birthday . December 2018  2018
• 

  Outreach & Engaged Scholarship

  • Instructor. Math Circles. Duke University. January 2022 - April 2022  2022

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