Home /  Topology of Stratified Spaces


Topology of Stratified Spaces September 08, 2008 - September 12, 2008
Registration Deadline: September 03, 2008 almost 16 years ago
To apply for Funding you must register by: June 08, 2008 about 16 years ago
Parent Program:
Organizers Greg Friedman, Eugénie Hunsicker, Anatoly Libgober, and Laurentiu Maxim

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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.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Sep 08, 2008
09:00 AM - 10:00 AM
  An introduction to L^2 cohomology
Xianzhe Dai (University of California, Santa Barbara)
10:30 AM - 11:30 AM
  L2 cohomology of QALE space
Gilles Carron (Université de Nantes)
01:15 PM - 02:15 PM
  Cohomology of compactifications of locally symmetric spaces
Les Saper
02:30 PM - 03:30 PM
  The signature operator on Witt spaces (joint work with Pierre Albin, Eric Leichtnam and Rafe Mazzeo)
Paolo Piazza (Università di Roma "La Sapienza'')
Sep 09, 2008
09:00 AM - 10:00 AM
  The Signature of Singular Spaces and its Refinements to Generalized Homology Theories.
Markus Banagl
10:30 AM - 11:30 AM
  Replacement of fixed points of group actions
Sylvain Cappell
01:15 PM - 02:15 PM
  Stratified Surgery and Functoriality
Shmuel Weinberger (University of Chicago)
02:30 PM - 03:30 PM
  The weight filtration for real algebraic varieties
Clint McCrory (University of Georgia)
04:00 PM - 04:30 PM
  Lattices with torsion and rational homology manifolds
Jim Fowler
04:30 PM - 05:00 PM
  The (intersection) homology groups of a fibre bundle over a sphere
Filipp Levikov
Sep 10, 2008
09:00 AM - 10:00 AM
  Elliptic genus of singular varieties
Anatoly Libgober (University of Illinois, Chicago)
10:30 AM - 11:00 AM
  Cohomology of complements to algebraic plane curves
Daniel Matei
11:00 AM - 11:30 AM
  Monodromy of curves and quasi-ordinary surfaces
Lee McEwan (The Ohio State University-Mansfield)
11:30 AM - 12:00 PM
  Leray-type Operators for Stratified Spaces and the Parshin's Reciprocity Law for Residues
Mikhail Mazin (Kansas State University)
Sep 11, 2008
09:00 AM - 10:00 AM
  Singular Elliptic Genus of Normal Surfaces
Robert Waelder
10:30 AM - 11:30 AM
  Singularities in the Minimal Model Program
Sándor Kovács (University of Washington)
01:15 PM - 02:15 PM
  Motivic Characteristic classes of singulare varieties
Shoji Yokura
02:30 PM - 03:30 PM
  The perverse filtration and the Lefschetz Hyperplane Theorem
Mark de Cataldo
Sep 12, 2008
09:00 AM - 10:00 AM
  Hodge Structures and Homological Mirror Symmetry
Ludmil Katzarkov (University of Miami)
10:30 AM - 11:30 AM
  Singularities of Normal Functions
Gregory Pearlstein
01:15 PM - 02:15 PM
  Characteristic classes of mixed Hodge modules
Joerg Schuermann
02:30 PM - 03:30 PM
  Hodge theory of Calabi-Yau fibrations
Matt Kerr