Christopher Lyons

Research

Research interests:

• Algebraic geometry and number theory

Papers

1. A simple formula for the Picard number of K3 surfaces of BHK type (With B. Olcken), Kyoto J. Math. 60 (2020), no. 3, 941–964
2. Some results on surfaces with p_g = q = 1 and K^2=2 (With P. Lewis), Int. Math. Res. Not. 2018 (2018), no. 6, 1878--1919
   • Computer code and data for this paper.
3. The secret life of 1/n: A journey far beyond the decimal point The Mathematics Enthusiast 13 (2016), no. 3, 189--216
4. The mirror symmetry of K3 surfaces with non-symplectic automorphisms of prime order (With P. Comparin, N. Priddis, and R. Suggs), Adv. Theor. Math. Phys. 18 (2014), no. 6, 1335--1368
5. The Tate Conjecture for a family of surfaces of general type with p_g = q = 1 and K^2=3 Amer. J. Math. 137 (2015), 281--311
   • Computer code and data for this paper.
6. A rank inequality for the Tate Conjecture over global function fields Expos. Math. 27 (2009), no. 2, 93--108.
   • Corrigendum for the published version

Preprints

1. A family of surfaces with p_g=q=1, K^2=2, and large Picard number Submitted.
   • Computer code and data for this paper.

Other

• Our Primitive Roots Extended notes from an undergraduate talk on decimal expansions, primitive roots, and class numbers.
  (The article The secret life of 1/n above is based upon these notes. But the article contains quite a bit more and is generally more accessible, so that might be a better place to start.)