Starting in October 2020, I will be 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.

Vishal Arul
MIT Department of Mathematics
77 Massachusetts Ave., Bldg. 2-239A
Cambridge, MA 02139, USA
Office: MIT, Simons Building (Building 2), 2-239A
Permanent email: varul.math@gmail.com
Institutional email: varul@mit.edu

# 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)

# 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.

# Expository

## Articles

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