I am a Heilbronn Fellow at University College London. I received my PhD in May 2020 from MIT, where I was a student of Bjorn Poonen.

My research interests lie in the intersection of algebraic geometry and number theory. I am currently particularly interested in the explicit arithmetic of superelliptic curves and jacobians.

Here is my CV.


Current Postal Address:
Department of Mathematics,
University College London,
Gower Street,
London WC1E 6BT, UK
Office: UCL, Department of Mathematics, Room 604
Permanent email: varul.math@gmail.com
Institutional email: v.arul@ucl.ac.uk


 

Research

Papers

  • Torsion points on Fermat quotients of the form \( y^{n} = x^{d} + 1 \) ,
    Submitted for publication,
    (pdf) (arXiv) (show abstract)
  • On the \(\ell\)-adic valuation of certain Jacobi sums,
    Submitted for publication,
    (pdf) (arXiv) (show abstract)
  • Division by \(1 - \zeta\) on superelliptic curves and jacobians,
    International Mathematics Research Notices, rnaa075,
    https://doi.org/10.1093/imrn/rnaa075,
    (
    pdf) (arXiv) (show abstract)
  • Computing Zeta Functions of Cyclic Covers in Large Characteristic,
    with Alex J. Best, Edgar Costa, Richard Magner, and Nicholas Triantafillou,
    The Open Book Series 2, no. 1 (2019): 37-53, (arXiv) (show abstract)
  • Parity-check multiplicity in binary cyclic codes,
    with Glen Frost and Derek Jung,
    Electronics Letters 49.23 (2013): 1456-1457, (show abstract)

Computer Programs

  • Hasse-Weil Zeta function of a cyclic cover of \(\mathbf{P}^{1}\) over finite fields, release 9.0 of SAGE computer algebra system (trac ticket)

 

Activities

Selected Research Talks

Poster Presentations

Seminars Organized


 

Teaching

√mathroots @ MIT

In Summer 2017-2019, I served as the Academic Coordinator for √mathroots @ MIT, a 14-day mathematical talent accelerator summer program hosted by MIT PRIMES for high-potential high school students from underrepresented backgrounds or underserved communities who are interested in exploring creative topics in mathematics and problem solving. As Academic Coordinator, I designed the curriculum, hired the mentors, and gave lectures for the program. In Summer 2016 and Summer 2020, I served as an academic mentor for the program.

√mathroots @ MIT received a 2020 AMS Epsilon Award, was featured on the MIT Homepage, and was covered by MIT News, Notices of the AMS, and AMS News.

Talks

Mentorship

Awards

Recitation Websites


 

Expository

Articles

  • Bounding the prime gaps (received the 2015 Stanford University Department of Mathematics Undergraduate Research Award for an outstanding honors senior thesis) (pdf)

Selected Talks