Travis Scholl

My research interests include elliptic curves and computational algebraic number theory.

Teaching

University California, Irvine

• Math 2E Fall 2018
• Math 120B Spring 2019
• Math 173B Winter 2019
• Math 3A Winter 2019
• Math 2E Fall 2018

University of Washington

• Math 125 Calculus II Summer 2017
• Math 125 Calculus II Summer 2016
• Math 125 Calculus II Summer 2015
• Math 125 Calculus II Summer 2014

Publications

• Adventures in Supersingularland. Experimental Mathematics. 2021.
• Products and polarizations of super-isolated abelian varieties. Mathematische Zeitschrift. 2021.
• Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant. Algebra & Number Theory. 2021.
• Super-Isolated Abelian Varieties. Journal of Number Theory. 2020.
• Abelian Varieties with Small Isogeny Class and Applications to Cryptography. PhD Thesis, University of Washington. 2018.
• Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography. Experimental Mathematics. 2018.
• Isolated elliptic curves and the MOV attack. Journal of Mathematical Cryptology. 2017.

Contact

Travis Scholl on GitHub

Travis Scholl on GitLab

Travis Scholl on LinkedIn

Outreach

AWM

I am a member of the University of Washington chapter of the Association for Women in Mathematics. I believe that promoting equality in STEM fields is extremely important.

WXML

The Washington Experimental Math Lab is an oppurtunity for teams of undergraduates to work on a project in math research with graduate student and faculty mentors. I have mentored the following projects.

• Fall 2017, Winter 2018, Spring 2018: Rational Points on Curves

  Learn about diophantine equations such as Pell's equation and Thue equations. Solutions to these equations have algebraic, analytic, and geometric interpretations. The goal of the project is to eventually search for rational points on higher genus curves (with genus at least 2). The results of the search will be compared with the uniformity conjecture. Later in the year, the focus was on projective algebraic curves, Siegel's Theorem, Falting's Theorem, and how to compute the genus of a curve. This included writing Sage code to compute rational points of genus 2 curves and compare the results with the LMFDB project.

• Spring 2017: Atkin-Goldwasser-Kilian elliptic Curve Primality Test

  Implement the elliptic curve primality test (which requires an implementation of Schoof's point counting algorithm on curves over finite rings) and compare timings with the previous primality tests. This requires learning some background on elliptic curve arithmetic.

• Winter 2017: Agrawal–Kayal–Saxena primality Test

  Implement the AKS primliaty test in Sage. Compare timings against brute force and standard probabilistic primality tests.

• Fall 2016: Experimental Evidence for the Bateman-Horn Conjecture

  Use Sage to gather evidence for the Bateman-Horn conjecture which gives an asymptotic density for how often a finite set of polynomials takes on prime values.

• Spring 2016: Wikipedia Taskforce

  Contribute sequences to The On-Line Encyclopedia of Integer Sequences® (OEIS®) database and new images of graphs to wikipedia articles.

Math Day

Math Day is an event for over a thousand high school students to come to UW and see some lectures about math/science. I have volunteered at Math Day the past four years. The past three years I have led the Sage workshop, which gives students a chance to explore programming and math. I have written my own cryptography focused worksheet so that they can also be exposed to some math behind modern cryptography.

Julia Robinson Math Festival

The Julia Robinson Math Festival is an event for elementary through high school students to visit UW and explore math. I have volunteered at the festival the past three years.

Employment

Visiting Assistant Professor University of California, Irvine (2018 - present)

As a VAP I write and give lectures, write exams, hold office hours, and evaluate student performance.

Teaching Assistant/Instructor University of Washington (2013 - 2018)

As a teaching assitant I grade exams, lead quiz sections, and hold office hours. I also teach my own classes where I am responsible for writing exams and assigning final grades.

Web Developer, University of Washington (2015-2017)

Lead developer, project manager, product designer, graphic designer, UI/UX developer, quality assurance, and support for an online math homework system called Hamstr.

Contract Web Designer (2013-2016)

I helped build and redesign websites for professors in math education at Virginia Tech, University California at San Diego, and Portland State University. This included rewriting HTML and CSS as well as implementing discussion boards and user accounts in PHP.

• IOLA
• TAAFU

Math Librarian, University of Oregon (2012-2013)

I worked in the Math Library at the University of Oregon during as an undergraduate. I learned about library systems as well as helped tutor students in math.

Pictures

Elliptic Curve

Riemann Sums

Abby