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MASTERCLASS WINTERSCHOOL
Complex Geometry: a Modern Viewpoint Scientific Committee
Comité scientifique Igor Dolgachev (University of Michigan) Organizing Committee
Comité d’organisation Julien Keller (Aix Marseille Université) |
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This week will be a winter school for young researchers, master’s and Ph.D students. The objective is to introduce the various subjects that will be developed during the following weeks.
Junior women mathematicians and those from under-represented minority groups will be given priority for financial help. |
Cette semaine sera consacrée à une école d’hiver à destination des jeunes chercheurs, des étudiants niveau Master ou Thèse. L’objectif sera d’introduire par 3 mini-cours les thématiques qui seront développées les semaines suivantes.
Les jeunes mathématiciennes et les personnes provenant de minorités seront considérés comme prioritaires pour l’obtention d’une aide financière. |
- Vestislav Apostolov (Université du Québec à Montréal) – The Kähler geometry of toric manifolds
(1) Symplectic toric varieties. Examples. Moment map, Atiyah and Guillemin-Sternberg convexity theorem. Delzant theorem. Fans.
(2) Kahler metrics on symplectic toric varieties. Theorems of Guillemin and Abreu. The scalar curvature as moment map and extremal toric metrics. Abreu’s equation. Uniqueness. Explicit solutions: Bryant’s metrics.
(3) Toric K-stability as necessary condition for existence of an extremal metric. Donaldson-Tian-Yau conjecture and its solution by Donaldson and Chen-Cheng. Examples of K-stable and K-unstable polytopes
(4) Monotone symplectic toric varieties: existence of Kahler-Ricci solitons and singular Kahler-Einstein metrics.
- Julien Grivaux (Aix-Marseille Université) – Hodge THEORY
(2) Weight one Hodge structures and Abelian varieties
(3) Kahler varieties and harmonic theory
(4) Hodge spectral sequences ) De Rham and Hodge decomposition Theorem
(5) Families of complex varieties and Hodge structure variations
(6) Gauss-Manin connexions and monodromy.
- Alessandra Sarti (Université de Poitiers) – TOPICS ON K3 Surfaces – VIDEOS –
(1) K3 surfaces in the Enriques Kodaira classification and examples – VIDEO –
(2) Kummer surfaces – VIDEO –
(3) Basic properties of K3 surfaces – VIDEO –
(4) Nèron-Severi group and automorphisms – VIDEO –
(5) Finite automorphism groups – VIDEO –
(6) Classification – VIDEO –
(1) A worshop session of questions/replies with V. Apostolov, J. Grivaux, A. Sarti
(2) Short research talks given by the participants (15-20mns). To be announced
(3) Poster session
