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Complex, p-adic, and logarithmic Hodge theory and their applications: March 6, 2016 – April 29, 2016

Complex, p-adic, and logarithmic Hodge theory and their applications

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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