# Mathematical Sciences Research Institute

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# Workshop

Topology of Stratified Spaces September 08, 2008 - September 12, 2008
 Registration Deadline: September 03, 2008 about 6 years ago June 08, 2008 over 6 years ago
Parent Program: Analysis on Singular Spaces
Organizers Greg Friedman, Eugénie Hunsicker, Anatoly Libgober, and Laurentiu Maxim
Speaker(s)

Description

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. Funding & Logistics ## Show Funding To apply for funding, you must register by the funding application deadline displayed above. Students, recent Ph.D.'s, 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. ## Show Lodging MSRI has preferred rates at the Rose Garden Inn, depending on room availability. 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 the MSRI rate on all room types available. MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code 123MSRI. Our preferred rate is$139 per night for a Deluxe Queen/King, based on availability.

MSRI has preferred rates of $149 -$189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

MSRI has preferred rates of $110 -$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

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Schedule
Sep 08, 2008
Monday
 09:00 AM - 10:00 AM An introduction to L^2 cohomology Xianzhe Dai 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
Sep 09, 2008
Tuesday
 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 02:30 PM - 03:30 PM The weight filtration for real algebraic varieties Clinton 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
Wednesday
 09:00 AM - 10:00 AM Elliptic genus of singular varieties Anatoly Libgober (University of Illinois) 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
Sep 11, 2008
Thursday
 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 Sandor Kovacs (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
Friday
 09:00 AM - 10:00 AM Hodge Structures and Homological Mirror Symmetry Ludmil Katzarkov (University of California, Irvine) 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