## Teaching-
Differential Geometry (MSc and 1st year PhD), Oct 2016 - Jan 2017. ### PhD/MSc lecture courses at SISSA 2016-17 -
Kaehler Geometry (Oct 2016 - Feb 2017; 1st year PhD). The first part of the course offered an introduction to the theory of canonical metrics on compact Kaehler manifolds, including Yau's proof of the Calabi conjecture and Tian's approach to the positive curvature case. In the second part of the course we covered the basics of Hodge theory for compact Kaehler manifolds. Topics of the forthcoming final seminars: V. Fantini: Hyperkaehler metrics; N. Fasolo: Deformation theory and Tian-Todorov; A. Giacchetto: variations of Hodge structures; A. Maiorana: Kodaira embedding; V. Peragine: Kodaira vanishing; C. Scarpa:Scalar curvature as a moment map; M. Stecconi: Sasaki-Einstein manifolds. -
Topics in algebro-geometric stability, second semester 2017. We covered various topics linking notions of stability in algebraic geometry to certain geometric PDEs, via the general moment map framework: Donaldson's lower bound on the Calabi functional; intersection-theoretic formulae for the Donaldson-Futaki invariant; introduction to the Li-Xu theorem on generic Q-Fano families; the J-flow critical equation; moment map interpretation for cscK, J-equation, HYM; coupling of moment maps (following Alvarez-Consul, Garcia-Fernandez, Garcia-Prada); Leimj-Szekelyhidi's lower bound for the J-equation; equations on a compact torus; Leimj-Szekelyhidi's conjecture on the J-equation; discussion of Zariski opennes of KE property following Odaka and Donaldson (in particular we studied in detail Donaldson's theorem on algebraic families of cscK metrics); Kento Fujita's work on K-stability for Fanos. Links to some references we followed: Lower bounds on Calabi, Kaehler-Yang-Mills , J-equation 1, J-equation 2, Generic Q-Fano families, Algebraic families of cscK manifolds, Filtrations and test-configurations, Fujita 1. ### Corsi svolti presso l'Universita' di Pavia -
__Geometria Superiore a.a. 2015-16.__ -
__Geometria a.a. 2015-16 (Ing. edile-architettura).__ -
__Geometria a.a. 2014-15 (Ing. edile-architettura).__ -
__Geometria 2 a.a. 2014-15 (con S. Brivio).__ -
__Geometria Superiore a.a. 2013-14.__ -
__Geometria a.a. 2013-14 (Ing. edile-architettura).__ -
__Geometria 2 a.a. 2012-13.__ -
__Complementi di Analisi Matematica e Statistica a.a. 2012-13 (Ing. industriale).__ -
__Analisi Matematica 2 a.a. 2012-13 (Bioingegneria, Ing. elettronica e informatica).__
## PhD/MSc lecture courses at SISSA 2017-18 |