Isabel Vogt
(Photo by Lori Nascimento.)

I am currently an assistant professor at Brown University. My work is partially supported by an NSF postdoc (DMS-1902743) and by DMS-2200655. I received my PhD in June 2019 from MIT, where I was a student of Bjorn Poonen and Joe Harris. During the 2019-2020 academic year I was an NSF postdoc at Stanford University, working with Ravi Vakil. During the 2020-2021 academic year I was an assistant professor at The University of Washington.

My research is in the intersection of algebraic geometry and number theory, including the geometry of algebraic curves and rational and low degree points on varieties.

Here is my CV, Google Scholar profile, mathscinet profile.

Current mailing address:
Brown University
Box 1917
151 Thayer Street
Providence, RI 02912
Office: Kassar House 315
Office Phone: (401) 863-1132
Permanent email: ivogt.math (guess) gmail.com
Institutional email: isabel_vogt (guess) brown.edu


I firmly believe Federico Ardila's basic axioms:

  • Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
  • Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
  • Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
  • Axiom 4. Every student deserves to be treated with dignity and respect.


 

Research

For a less-technical introduction to my research, watch my talk Interpolation problems for curves from YMC 2022.

Papers

  • Quadratic enrichment of the logarithmic derivative of the zeta function, with , , , and
    (pdf) (arXiv) (show abstract)

  • Subspace configurations and low degree points on curves, with
    (pdf) (arXiv) (show abstract)

  • Stability of Tschirnhausen bundles, with and
    (pdf) (arXiv) (show abstract)

  • Curve classes on conic bundle threefolds and applications to rationality,
    with , , and
    (pdf) (arXiv) (code) (show abstract)

  • The normal bundle of a general canonical curve of genus at least 7 is semistable,
    with and
    (pdf) (arXiv) (show abstract)

  • Interpolation for Brill--Noether curves, with
    (pdf) (arXiv) (show abstract) (Quanta article)

  • A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold, with , , , with an appendix by
    Research in Number Theory, 2022 (pdf) (arXiv) (journal) (show abstract)

  • Global Brill--Noether theory over the Hurwitz Space, with and
    (pdf) (arXiv) (show abstract)

  • Stability of normal bundles of space curves, with and
    Algebra and Number Theory, to appear (pdf) (arXiv) (show abstract)

  • An enriched count of the bitangents to a smooth plane quartic curve, with
    Research in the Mathematical Sciences, 2021 (pdf) (arXiv) (journal) (show abstract) (video)

  • Low degree points on curves, with
    International Mathematics Research Notices, 2020 (pdf) (arXiv) (journal) (show abstract) (video)

  • A local-global principle for isogenies of composite degree,
    Proceedings of the London Mathematical Society, 2020 (pdf) (arXiv) (code) (journal, errata) (show abstract)

  • Interpolation for Brill-Noether curves in P^4, with
    European Journal of Mathematics, 2020 (pdf) (arXiv) (journal) (show abstract)

  • Abelian varieties isogenous to a power of an elliptic curve over a Galois extension,
    Journal de Théorie des Nombres de Bordeaux, 31(1): 205-213, 2019 (pdf) (arXiv) (journal) (show abstract)

  • Constants in Titchmarsh divisor problems for elliptic curves,
    with , Cliff Blakestad, , , , and
    Research in Number Theory, 6(1): Art. 1, 24, 2020, (pdf) (arXiv) (journal) (show abstract)

  • Elliptic fibrations on covers of the elliptic modular surface of level 5,
    with , , , , and
    WINE II: Contributions to Number Theory and Arithmetic Geometry, AWM Springer Series 11 (2018)
    (pdf) (arXiv) (book) (show abstract)

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

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

Computer Programs

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



 

Activities

Upcoming (Hybrid) Travel

  • October 7, Number theory seminar, UVA
  • October 19, Colloquium, Rutgers University
  • October 21, Colloquium, Virgina Tech
  • October 25, Colloquium, CCR Princeton
  • October 25, Algebraic geometry seminar, Princeton
  • November 3, Algebra, Geometry, and Number Theory Seminar, Tufts
  • November 15, Distinguished Colloquium Series of the Turkish Mathematical Society
  • December 10-11, Palmetto Number Theory Series, University of South Carolina
  • January -- May 2023, MSRI semester on Diophantine Geometry, Berkeley CA
  • June 18-24 2023, Recent Trends in Algebraic Geometry, Oberwolfach
  • July 3-7 2023, GAeL, University of Warwick, UK
  • August 6-11 2023, Curves: Algebraic, Tropical, and Logarithmic, BIRS

Conferences



 

Teaching

Teaching on Zoom
Teaching on Zoom
(cartoon by UW student Maya Vita)

Current Teaching

  • Fall 2022: Math 1530 Abstract Algebra: Groups, Rings and Fields at Brown University

Previous Teaching

  • Fall 2021: Math 540 Honors Linear Algebra at Brown University
  • Winter 2021: Math 308 Linear Algebra at UW
  • Fall 2017: 18.06 Linear Algebra at MIT

Arizona Winter School Problem Set



 

Expository Writing

Published Writing

  • Global Brill--Noether theory over the Hurwitz space,
    for the ZAG’s Handbook of Modern Algebraic Geometry (2020–21), (pdf)

  • Practical Suggestions for Mathematical Writing,
    with , , ,
    Notices of the American Mathematical Society, 2021 (pdf)

  • A Guide to Organizing a Virtual Conference, with and
    Notices of the American Mathematical Society, 2020 (pdf)

  • How to organize a graduate workshop, with
    Notices of the American Mathematical Society, 2019 (pdf)

  • Thinking positive: arithmetic geometry in characteristic p,
    with , , and
    Notices of the American Mathematical Society, 2019 (pdf)