02 / Maths Lab
Maths you can explore.
Choose an experiment. Change a parameter. Follow the mathematics back to the paper.
01 / Algebra & convex geometry
ECO & Complexity
Bound complexity. Count monomials and rational numbers. Watch the geometric picture emerge.
Degree · Rational height · Convex limits02 / Arakelov geometryArithmetic Heights
Explore Faltings heights of curves and exact Néron–Tate heights of tautological cycles on Jacobians.
Faltings heights · Néron–Tate cycles · Exact formulas03 / Arithmetic statisticsPolynomial Zeros
Draw an integer polynomial at random and see where its zeros fall in the complex plane.
Two conventions · Random samples · Complex zeros04 / Geometry & Diophantine problemsBounds & Invariants
Vary the genus to explore the Zhang–Kawazumi lower bound and the Looper–Silverman–Wilms torsion bound.
Lower bounds · Torsion points · Genus