XI Solomon Lefschetz Memorial Lecture Series: Hodge structures in non-commutative geometry. (Notes by Ernesto Lupercio)

Abstract

Traditionally, Hodge structures are associated with complex projective varieties. In my expository lectures I discussed a non-commutative generalization of Hodge structures in deformation quantization and in derived algebraic geometry.

Lecture notes for the Solomon Lefschetz Memorial Lecture Series, September 8-9, 2005 by Maxim Kontsevich at Cinvestav, Mexico. Notes by Ernesto Lupercio. http://www.math.cinvestav.mx/KontsevichEnglish.htm. To appear in Contemporary Mathematics

References in corpus (5)

• Black Hole Entropy from Near-Horizon Microstates
• Triangulated categories of singularities and D-branes in Landau-Ginzburg models
• Deformation quantization of algebraic varieties
• Fukaya categories and deformations
• Non-commutative Cartier operator and Hodge-to-de Rham degeneration

Cited by in corpus (9)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Co-periodic cyclic homology
• Higher nonunital Quillen K'-theory, KK-dualities and applications to topological $\mathbb{T}$-dualities
• Free products, cyclic homology, and the Gauss-Manin connection
• A Note on Support in Triangulated Categories
• Algebraic K-theory, K-regularity, and T-duality of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• On a Teichmueller functor between the categories of complex tori and the Effros-Shen algebras
• Remark on the rank of elliptic curves
• Cycle maps on cohomology theories for dg-categories and their applications