SPECIAL LECTURES

Lectures on Special Lagrangian Submanifolds

These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer an appropriate language for describing many significant features of the Strominger-Yau-Zaslow approach to mirror symmetry.

Abstracts of invited special lectures

s of invited special lectures WILLIAM A. HOWARD, Aspects of proof theory and foundations, 1950–1985. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA. E-mail: [email protected]. The motivating question for me in the early 1950s was as follows. Functional analysis, developed within the framework of se...

Lectures

ov 2 00 1 Lectures on special Lagrangian geometry

Calabi–Yau m-folds (M,J, ω,Ω) are compact complex manifolds (M,J) of complex dimension m, equipped with a Ricci-flat Kähler metric g with Kähler form ω, and a holomorphic (m, 0)-form Ω of constant length |Ω| = 2. Using Algebraic Geometry and Yau’s solution of the Calabi Conjecture, one can construct them in huge numbers. String Theorists (a species of theoretical physicist) are very interested ...

TASI lectures: special holonomy in string theory and M-theory

A brief, example-oriented introduction is given to special holonomy and its uses in string theory and M-theory. We discuss Ak singularities and their resolution; the construction of a K3 surface by resolving T /Z2; holomorphic cycles, calibrations, and worldsheet instantons; aspects of the low-energy effective action for string compactifications; the significance of the standard embedding of th...