Isabel Vogt
(Photo by Joe Rabinoff.)

I am currently an NSF postdoc at Stanford University, working with Ravi Vakil. I received my PhD in June 2019 from MIT, where I was a student of Bjorn Poonen and Joe Harris. Beginning in September 2020, I will be an assistant professor at University of Washington at Seattle.

My research is in the intersection of algebraic geometry and number theory. I am currently particularly interested in the geometry of algebraic curves and applications of geometric methods to rational points.

Together with Eric Larson and Ravi Vakil, I organize the Stanford Algebraic Geometry Seminar.

Here is my CV.

Current Postal Address:
Stanford University
Department of Mathematics
450 Jane Stanford Way, Building 380
Stanford, CA 94305-2125
Office: Stanford University, Sloan Hall 382-N
Permenant email: ivogt.math (guess) gmail.com
Institutional email: vogti (guess) stanford.edu


 

Research

Papers

  • Stability of normal bundles of space curves, with Izzet Coskun and Eric Larson
    (pdf) (arXiv) (show abstract)

  • An enriched count of the bitangents to a smooth plane quartic curve, with Hannah Larson
    (pdf) (arXiv) (show abstract) (video)

  • Low degree points on curves, with Geoffrey Smith
    (pdf) (arXiv) (show abstract) (video)

  • A local-global principle for isogenies of composite degree,
    (pdf) (arXiv) (show abstract)

  • Interpolation for Brill-Noether curves in P^4, with Eric Larson
    European Journal of Mathematics, to appear (pdf) (arXiv) (show abstract)

  • Abelian varieties isogenous to a power of an elliptic curve over a Galois extension,
    Journal de Théorie des Nombres de Bordeaux, to appear (pdf) (arXiv) (show abstract)

  • Constants in Titchmarsh divisor problems for elliptic curves,
    with Renee Bell, Cliff Blakestad, Alina Cojocaru, Alex Cowan, Nathan Jones, Vlad Matei, and Geoffrey Smith
    Research in Number Theory, to appear (pdf) (arXiv) (show abstract)

  • Elliptic fibrations on covers of the elliptic modular surface of level 5,
    with Francesca Balastrieri, Julie Desjardins, Alice Garbagnati, Céline Maistret, and Cecília Salgado,
    WINE II: Contributions to Number Theory and Arithmetic Geometry, AWM Springer Series 11 (2018)
    (pdf) (book) (arXiv) (show abstract)

  • Interpolation for Brill-Noether space curves,
    manuscripta mathematica 156(1), (2018) (pdf) (journal) (arXiv) (show abstract)

  • Powers in Lucas sequences via Galois representations, with Jesse Silliman,
    Proc. Amer. Math. Soc., 143 (2015) (pdf) (journal) (arXiv) (show abstract)

Computer Programs

  • Binary Recurrence Sequences, release 5.13 of SAGE computer algebra system (trac ticket)



 

Activities

Upcoming (Virtual) Travel

Conferences



 

Teaching

Arizona Winter School Problem Set

Recitation Websites

Notes and Problems

  • A presentation I gave on MIT PRIMES Circle at the MIT SEPT program in June, 2015: (pdf)
  • Linear Algebra Problems:
  • Functions, Differential Calculus, Point-Set Topology Problems:
  • A (very brief) Introduction to LaTeX for math students: (pdf) (tex)


 

Expository Writing

Published Writing

Older expository papers and presentations

  • The Local Langlands Correspondence for GL_n over a p-adic Field (pdf)
  • Vector Fields on Spheres (pdf)
  • Lefschetz Fixed Point Theorem (pdf)
  • A Brief History of Homotopy Theory (slides from talk for the Harvard History of Math Seminar) (pdf)
  • An Introduction to the Euler Characteristic (pdf)