Photo Credit: Marcy Daniels

Photo courtesy of Marcy L. Daniels

  Harris B. Daniels
office 203 Seeley Mudd
e-mail hdaniels AT amherst DOT edu
phone 413-542-5656
office hours M: 10:00am - 10:50am & 1:00pm - 3:00pm
W: 10:00am - 10:50am & 2:00pm - 3:00pm
F: 1:00pm - 2:00pm
about me
My research interests lie generally in the field of algebraic number theory and arithmetic geometry, but more specifically include elliptic curves, hyperelliptic curves, and Galois representations associated to torsion points of elliptic curves. I received my Ph.D. in 2013 under Álvaro Lozano-Robledo.
  Research Statement
  Teaching Statement
current courses Math 105 - Calculus with Algebra
  Math 271 - Linear Algebra
past courses Math 111 - Introduction to the Calculus
  Math 271 - Linear Algebra
  Math 350 - Groups, Rings and Fields
  Math 355 - Introduction to Analysis
  Math 359 - An Introduction to the p-adic Numbers
  Math 450 - Functions of a Real Variable
[9] Torsion subgroups of rational elliptic curves over the compositum of all extensions of generalized D4-type (Submitted, Magma Code)
[8] Bounds of the rank of the Mordel-Weil group of jacobians of hyperelliptic curves (Submitted, Magma Code and Data)
joint with
Álvaro Lozano-Robledo and Erik Wallace
[7] What is... an Elliptic Curve (Notices of the American Mathematical Society., Vol 64, Issue 3, March 2017, pp. 241-243)
joint with
Álvaro Lozano-Robledo
[6] On the Ranks of Elliptic Curves with Isogenies (Int. J. Number Theory 13 (2017), no. 9, 2215–2227, Data)
joint with Hannah Goodwillie
[5] Torsion Points on Rational Elliptic Curves Over the Compositum of All Cubic Fields (To Appear in Math. Comp.)
joint with Álvaro Lozano-Robledo, Filip Najman, and Andrew V. Sutherland
[4] Elliptic curves with maximally disjoint division fields (Acta Arith., Vol. 175, No. 3 (2016), 211-223)
joint with Jeffrey Hatley and James Ricci


On the Number of Isomorphism Classes of CM Elliptic Curves Defined Over a Number Field,
joint with Álvaro Lozano-Robledo (J. Number Theory, Volume 157, December 2015, Pages 367–396)
An Infinite Family of Serre Curves (J. Number Theory, Volume 155, October 2015, Pages 226247)
Siegel Functions, Modular Curves, and Serre's Uniformity Problem (Albanian J. Math. 9, (2015), no. 1, Pages 3-29. )
Ph.D. Thesis: Siegel Functions, Modular Curves, and Serre's Uniformity Problem (DigitalCommons)