Please join us on Friday, June 9, 2010 as Dr. Alexandru Suciu of Northeastern University will be giving a lecture about Dwyer-Fried Invariants. We will be serving coffee, tea, and cookies starting at 3:30pm and the lecture will begin at 4:00pm. The lecture will be held in our studio classroom at 929 Massachusetts Avenue Suite #102 in Cambridge. The abstract is listed below and we look forward to seeing you!
Abstract: Given a finite CW-complex X and a positive integer k, the Galois covers of X with group of deck transformations Z^k are parametrized by the Grassmannian of k-planes in the vector space V = H^1(X, Q). Moving about this rational Grassmannian, and recording when the Betti numbers of the corresponding covers are all finite (up to some fixed degree i) defines certain subsets Omega^i_k(X) of Gr_k(V).
These sets (first studied by Dwyer and Fried in the 1980s) record delicate information on the homological finiteness properties of spaces and groups. I will present a method for determining the sets Omega^i_k(X), using the cohomology jumping loci of X, and the classical incidence correspondence between projective varieties and subvarieties of the Grassmannian. Under favorable conditions, the Omega-invariants are controlled by suitable arrangements of special Schubert varieties. In turn, these arrangements can be computed directly from the cohomology ring of X.
The Worldwide Center of Mathematics, www.centerofmath.org , is located midway between Harvard and Central Squares, at 929 Massachusetts Avenue, Cambridge, MA, in Suite #102. Travel to the Center by public transportation is easy via the #1 bus, or by taking the subway (the T) to Central Square, and walking for 10 minutes. Suite #102 is located on floor 01.
All attendees will need to sign a release form, as the lecture will be recorded for distribution on the Web.
