Higher Chow Cycles Arising from Some Laurent Polynomials

Explore a one-hour lecture on higher Chow cycles arising from Laurent polynomials, delivered by Tokio Sasaki from the University of Miami. Delve into the construction of Calabi-Yau hypersurface sections in toric Fano varieties using pencils defined by Laurent polynomials. Examine how non-trivial families of higher Chow cycles can be constructed from rational irreducible components on the base locus. Investigate two examples of such families and their significant properties related to higher normal functions. Discover the B-model explanation of Golyshev's Apéry constant on rank one Fano threefolds, illustrating the arithmetic mirror conjecture. Analyze a second example defined on general cubic fourfolds containing a plane, exploring its potential connection to the rationality problem through the identification of 2-torsion parts in Brauer groups and indecomposable cycles.