Program

The program is intended to be flexible, based on the decisions of the speakers.

Part 1 - Motivation

• Lecture 1: Ettore
  - Principal bundles, connections and curvature [Chapter 2, J].

• Lecture 2: Corrado
  - Holonomy - basic definitions and results. Berger's list [Chapter 3, J; Sec. 5, K].

• Lecture 3: Lapo
  - G-structures. Standard G2  structure on R^7.

Part 2 - G2  geometry 

• Lecture 4: Lorenzo Maniscalco
  - G2  structures on manifolds, differential forms decompositions [4.1, 4.2, 4.3, K].

• Lecture 5: Letizia
  - Torsion of a G2  structure, closed G2  structures, curvature [4.4, 4.5, K, Chapter 4, B].

• Lecture 6: Marco Miceli
  - Torsion-free G2  manifolds [6.1, 6.3, 6.4, K].

• Lecture 7: Federico Thiella
  - Compact torsion-free G2  manifolds [Chapter 7, K; Kovalev's paper in KLL].

• Lecture 8: Udhav
  - Overview talk of G2  geometry, known examples and constructions.

• Lecture 9: Fedes
  - Spin geometry.

Part 3 - Selected papers

• Lecture 10,  Feb 3rd, and  lecture 11,  Feb 10th.
  Lotay, Sa Earp - The heterotic G2  system on contact Calabi–Yau 7-manifolds
  El Fedes, Corrado.

Future papers (in a random order)

• da Silva, Garcia-Fernandez, Lotay, Sá Earp - Coupled G2-instantons
  Lecture 12 ?

• Corti, Haskins, Nordstrom, Pacini - G2 -manifolds and associative submanifolds via semi-Fano 3-folds
  Elia and at least 3 others.

• Joyce, Karigiannis - A new construction of compact torsion-free G2 -manifolds by gluing families of Eguchi–Hanson spaces
  Udhav and others.

• Geometric flows of G2  structures. Chapter 5 in Lectures and surveys on G2 -Manifolds and related topics
  Giovanni Gentili and possibly others.

• Fino, Grantcharov, Russo - On the ν-invariant of two-step nilmanifolds with closed G2 -structure
  Giovanni Russo and possibly others.

• Moduli space of  heterotic G2  systems,  cf.  Larfors, de la Ossa, for instance The infinitesimal moduli space of heterotic G2  systems  
  Lorenzo Sillari and possibly others.

Participants

• Marco Bernardini (Università dell'Aquila)

• Letizia Branca (Università degli Studi di Milano Statale)

• Beatrice Brienza (Università di Torino)

• Pietro Ciusa (SISSA)

• Davide Dameno (Università degli Studi di Milano Statale)

• Udhav Fowdar (Università di Torino)

• Elia Fusi (Università di Parma) 

• Giovanni Gentili (Università di Torino)

• Federico Giusti (ICMAT)

• Federico Thiella (Università di Firenze)

• Ettore Lo Giudice (Università di Parma)

• Asia Mainenti (Università di Torino)

• Lorenzo Maniscalco (Università di Torino)

• Victor Gustavo May Custodio (Università di Parma)

• Corrado Mazzoccoli (Università di Firenze)

• Marco Miceli (SISSA)

• Giorgia Petracci (Università dell'Insubria)

• Riccardo Piovani (Università di Torino)

• Lapo Rubini (Università di Firenze)

• Giovanni Russo (SISSA)

• Lorenzo Sillari (SISSA)

• Tommaso Sferruzza (Università di Torino)

• Alessandro Vannini