Slides

1. Algebraic invariants of algebraic varieties: the case of derived categories (Colloquium University of California at Santa Cruz), beamer presentation (pdf).
2. Derived categories and the geometry of projective varieties (XXII Congresso dell'Unione Matematica Italiana, Pisa, 2023), beamer presentation (pdf).
3. Derived categories in algebraic geometry - a first glance, slides (pdf) or beamer presentation (pdf).
4. Derived categories and stability structures (Hamburg, September 2009), slides (pdf) or beamer presentation (pdf).
5. Fourier-Mukai functors: existence (Bologna, September 2011), slides (pdf) or beamer presentation (pdf).

1. A tour on Bridgeland stability, slides (pdf) or beamer presentation (pdf).
2. Inducing stability conditions, slides (pdf) or beamer presentation (pdf).
3. Stability conditions on generic K3 surfaces (pdf).

1. Cubic hypersurfaces and derived categories: results and open problems, slides (pdf) .
2. Cubic fourfolds, noncommutative K3 surfaces and stability conditions, slides (pdf) or beamer presentation (pdf).
3. Bridgeland stability for semiorthogonal decompositions, hyperkaehler manifolds and cubic fourfolds, slides (pdf) or beamer presentation (pdf).
4. Derived categories and cubic hypersurfaces (Roma, February 2011), slides (pdf) or beamer presentation (pdf).

1. Deformations of K3 surfaces and orientation, slides (pdf) or beamer presentation (pdf).
2. Equivalences of K3 Surfaces: Deformations and Orientation, slides (pdf) or beamer presentation (pdf).
3. Equivalences of K3 Surfaces and Orientation II - The Projective Case, slides (pdf) or beamer presentation (pdf). (Talk given in Salamanca.)
4. Equivalences of K3 Surfaces and Orientation, slides (pdf) or beamer presentation (pdf). (This version includes the final result in arXiv:0710.1645.)
5. Derived Torelli Theorem and Orientation, slides (pdf) or beamer presentation (pdf). (This version does not include the final result in arXiv:0710.1645.)

1. Derived Torelli Theorem and Orientation (Part 1 - the twisted case), slides (pdf) or beamer presentation (pdf).
2. A Twisted Derived Torelli Theorem for K3 surfaces, slides (pdf) or beamer presentation (pdf).
3. Twisted derived categories and K3 surfaces (pdf).
4. Categorie derivate twistate e superfici K3, Italian, talk delivered at the conference "Giornate di Geometria Algebrica e Argomenti Correlati VIII", Trieste, Italy (May 2006) (pdf).

Videos

1. Morita theory: interplay between dg and weakly approximable triangulated categories, Derived Workshop (Hausdorff Institute of Mathematics, Bonn, November 2023) (video).
2. Stability conditions in the trivial canonical bundle case: Hilbert schemes of points, New Directions in Group Theory and Triangulated Categories, online seminar (video).
3. Uniqueness of enhancements: derived and geometric categories, Derived Seminar (video).
4. Uniqueness of enhancements for derived and geometric categories, LAGOON Leicester Algebra and Geometry Open ONline Seminar, UK (video).
5. Cubic fourfolds, noncommutative K3 surfaces and stability conditions, Workshop - Stability Conditions and Representation Theory of Finite-Dimensional Algebras (CMO, Oaxaca, Mexico, October 2018) (video).
6. Uniqueness of dg enhancements in geometric contexts, Conference - AMS Summer Research Institute 2015 (Salt Lake City, July 2015) (video).
7. Stability conditions on threefolds, II, Conference - New Techniques in Birational Geometry (Stony Brook University, Stony Brook, April 2015) (video).
8. Stable ACM bundle on cubic threefolds and fourfolds, Workshop - Brill-Noether methods in the study of hyper-Kähler and Calabi-Yau manifolds (Hausdorff Institute of Mathematics, Bonn, March 2014) (video).
9. Fourier-Mukai functors in the supported setting, Conference - Derived categories in Algebraic Geometry (Steklov Mathematical Institute, Moscow, September 2011) (video).