Complex, p-adic, and logarithmic Hodge theory and their applications
Organized by Mark de Cataldo, Radu Laza, Christian Schnell
March 7, 2016 – April 29, 2016
Hodge theory is a very powerful tool for understanding the geometry of complex algebraic varieties and it has a wide range of applications in complex and algebraic geometry, mirror symmetry, representation theory, combinatorics, etc. This program focuses on different aspects of Hodge theory, their applications in algebraic geometry and related areas and, very importantly, on their interactions. We plan to cover the following four themes:
(1) p-adic Hodge theory and arithmetic geometry
(2) mixed Hodge modules and their applications
(3) log geometry, with an emphasis on degenerations and moduli problems
(4) applications of Hodge theory to questions about algebraic cycles
There will be four lecture series, “Hitchin systems and Hodge theory” (R. Donagi and T. Pantev), “p-adic Hodge theory” (B. Bhatt), “Log geometry and log Hodge structures” (M. Olsson), and “Mixed Hodge modules” (Ch. Schnell), a weekly seminar, and several mini-courses.
Talk Schedule
| Date | Time | Title | Speaker | Location |
| Tues. March 8 | 2:15 pm | Higgs bundles, T-duality, and Hodge theory | Tony Pantev | SCGP 313 |
| Wed. March 9 | 1:00 pm | The Lefschetz (1,1) theorem for a singular variety. | Donu Arapura | SCGP 313 |
| Wed. March 9 | 4:00 pm | Rota’s conjecture for matroids via toric varieties | Mircea Mustata | Math P131 |
| Thurs. March 10 | 11:30 am | Classifying spaces of degenerating mixed Hodge structures, IV:The fundamental diagram (with Kazuya Kato, Chikara Nakayama) |
Sampei Usui | SCGP 313 |
| Thurs. March 10 | 2:00 pm | Higgs bundles, T-duality, and Hodge theory | Tony Pantev | SCGP 313 |
| Date | Time | Title | Speaker | Location |
| Tues. March 15 | 2:00 pm | Introduction to mixed Hodge modules 1 | Christian Schnell | SCGP 313 |
| Thurs. March 17 | 2:00 pm | Introduction to mixed Hodge modules 2 | Christian Schnell | SCGP 313 |
Mini-Workshop on Moduli and Hodge Theory: https://services.math.duke.edu/~robles/FRGw6/schedule.html
| Date | Time | Title | Speaker | Location |
| Tues. March 22 | 2:15 pm | Introduction to Mixed Hodge Modules 3 | Claude Sabbah | SCGP 313 |
| Wed. March 23 | 1:00 pm | Introduction to Mixed Hodge Modules 4 | Claude Sabbah | SCGP 313 |
| Wed. March 23 | 4:00 pm | Complex varieties with infinite Chow groups modulo 2 | Burt Totaro | Math P131 |
| Thurs. March 24 | 11:30 am | Generic vanishing and minimal cohomology classes on abelian fivefolds | Stefan Schreieder | SCGP 313 |
| Thurs. March 24 | 2:00 pm | Introduction to Mixed Hodge Modules 5 | Christian Schnell | SCGP 313 |
| Date | Time | Title | Speaker | Location |
| Tues. March 29 | 2:15 pm | Introduction to Mixed Hodge Modules 6 | Christian Schnell | SCGP 313 |
| Tues. March 29 | 4:00 pm | Some aspects of Lefschetz theorems in algebraic geometry | Hélène Esnault | SCGP 313 |
| Wed. March 30 | 1:00 pm | Examples of Maximally Degenerate Curves and Surfaces | Mark Green | SCGP 313 |
| Wed. March 30 | 4:00 pm | On descending cohomology geometrically | Charles Vial | Math P131 |
| Thurs. March 31 | 11:30 am | Moduli and Periods | Phillip Griffiths | SCGP 313 |
| Thurs. March 31 | 2:00 pm | Introduction to Mixed Hodge Modules 7 | Claude Sabbah | SCGP 313 |
| Date | Time | Title | Speaker | Location |
| Tues. April 5 | 2:15 pm | Hitchin Systems, Geometric Langlands, and Hodge Theory | Ron Donagi | SCGP 313 |
| Tues. April 5 | 4:00 pm | Transcendental Hodge algebra and some conjectures | Misha Verbitsky | SCGP 313 |
| Wed. April 6 | 1:00 pm | Hitchin Systems, Geometric Langlands, and Hodge Theory | Ron Donagi | SCGP 313 |
| Wed. April 6 | 4:00 pm | Hodge theory and Gromov-Witten invariants | Dave Morrison | Math P131 |
| Thurs. April 7 | 11:30 am | On hyperplane sections of K3 surfaces | Andrea Bruno | SCGP 313 |
| Thurs. April 7 | 2:00 pm | Constructing algebraic cycles on products of K3 surfaces via hyperholomorphic bundles | Eyal Markman | SCGP 313 |
| Date | Time | Title | Speaker | Location |
| Tues. April 12 | 2:15 pm | Log geometry and log Hodge structures | Martin Olsson | SCGP 313 |
| Tues. April 12 | 4:00 pm | Hodge Groups of Hodge Structures with Hodge Numbers (n,0,…,0,n) | Laure Flapan | SCGP 313 |
| Wed. April 13 | 1:00 pm | Fake tori | Zhiyu Tian | SCGP 313 |
| Wed. April 13 | 4:00 pm | The Miyaoka-Yau inequality for minimal models of general type and ball quotients | Behrouz Taji | Math P131 |
| Thurs. April 14 | 11:30 pm | Cycle transversal Mumford-Tate domains associated to period domains | Ana-Maria Brecan | SCGP 313 |
| Thurs. April 14 | 2:00 pm | Log geometry and log Hodge structures | Martin Olsson | SCGP 313 |
| Date | Time | Title | Speaker | Location |
| Tues. April 19 | 2:15 pm | p-adic Hodge theory | Bhargav Bhatt | SCGP 313 |
| Wed. April 20 | 2:00 pm | Log geometry and log Hodge structures | Martin Olsson | SCGP 313 |
| Wed. April 20 | 4:00 pm | Hodge ideals | Mihnea Popa | Math P131 |
| Thurs. April 21 | 11:30 am | Log geometry and log Hodge structures | Martin Olsson | SCGP 313 |
| Thurs. April 21 | 2:00 pm | p-adic Hodge theory | Bhargav Bhatt | SCGP 313 |
| Date | Time | Title | Speaker | Location |
| Tues. April 26 | 2:15 pm | p-adic Hodge theory | Bhargav Bhatt | SCGP 313 |
| Wed. April 27 | 4:00 pm | Iitaka’s conjecture over abelian varieties | Christian Schnell | Math P131 |
| Thurs. April 28 | 11:30 am | K3 surfaces and complex multiplication | Madhav Nori | SCGP 313 |
| Thurs. April 28 | 2:00 pm | p-adic Hodge theory | Bhargav Bhatt | SCGP 313 |