Winter
School Gauge Theory
and Geometry

Jose
FigueroaO'Farrill (Edinburgh) 
Lecture 12: "Selfduality in higher dimensions"
Motivation from the division algebras.
Higherdimensional instantons and special holonomy.
Concentrating on the cases of instanton on
Spin(7)holonomy manifolds and the related notion of
monopoles on G_2holonomy manifolds.
Lectures 34: "Selfduality and supersymmetry" 10dimensional supersymmetric YangMills theory. Dimensional reduction and higherdimensional selfduality. Some consequences of supersymmetry: e.g., triholomorphic curves and octonionic instantons. 
Balázs
Szendröi (Oxford) 
Lectures
12 U(1) gauge theory in three complex
dimensions:
DonaldsonThomas theory. Toric threefolds and the topological vertex. Gaugestring duality: the MNOP conjecture. Lecture 3 CalabiYau algebras and noncommutative U(1) gauge theory Lecture 4 Higherrank theory: bundles on threefolds. Fibred varieties: elliptic and ALE fibrations 
Urs
Frauenfelder (München) 
Lecture 1: "The ArnoldGivental conjecture and Moment Floer homology" The ArnoldGivental conjecture asks for a lower bound on the number of intersection points of two Hamiltonian isotopic Lagrangians which intersect transversally and are fixed points of an antisymplectic involution. We are proving this conjecture for a class of Lagrangians in MarsdenWeinstein quotients using Moment Floer homology. Moment Floer homology is an infinite dimensional analogon of Morse homology for a Lagrange multiplier action functional whose gradient flow lines are the symplectic vortex equations. These have better compactness properties than Floer's equations which enables us to define Moment Floer homology even in situations where the ordinary Floer homology cannot be defined via standard means. Lecture 2: "Vortices on the cylinder" We give a new proof of a result of Jaffe and Taubes on the structure of moduli spaces of vortices on the cylinder which also sheds new light on the connection between the moduli space of holomorphic curves in a toric variety and Givental's toric map spaces. Our proof is based on Floer theoretic methods, finite dimensional approximation, and a homotopy argument for Lagrange multiplier functionals which enables us to overcome an adiabatic limit analysis. Lecture 3: "Rabinowitz action functional and obstructions for exact contact embeddings" This is joint work with Kai Cieliebak. We define Floer homology for a Lagrange multiplier action functional generalizing the Moment action functional arising in the theory of Moment Floer homology. As an application of some computations we get obstructions for exact contact embeddings. 
Roger
Bielawski (Leeds) 
Lecture 1
"Introduction to monopoles"
This will be an introduction to monopoles and their moduli spaces on 3manifolds, in particular R3 and H3, together with some of their physical relevance. Lecture 2 "Differential and algebraic geometry of monopole moduli spaces" I shall discuss the deep interplay of differential and algebrogeometric methods in the study of monopole moduli spaces and their still mysterious geometries. 
Further
information and registration: dingen@unimath.gwdg.de 
Graduiertenkolleg Gruppen und
Geometrie Mathematisches
Institut GeorgAugustUniversität Bunsenstr. 35 D37073 Göttingen 