# Matt Kerr

## Algebraic K-theory of Toric Hypersurfaces

We describe how to use toric data to construct relative higher Chow
cycles for families of Calabi-Yau (n-1)-folds. The regulator
"periods" of such elements, which may be regarded as generalized
"normal functions", satisfy an inhomogeneous Picard-Fuchs equation
related to the Yukawa coupling. This setting leads to motivic proofs
of irrationality of zeta(2) and zeta(3) and unusual series
expressions for arithmetic constants. We will also explain relations
to Mahler measure, modular forms, and local mirror symmetry. The
first half of the talk will feature a detailed geometric example for
an elliptic curve family, emphasizing the direct relationship between
regulators on higher Chow cycles and Griffiths's Abel-Jacobi mapping
for usual algebraic cycles.