Isabel Vogt
(Photo by Joe Rabinoff.)

I am a fifth year PhD student in Mathematics at MIT advised by Bjorn Poonen and Joe Harris. I expect to graduate in June 2019, and am on the academic job market this year.

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.

For the 2018-2019 academic year, I am a visiting student at Stanford University, working with Ravi Vakil.

Here is my CV.

Current Postal Address:
Stanford University
Department of Mathematics
450 Serra Mall, Building 380
Stanford, CA 94305-2125
Office: Stanford University, Sloan Hall 381B
Email address: ivogt (guess) mit.edu, vogti (guess) stanford.edu


 

Research

Papers

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

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

  • Interpolation for Brill-Noether curves in P^4, with Eric Larson
    (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
    (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 Travel

  • November 30, Georgia Tech, Algebra seminar
  • December 3, University of Illinois at Chicago, Colloquium
  • January 18, JMM Special Session on Arithmetic Statistics
  • March 22-24, AMS Sectional Meeting in Honolulu, Special Session on Arithmetic Geometry and Its Connections
  • June 3-7, ICERM workshop on Arithmetic of Low-Dimensional Abelian Varieties

Seminars

  • Fall 2018, I'm co-organizing the Stanford Student Algebraic Geometry Seminar (SAGS) with Libby Taylor. See the SAGS schedule for more information.

Conferences



 

Teaching

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

Old expository papers and presentations I have prepared which may be of interest:

  • 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)