Mixed Hodge Modules and Their Applications
August 19-23, 2013
Clay Mathematics Institute
Mathematical Institute
University of Oxford
The goal of this workshop is to discuss the basics of mixed Hodge theory, some of its important applications, and recent developments and connections to other areas.
The theory of mixed Hodge modules is a vast generalization of classical Hodge theory. It was introduced by Morihiko Saito in two papers in 1988 and 1990, building on the foundations created by many people during the 1970s and 1980s, such as D-module theory, the theory of perverse sheaves, and the study of variations of mixed Hodge structure and of their degenerations. In spite of its power, and of the potential applications to complex algebraic geometry, mixed Hodge modules has remained a largely esoteric field. The main aim of the workshop is to make this theory more accessible.
Introductory lectures will cover the basics of the theory, with particular emphasis on examples and applications. A small number of talks will focus on mixed Hodge modules themselves, explaining the objects and functors, their basic properties, and some of the problems Saito had to overcome when he created the theory. The majority of talks will be dedicated to a specific result in order to show mixed Hodge modules "in action." The deeper properties of the theory used in each example will be discussed. Additional talks will cover recent developments and connections to other areas, such as generic vanishing theorems, geometric representation theory, or Donaldson-Thomas invariants.
Schedule
Monday, August 19
| 8:30 | Registration |
| 9:00-10:00 | Claude Sabbah Pre-Hodge modules |
| 10:00-12:00 | Break and discussion session |
| 12:00-2:00 | Lunch |
| 2:00-3:00 | Donu Arapura Polarized Hodge modules |
| 3:00-4:30 | Break and discussion session |
| 4:30-5:30 | Takuro Mochizuki Mixed Hodge modules |
Tuesday, August 20
| 9:00-10:30 | Balazs Szendroi Mircea Mustata |
| 10:30-12:00 | Break and discussion session |
| 12:00-2:00 | Lunch |
| 2:00-3:00 | Florian Ivorra Examples of computations |
| 3:00-4:30 | Break and discussion session |
| 4:30-5:30 | Nero Budur Applications to multiplier ideals |
Wednesday, August 21
| 9:00-10:00 | Christian Schnell Direct image and F-filtration |
| 10:00-12:00 | Break and discussion session |
| 12:00-2:00 | Lunch |
| 2:00-3:00 | Sabin Cautis Open embeddings |
| 3:00-4:30 | Break and discussion session |
| 4:30-5:30 | Mihnea Popa Kodaira vanishing |
Thursday, August 22
| 9:00-10:30 | Laurentiu Maxim and Jörg Schürmann Characteristic classes |
| 10:30-12:00 | Break and discussion session |
| 12:00-2:00 | Lunch |
| 2:00-3:00 | Mark de Cataldo Classic Hodge theory and MHM |
| 3:00-4:30 | Break and discussion session |
| 4:30-5:30 | Patrick Brosnan Recovering older results |
Friday, August 23
| 9:00-10:30 | Pramod Achar G-equivariant MHs |
| 10:30-12:00 | Break and discussion session |
| 12:00-2:00 | Lunch |
| 2:00-3:00 | Chris Peters Hodge modules on Shimura varieties |
| 3:00-4:30 | Break and discussion session |
| 4:30-5:30 | Kari Vilonen Unitary representations of reductive Lie groups |
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