Geometry and Analysis of Manifolds with Reduced Holonomy
Cortona, 16 July - 3 August 2007

SMI webpage with course details


Student Seminars
Proposals "Course A" (Salamon)
"Course B" (Kovalev)
Weds
18/07
Kähler manifold v Hermitian manifolds - some counterexamples (Rollenske 16.30)
Connections, curvature and holonomy (De Nicola 17.30)
Thurs
19/07
Riemannian symmetric spaces (Becker-Bender 15.45)
Elliptic complexes (Gentile 17.15)
Fri
20/07
Kähler manifolds: equivalent definitions and properties (Povero 16.45)
Sobolev spaces and conformal geometry (Profir 17.15)
Mon
23/07
Asymptotically cylindrical Ricci-flat manifolds (Pilca 15.45)
Spinors and holonomy (Penegini 17.15)
Tues
24/07
Holomorphic vector bundles (Della Piazza 15.45)
An SU(m+1) metric on the canonical bundle of a Kähler-Einstein manifold (Gentile 17.15)
Weds
25/07
Reducible holonomy and compact Ricci-flat Kähler manifolds (Profir 15.45)
Hyper-Kähler and quaternionic geometry (Mihaylov 17.15)
Thurs
26/07
Continuity method and overview of the Calabi conjecture (Sa Earp 15.45)
Octonians and 6-submanifolds of R7 (De Nicola 17.15)
Fri
27/07
Explicit Ricci-flat Kähler metrics (Nisoli 15.45)
Uniqueness proof for the Calabi conjecture (Pilca 17.15)
Mon
30/07
Intrinsic torsion and G2 structures (Mihaylov 15.15)
Stable differential forms (Mazzucchelli 16.30)
Anti-self-dual Riemannian 4-manifolds (Povero 17.45)
Tues
31/07
The K3 surface as a generalized connected sum (Penegini 16.30)
Moduli of G2 metrics and b3 (Rollenske 17.40)
Weds
01/08
Study of examples of finite group actions on T7 (Della Piazza 15.15)
Calibrated submanifolds of Rn (Becker-Bender 16.30)
SU(3) structures and evolution equations for G2 metrics (Nisoli 17.30)
Thurs
02/08
Existence of isothermal coordinates on surfaces (Mazzucchelli 15.15)
Topological criterion for G2 holonomy involving π1 (Sa Earp 16.30)

Additional material

Riemannian Geometry and Holonomy Groups (Salamon's "red" book)

Kovalev's lectures notes for Cambridge Part III course "Differential Geometry"

A. Kovalev "Twisted connected sums and special Riemannian holonomy" is a research paper constructing compact manifolds with holonomy G2;
there is a less technical overview "From Fano threefolds to compact G2-manifolds" - follow the links from this page

Chapter on the quaternions from the book Modern Differential Geometry of Curves and Surfaces by Gray-Abbena-Salamon (see §23.2)
Short early paper on G2 holonomy
A tour of exceptional geometry (survey article)

Photo gallery



Updated 30/08/2007