{"id":229,"date":"2023-11-09T11:17:24","date_gmt":"2023-11-09T11:17:24","guid":{"rendered":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=229"},"modified":"2023-11-09T11:19:08","modified_gmt":"2023-11-09T11:19:08","slug":"noncommutative-hodge-theory-learning-seminar","status":"publish","type":"page","link":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=229","title":{"rendered":"Noncommutative Hodge theory learning\u00a0seminar"},"content":{"rendered":"\n

Schedule<\/a><\/h2>\n\n\n\n


Organizer: Brent Pym
Winter 2018 (Semester 2)
Mondays and\/or Fridays at 16:10
JCMB 5327<\/s> 6206<\/p>\n\n\n\n

Date<\/td>Speaker<\/td>Topic<\/td>Notes (no guarantee of correctness)<\/td><\/tr>
Jan 22<\/td>Brent Pym<\/td>Introduction and motivation<\/td>nc-hodge-01.pdf<\/a><\/td><\/tr>
Jan 29<\/td>Matt Booth<\/td>Hochschild homology for algebras and dg categories<\/td>nc-hodge-02.pdf<\/a><\/td><\/tr>
Feb 5<\/td>Tim Weelinck<\/td>The Hochschild-Kostant-Rosenberg theorem<\/td>nc-hodge-03.pdf<\/a><\/td><\/tr>
Feb 12<\/td>David Jordan<\/td>Cyclic homology and the NC Hodge filtration<\/td>nc-hodge-04.pdf<\/a><\/td><\/tr>
Mar 9<\/td>Sjoerd Beentjes<\/td>The Gysin triangle<\/td>nc-hodge-05.pdf<\/a><\/td><\/tr>
Mar 26<\/td>Sue Sierra<\/td>Invariants of noncommutative projective schemes<\/td>nc-hodge-06.pdf<\/a><\/td><\/tr>
Apr 9 & 13<\/td>Theo Raedschelders<\/td>The Hodge-de Rham degeneration theorem I & II<\/td>nc-hodge-07-08.pdf<\/a><\/td><\/tr>
Apr 23<\/td>Peter Samuelson<\/td>K-theory and the Chern character<\/td>nc-hodge-09.pdf<\/a><\/td><\/tr>
Apr 30<\/td>Johan Martens<\/td>The Gauss-Manin connection<\/td><\/td><\/tr>
May 14<\/td>Brent Pym<\/td>Hodge structures in deformation quantization (cyclic formality)<\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n

References and links<\/a><\/h2>\n\n\n\n

Lecture notes<\/a><\/h3>\n\n\n\n

Kaledin, Lecture notes from a mini-course in Tokyo in 2008<\/a>
Stern et al, Notes from a similar seminar in Bonn in 2016<\/a><\/p>\n\n\n\n

Classical Hodge theory<\/a><\/h3>\n\n\n\n

Deligne, Th\u00e9orie de Hodge II<\/a> and III<\/a>
Filippini-Ruddat-Thompson, An introduction to Hodge structures<\/a>
Griffiths-Harris, Principles of Algebraic Geometry<\/a>
Peters-Steenbrink, Mixed Hodge structures<\/a>
Voisin, Hodge Theory and Complex Algebraic Geometry I<\/a><\/p>\n\n\n\n

Noncommutative Hodge structures<\/a><\/h3>\n\n\n\n

Kontsevich, Solomon Lefschetz Memorial Lectures on “Hodge structures in non-commutative geometry”<\/a>
Katzarkov-Kontsevich-Pantev, Hodge theoretic aspects of mirror symmetry<\/a>
Sabbah, Introduction to pure non-commutative Hodge structures<\/a><\/p>\n\n\n\n

Noncommutative motives<\/a><\/h3>\n\n\n\n

Tabuada, Higher K-theory via universal invariants<\/a>
Tabuada, Noncommutative motives<\/a><\/p>\n\n\n\n

Differential graded categories<\/a><\/h3>\n\n\n\n

Drinfeld, DG quotients of DG categories<\/a>
Keller, On differential graded categories<\/a>
Thomason-Trobaugh Higher Algebraic K-Theory of Schemes and of Derived Categories<\/a>
To\u00ebn, Lectures on DG-categories<\/a><\/p>\n\n\n\n

Cyclic homology<\/a><\/h3>\n\n\n\n

Connes, Non-commutative differential geometry<\/a>
Loday, Cyclic homology<\/a>
Kassel, Cyclic homology, comodules, and mixed complexes<\/a>
Keller, Invariance and localization for cyclic homology of DG algebras<\/a>
Keller, On the cyclic homology of exact categories<\/a>
Keller, On the Cyclic Homology of Ringed Spaces and Schemes<\/a>
Tsygan, Cyclic homology<\/a>
Voigt, Introduction to cyclic homology<\/a>
Weibel, Cyclic homology for schemes<\/a>
Weibel, An introduction to homological algebra<\/a><\/p>\n\n\n\n

Gauss-Manin connection<\/a><\/h3>\n\n\n\n

Dolgushev-Tamarkin-Tsygan, Noncommutative calculus and the Gauss-Manin connection<\/a>
Getzler, Cartan homotopy formulas and the Gauss-Manin connection in cyclic homology<\/a>
Tsygan, On the Gauss-Manin connection in cyclic homology<\/a>
Sheridan, Formulae in noncommutative Hodge theory<\/a><\/p>\n\n\n\n

Hodge to de Rham degeneration<\/a><\/h3>\n\n\n\n

Kontsevich-Soibelman, Notes on A\u221e-Algebras, A\u221e-Categories and Non-Commutative Geometry<\/a> (statement of the conjecture)
Kaledin, several papers on the proof math\/0511665<\/a>, math\/0611623<\/a>, 0708.1574<\/a>, 1601.00637<\/a>
Mathew, Kaledin’s degeneration theorem and topological Hochschild homology<\/a><\/p>\n\n\n\n

K-theory<\/a><\/h3>\n\n\n\n

Blanc, Topological K-theory of complex noncommutative spaces<\/a>
Weibel, The K-book: an introduction to algebraic K-theory<\/a><\/p>\n\n\n\n

Riemann-Roch<\/a><\/h3>\n\n\n\n

Shklyarov, Hirzeburch-Riemann-Roch theorem for differential graded algebras<\/a><\/p>\n\n\n\n

Deformation quantization<\/a><\/h3>\n\n\n\n

Dolgushev, A Proof of Tsygan’s Formality Conjecture for an Arbitrary Smooth Manifold<\/a>
Dolgushev-Tamarkin-Tsygan, Formality theorems for Hochschild complexes and their applications<\/a>
Kontsevich, Deformation quantization of Poisson manifolds<\/a> and algebraic varieties<\/a>
Shoikhet, A proof of the Tsygan formality conjecture for chains<\/a>
Willwacher, Formality of cyclic chains<\/a><\/p>\n\n\n\n

Matrix factorizations\/Landau-Ginzburg models<\/a><\/h3>\n\n\n\n

Shklyarov, Non-commutative Hodge structures: Towards matching categorical and geometric examples<\/a>
Dyckerhoff, Compact generators in categories of matrix factorizations<\/a>
Katzarkov-Kontsevich-Pantev, Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models<\/a><\/p>\n\n\n\n

Hodge theory of generalized complex manifolds<\/a><\/h3>\n\n\n\n

Cavalcanti, The decomposition of forms and cohomology of generalized complex manifolds<\/a>
Gualtieri, Generalized geometry and the Hodge decomposition<\/a>
Gualtieri, Generalized complex manifolds<\/a><\/p>\n\n\n\n

Videos of talks<\/a><\/h3>\n\n\n\n

Pantev, Hodge Structures in Symplectic Geometry<\/a>
Kontsevich, Noncommutative Motives<\/a>
Shklyarov, Semi-infinite Hodge structures in noncommutative geometry<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Schedule Organizer: Brent PymWinter 2018 (Semester 2)Mondays and\/or Fridays at 16:10JCMB 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 […]<\/p>\n","protected":false},"author":1,"featured_media":76,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-229","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/229","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=229"}],"version-history":[{"count":2,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/229\/revisions"}],"predecessor-version":[{"id":240,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/229\/revisions\/240"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/media\/76"}],"wp:attachment":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}