Schedule
Organizer: Brent Pym
Winter 2018 (Semester 2)
Mondays and/or Fridays at 16:10
JCMB 5327 6206
| Date | Speaker | Topic | Notes (no guarantee of correctness) |
| Jan 22 | Brent Pym | Introduction and motivation | nc-hodge-01.pdf |
| Jan 29 | Matt Booth | Hochschild homology for algebras and dg categories | nc-hodge-02.pdf |
| Feb 5 | Tim Weelinck | The Hochschild-Kostant-Rosenberg theorem | nc-hodge-03.pdf |
| Feb 12 | David Jordan | Cyclic homology and the NC Hodge filtration | nc-hodge-04.pdf |
| Mar 9 | Sjoerd Beentjes | The Gysin triangle | nc-hodge-05.pdf |
| Mar 26 | Sue Sierra | Invariants of noncommutative projective schemes | nc-hodge-06.pdf |
| Apr 9 & 13 | Theo Raedschelders | The Hodge-de Rham degeneration theorem I & II | nc-hodge-07-08.pdf |
| Apr 23 | Peter Samuelson | K-theory and the Chern character | nc-hodge-09.pdf |
| Apr 30 | Johan Martens | The Gauss-Manin connection | |
| May 14 | Brent Pym | Hodge structures in deformation quantization (cyclic formality) |
References and links
Lecture notes
Kaledin, Lecture notes from a mini-course in Tokyo in 2008
Stern et al, Notes from a similar seminar in Bonn in 2016
Classical Hodge theory
Deligne, Théorie de Hodge II and III
Filippini-Ruddat-Thompson, An introduction to Hodge structures
Griffiths-Harris, Principles of Algebraic Geometry
Peters-Steenbrink, Mixed Hodge structures
Voisin, Hodge Theory and Complex Algebraic Geometry I
Noncommutative Hodge structures
Kontsevich, Solomon Lefschetz Memorial Lectures on “Hodge structures in non-commutative geometry”
Katzarkov-Kontsevich-Pantev, Hodge theoretic aspects of mirror symmetry
Sabbah, Introduction to pure non-commutative Hodge structures
Noncommutative motives
Tabuada, Higher K-theory via universal invariants
Tabuada, Noncommutative motives
Differential graded categories
Drinfeld, DG quotients of DG categories
Keller, On differential graded categories
Thomason-Trobaugh Higher Algebraic K-Theory of Schemes and of Derived Categories
Toën, Lectures on DG-categories
Cyclic homology
Connes, Non-commutative differential geometry
Loday, Cyclic homology
Kassel, Cyclic homology, comodules, and mixed complexes
Keller, Invariance and localization for cyclic homology of DG algebras
Keller, On the cyclic homology of exact categories
Keller, On the Cyclic Homology of Ringed Spaces and Schemes
Tsygan, Cyclic homology
Voigt, Introduction to cyclic homology
Weibel, Cyclic homology for schemes
Weibel, An introduction to homological algebra
Gauss-Manin connection
Dolgushev-Tamarkin-Tsygan, Noncommutative calculus and the Gauss-Manin connection
Getzler, Cartan homotopy formulas and the Gauss-Manin connection in cyclic homology
Tsygan, On the Gauss-Manin connection in cyclic homology
Sheridan, Formulae in noncommutative Hodge theory
Hodge to de Rham degeneration
Kontsevich-Soibelman, Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry (statement of the conjecture)
Kaledin, several papers on the proof math/0511665, math/0611623, 0708.1574, 1601.00637
Mathew, Kaledin’s degeneration theorem and topological Hochschild homology
K-theory
Blanc, Topological K-theory of complex noncommutative spaces
Weibel, The K-book: an introduction to algebraic K-theory
Riemann-Roch
Shklyarov, Hirzeburch-Riemann-Roch theorem for differential graded algebras
Deformation quantization
Dolgushev, A Proof of Tsygan’s Formality Conjecture for an Arbitrary Smooth Manifold
Dolgushev-Tamarkin-Tsygan, Formality theorems for Hochschild complexes and their applications
Kontsevich, Deformation quantization of Poisson manifolds and algebraic varieties
Shoikhet, A proof of the Tsygan formality conjecture for chains
Willwacher, Formality of cyclic chains
Matrix factorizations/Landau-Ginzburg models
Shklyarov, Non-commutative Hodge structures: Towards matching categorical and geometric examples
Dyckerhoff, Compact generators in categories of matrix factorizations
Katzarkov-Kontsevich-Pantev, Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models
Hodge theory of generalized complex manifolds
Cavalcanti, The decomposition of forms and cohomology of generalized complex manifolds
Gualtieri, Generalized geometry and the Hodge decomposition
Gualtieri, Generalized complex manifolds
Videos of talks
Pantev, Hodge Structures in Symplectic Geometry
Kontsevich, Noncommutative Motives
Shklyarov, Semi-infinite Hodge structures in noncommutative geometry