 
Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
K3 surfaces, modular forms, and
nongeometric heterotic compactifications
Dave Morrison
UCSB
Friday, January 14, 2011, 4:00 p.m.
Room 6635 South Hall
Abstract: Type IIB string theory has an SL(2, Z) symmetry and a complex scalar
field valued in the upper half plane, on which SL(2, Z) acts by fractional linear
transformations; this naturally suggests building models in which is allowed to
vary. Although the SL(2, Z)invariant function j() can reveal some of the structures
of these models, for their full construction and study we need SL(2, Z) modular forms,
particularly the Eisenstein series E4() and E6() and the corresponding Weierstrass
equations. The Weierstrass equations can also be analyzed in algebraic geometry via
the theory of elliptic curves. This approach leads to the "Ftheory" compactifications
of type IIB theory.
Similarly, the heterotic string compactified on T2
