Yassine El Maazouz


I am a Harry Bateman Postdoctoral Scholar in the Division of Physics, Mathematics and Astronomy at Caltech. My faculty mentor is Matilde Marcolli.

My research interests include: Algebraic and Non-Archimedean Geometry, Commutative Algebra, Combinatorics and Mathematical Physics.

Address: Mathematics Department, Caltech, 1200 E.California Blvd. Pasadena, CA 91125, USA.

Email: maazouz [at] caltech [dot] edu

Research

On:     [arXiv] [Google scholar] [MathScinet]

Preprints

  1. Totally positive skew-symmetric matrices (with Jonathan Boretsky and Veronica Calvo Cortes)
    (submitted) [arxiv]

  2. Gram Matrices for Isotropic Vectors (with Bernd Sturmfels and Svala Sverrisdóttir)
    (submitted) [arxiv]

  3. Spinor-Helicity Varieties (with Anaëlle Pfister and Bernd Sturmfels)
    (submitted) [arxiv]

Publications

  1. The positive orthogonal Grassmannian (with Yelena Mandelshtam)
    To appear in Le Matematiche special volume on Positive Geometry. [arxiv][journal]

  2. Sampling from $p$-adic algebraic manifolds. (with Enis Kaya)
    To appear in SIAM Journal on Applied Algebra and Geometry. [arxiv][journal]

  3. $\mathrm{GL}(n,\mathbb{Z}_p)$-invariant Gaussian measures on the space of $p$-adic polynomials. (with Antonio Lerario)
    Electronic Journal of Probability. Vol. 30 (2025) [arxiv][journal]

  4. On the topology of the moduli of tropical unramified $p$-covers (with Paul A. Helminck, Felix Röhrle, Pedro Souza, and Claudia Yun)
    Selecta Mathematica Vol. 31, N. 14, (2025) [arxiv] [journal]

  5. The Bernoulli clock: probabilistic and combinatorial interpretations of the Bernoulli polynomials by circular convolution. (with Jim Pitman)
    Combinatorics, Probability and Computing. Vol. 33, Issue 2, March 2024, pp. 210-237. [arxiv] [journal]

  6. Tropical invariants for binary quintics and reduction types of Picard curves. (with Paul A. Helminck and Enis Kaya)
    Glasgow Mathematical Journal. Vol. 66 , Issue 1, January 2024, pp. 65-87. [arxiv] [journal]

  7. Lines on $p$-adic and real cubic surfaces. (with Rida Ait El Manssour, Kemal Rose and Enis Kaya)
    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. Vol. 93, September 2023, pp. 149-162. [arxiv] [journal]

  8. Bolytrope orders. (with Gabriele Nebe and Mima Stanojkovski)
    International Journal of Number Theory. Vol. 19, Issue 05, June 2023, pp. 973-954. [arxiv] [journal]

  9. Orders and Polytropes: Matrix Algebras from Valuations. (with Marvin A. Hahn, Gabriele Nebe, Mima Stanojkovski and Bernd Sturmfels)
    Beiträge zur Algebra und Geometrie 63. Vol. 19, Issue 05, 2021, pp. 515-531 [arxiv] [journal]

  10. Valued rank-metric codes. (with Marvin A. Hahn, Alessandro Neri and Mima Stanojkovski)
    Journal of algebra and its applications. Vol 24 (2025), no. 4. [arxiv][journal]

  11. The Gaussian entropy map in valued fields.
    Algebraic statistics. Vol. 13, Issue 1, December 2022, pp. 1-18. [arxiv] [journal]

Conference Proceedings

  1. The positive orthogonal Grassmannian (with Yelena Mandelshtam)
    Proceedings of the 37th Conference on Formal Power Series and Algebraic Combinatorics (Sapporo 2025). [extended abstract]

Teaching

Caltech

UC Berkeley

Seminars

Caltech

Code

  1. Sampling from $p$-adic algebraic manifolds.
  2. Lines on $p$-adic and real cubic surfaces.
  3. Orders and Polytropes: Matrix algebras from valuations .
  4. Gaussian entropy map on the field of Puiseux series.
  5. Implementation of a Predictor-Corrector Interior Point Method in Arbitrary Precision.

Notes

Number theory

  1. Local Class field theory via Lubin Tate Formal groups
  2. Infinite Galois theory
  3. Abelian varieties (coming soon)

Probability

  1. On Choquet's theorem
  2. Conformal Martingales, Brownian Martingales and Integral Representation
  3. On Bessel processes
  4. Burkholder-Davis-Gundy inequalities

Representation theory and Harmoic analysis

  1. $p$-adic harmonic analysis
  2. Introduction to modular representation theory of finite groups
  3. A (very) brief introduction to symmetric spaces
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