Summer School And Workshop:Dirac Operators:Yesterday And Today

August 27-September 7, 2001

AUB-CAMS


 Monday August 27Tuesday August 28Wednesday August 29Thursday August 30Friday August 31
9:00-10:30Registration/ Opening (10:00-10:30) College Hall Auditorium B1Jean-Pierre Bourguignon I
Introduction to Riemannian Geometry: Metric, Levi-Civita Connection, Curvature 		Robert Bryant I
Holonomy: Parallel Transport, Holonomy, Parallel Sections		Jean-Pierre Bourguignon II
Introduction to Spin Geometry: Spin Structures, Spinorial frames, Spin metrics and Spin Structures, Dependence on the metric 		Jean-Pierre Bourguignon III
The Dirac Operator: Schroedinger-Linchnerowicz formula and the Penrose operator
10:30-11:00Coffee Break Coffee BreakCoffee BreakCoffee BreakCoffee Break
11:00-12:30H. Blaine Lawson
The Dirac Operator (until 12:00) 		Oussama Hijazi II
Basic Relevant Algebra: The Spin Groups		 Robert J. Stanton II
A Visit to Representation Theory: Homogenous bundles; G-invariant Operators, Stein-Weiss Operators 		Robert Bryant II
Special Geometries: General setup and non spinorial examples 		Robert Bryant III
Special Geometries: Parallel Spinors and Killing Spinors
12:30-15:00Lunch Break (Starting 12:00)Lunch BreakLunch BreakLunch BreakLunch Break
15:00-16:30Christian Baer I
Introduction to Differential Geometry: Manifolds, Differential Forms, and all that. 		Robert J. Stanton I
A Visit to Representation Theory: Compact groups; Representations-reducibility, Classification, Construction 		Free AfternoonAli Chamseddine I
Dirac Equation for the relativistic electron: Supersymmetric Lagrangians 		Christian Baer II
Spectrum of the Dirac Operator: Dirac Eigenvalues of Compact Manifolds
16:30-17:00Coffee Break (Bliss Hall 3rd floor)Coffee Break Coffee BreakCoffee Break
17:00-18:30Oussama Hijazi I
Basic Relevant Algebra: Clifford Algebras and their Classification		Oussama Hijazi III
Basic Relevant Algebra: The Spinor Representation		  Robert J. Stanton III
A Visit to Representation Theory: Noncompact Groups; Dirac induction, Discrete Series, Consequences of Weitzenboeck 		Ali Chamseddine II
Supergravity Dirac equation in higher dimensions
20:00-23:00  Dinner  



 Monday September 3Tuesday September 4Wednesday September 5Thursday September 6
9:00-10:30H. Blaine Lawson I
Relations to topology and geometry via the Index Theorem: K-theory characteristic classes 		H. Blaine Lawson II
Relations to topology and geometry via the Index Theorem: Atiyah-Singer Index Theorems, the Lichnerowicz formula 		Thomas Branson I
Consequences of the conformal behavior of natural differential operators on manifolds with spin sturcture: Weitzenboeck formulas 		Marie-Louise Michelson
Relations to topology and geometry via the Index Theorem: Applications topology and geometry
10:30-11:00Coffee BreakCoffee BreakCoffee BreakCoffee Break
11:00-12:30Christian Baer III
Spectrum of the Dirac Operator: Open Manifolds 		Robert Bryant IV
Special Geometries: Parallel Spinors and Killing Spinors on Pseudo-Riemannian Spin Manifolds 		Helga Baum
Spinors and CR-Geometry (11:00-11:40)
Andrei Moroianu
On manifolds whose Ricci tensor has two constant eigenvalues (11:50-12:30)		Ali Chamseddine III
Killing spinors and holonomy. Finding compactification solutions of higher dimensional supergravity Theories
12:30-15:00Lunch BreakLunch BreakFree AfternoonLunch Break (until 14:30)
15:00-15:40Sebastian Montiel
Dirac operator and hypersurfaces 		Aziz El Kacimi
Transversely elliptic operators on foliations		 Leitner Felipe
Twistor spinors in Lorenztian geometry (14:30-15:10)
15:50-16:30Mattias Dahl
Surgery and the spectrum of the Dirac operator		Bernd Ammann
Title to be announced 		 Coffee Break (15:10-15:30)
16:30-16:50Coffee BreakCoffee Break Thomas Branson
Consequences of the confirmed behavior of natural differential operators on manifolds with spinstructure: Conformally invariant constructions. (15:30- 17:00)
16:50-17:30Nicolas Ginoux
Title to be announced		Fida Sayah
Spectre geometrique de certaines varietes isospectrals et non isometriques		 Closing