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Topology of Stratified Spaces

September 08, 2008 to September 12, 2008
Organized By: Greg Friedman, Eugénie Hunsicker, Anatoly Libgober, and Laurentiu Maxim
 
Parent Programs:
Analysis on Singular Spaces
 
Participant List:
View a List of Registered Participants
 
Stratified spaces occur naturally in high- and low-dimensional topology, various fields of pure mathematics, including algebraic geometry and number theory, and also in more applied fields, such as the study of configuration spaces for robot motion planning. In recent years, there has been extensive interest and success in expanding to stratified spaces the triumphs of algebraic topology in manifold theory, including the vast progress in the mid-20th century on signatures, characteristic classes, surgery theories, and the special homological properties of nonsingular analytic and algebraic varieties, such as the Kähler package. Yet such extensions from manifold theory to stratified space theory are rarely straightforward; they tend to involve the discovery and study of subtle interactions between local and global behavior. Furthermore, research in these areas turns out to have a rich interaction with the question being addressed by the Analysis of Singular Spaces program running simultaneously at MSRI of how to do analysis on spaces that are not locally Euclidean.

The workshop will be organized into days dedicated to each of the four main themes: topology of complex varieties, signature theory on singular spaces, L^2 and intersection cohomology, and mixed Hodge theory and singularities. Each day except Wednesday will include one introductory talk aimed at audience members from both topology and analysis of singular spaces, and three research talks. There will also be room for some shorter talks by PhD students or recent graduates and for a few talks on Wednesday morning on related subjects that do not fit one of these categories.

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.
The cut-off date for reservations is August 22, 2008.

A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail only: K00000. The cut-off date for reservations is August 8, 2008. Reservations can not be made on the website. Room Rate $159/ night.
 

Follow this link to read about the new U.S. visa requirements

 

Schedule

Monday September 8, 2008

09:00AM - 10:00AM  Xianzhe Dai An introduction to L^2 cohomology    (See Abstract)
10:00AM - 10:30AM  Coffee, Tea in the Atrium
10:30AM - 11:30AM  Gilles Carron L2 cohomology of QALE space    (See Abstract)
11:30AM - 01:15PM  Lunch
01:15PM - 02:15PM  Les Saper Cohomology of compactifications of locally symmetric spaces    (See Abstract)
02:30PM - 03:30PM  Paolo Piazza The signature operator on Witt spaces (joint work with Pierre Albin, Eric Leichtnam and Rafe Mazzeo)    (See Abstract)
03:30PM - 04:00PM  Coffee, Tea in the Atrium
04:00PM - 05:30PM  Evans lecture

Tuesday September 9, 2008

09:00AM - 10:00AM  Markus Banagl "The Signature of Singular Spaces and its Refinements to Generalized Homology Theories."    (See Abstract)
10:00AM - 10:30AM  Coffee, tea in the Atrium
10:30AM - 11:30AM  Sylvain Cappell Replacement of fixed points of group actions    (See Abstract)
11:30AM - 01:15PM  Lunch
01:15PM - 02:15PM  Shmuel Weinberger Stratified Surgery and Functoriality    (See Abstract)
02:30PM - 03:30PM  Clinton McCrory The weight filtration for real algebraic varieties    (See Abstract)
03:30PM - 04:00PM  coffee, Tea in the Atrium
04:00PM - 04:30PM  Jim Fowler Lattices with torsion and rational homology manifolds    (See Abstract)
04:30PM - 05:00PM  Filipp Levikov The (intersection) homology groups of a fibre bundle over a sphere    (See Abstract)
05:00PM - 08:00AM  Welcome Reception

Wednesday September 10, 2008

09:00AM - 10:00AM  Anatoly Libgober Elliptic genus of singular varieties.    (See Abstract)
10:00AM - 10:30AM  Coffee, Tea in Atrium
10:30AM - 11:00AM  Daniel Matei Cohomology of complements to algebraic plane curves    (See Abstract)
11:00AM - 11:30AM  Lee McEwan Monodromy of curves and quasi-ordinary surfaces    (See Abstract)
11:30AM - 12:00PM  Mikhail Mazin Leray-type Operators for Stratified Spaces and the Parshin's Reciprocity Law for Residues

Thursday September 11, 2008

09:00AM - 10:00AM  Robert Waelder Singular Elliptic Genus of Normal Surfaces    (See Abstract)
10:00AM - 10:30AM  Coffee, Tea in the Atrium
10:30AM - 11:30AM  Sandor Kovacs Singularities in the Minimal Model Program    (See Abstract)
11:30AM - 01:15PM  Lunch
01:15PM - 02:15PM  Shoji Yokura Motivic Characteristic classes of singulare varieties    (See Abstract)
02:30PM - 03:30PM  Mark de Cataldo the perverse filtration and the Lefschetz Hyperplane Theorem    (See Abstract)
03:30PM - 04:00PM  Cofee, tea in the Atrium
04:00PM - 05:30PM  Berkeley Colloquium

Friday September 12, 2008

09:00AM - 10:00AM  Ludmil Katzarkov Hodge Structures and Homological Mirror Symmetry
10:00AM - 10:30AM  Coffee, Tea in the Atrium
10:30AM - 11:30AM  Gregory Pearlstein Singularities of Normal Functions
11:30AM - 01:15PM  Lunch
01:15PM - 02:15PM  Joerg Schuermann Characteristic classes of mixed Hodge modules    (See Abstract)
02:30PM - 03:30PM  Matt Kerr Hodge theory of Calabi-Yau fibrations    (See Abstract)
03:30PM - 04:00PM  Coffee, tea in the Atrium
04:00PM - 05:00PM  Eugenie Hunsicker Problem Session

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