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Caltech
Yuxin Lin

Yuxin Lin

I am a fifth year math PhD student at Caltech, working under Elena Mantovan. I am interested in number theory and algebraic geometry, especially p-divisible groups associated to abelian varieties. I did my undergraduate studies at University of Notre Dame. I can speak Mandarin, English, Japanese, Cantonese and Teochew.

Research

I have conducted research in:

  1. Arithmetic Geometry: I have done projects studying the stratification of moduli spaces of curves by discrete invariants.
    I am currently doing a project on the structure of the ring of automorphic forms on certain Shimura varieties.
  2. Algebraic Geometry/ Coding Theory: I have worked on a project to compute the generalized hamming weights of projective Reed Muller codes using techniques in algebraic geometry.
  3. Discrete math: I have done some projects on statistical questions in number rings, numerical semigroups and their higher dimensional counterparts.

Here is a list of my published papers:

  1. On a Conjecture of Ghorpade, Datta and Beelen for the Number of Points of Varieties over Finite Fields (With D. Singhal). (2025) European Journal of Mathematics. https://doi.org/10.1007/s40879-025-00844-7
  2. Abelian covers of P1 of p-ordinary Ekedahl-Oort type (with E. Mantovan, D. Singhal). (2024) International Mathematics Research Notes. https://doi.org/10.1093/imrn/rnae241
  3. Density questions in rings of the form 𝓞𝑲 [𝜸]⋂𝑲 (With D.Singhal). (2023) International Journal of Number Theory, https://doi.org/10.1142/S1793042124500581
  4. Primes in denominators of Algebraic Numbers (With D.Singhal). (2023) International Journal of Number Theory, https://doi.org/10.1142/S1793042124500167
  5. Density of Numerical sets associated to a Numerical semigroup (with D. Singhal). (2021) Communications in Algebra, 49:10, 4291-4303, DOI: 10.1080/00927872.2021.1918136
  6. Frobenius allowable gaps of Generalized Numerical Semigroups (with D. Singhal). (2022) Electronic Journal of Combinatorics. Volume 29, Issue 4. https://doi.org/10.37236/10748
  7. The Limiting Spectral Measure for an Ensemble of Generalized Checkerboard Matrices (with F. Chen, S. J. Miller, J.Yu). (2021) The PUMP Journal of Undergraduate Research, 4, 202-221. https://journals.calstate.edu/pump/article/view/2544

Here is a list of my preprints:

  1. Non mu-ordinary Newton polygons in the Torelli Locus (With D. Singhal and E. Mantovan). https://arxiv.org/abs/2406.09632
  2. The p-rank stratification of the moduli space of double covers of a fixed elliptic curve (with K. Chang, D. Dragutinovic, S. Groen, D. Singhal). arXiv:2502.09540
  3. Largest zero-dimensional intersection of r degree d hypersurfaces in (with D. Singhal). arXiv:2507.05732

Teaching

  • Primary Instructor – Math 1d: Calculus Series and Math 8: Problem Solving in Calculus:
    Designed and delivered lectures, developed course syllabi and materials, and supported students through office hours.
  • Teaching Assistant – Graduate courses (Algebraic Topology, Abstract Algebra) and undergraduate calculus & linear algebra:
    Led recitation sessions, graded assignments, and prepared students for qualifying exams.
  • Mentoring & Outreach – Problem Session Leader at Preliminary Arizona Winter School (2023); Math Help Room and Math Bunker Tutor, University of Notre Dame (2019–2020).

Email: [email protected]

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Teaching CV
Teaching CV