Rice University Math Department Calendar

    September 2009          October 2009          November 2009    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
        1  2  3  4  5                1  2  3    1  2  3  4  5  6  7
  6  7  8  9 10 11 12    4  5  6  7  8  9 10    8  9 10 11 12 13 14
 13 14 15 16 17 18 19   11 12 13 14 15 16 17   15 16 17 18 19 20 21
 20 21 22 23 24 25 26   18 19 20 21 22 23 24   22 23 24 25 26 27 28
 27 28 29 30            25 26 27 28 29 30 31   29 30

4:00 pm Monday, September 28, 2009
Stulken Topology Seminar: A Gentle introduction to Massey Products
by Tim Cochran (Rice) in HB 427

"How do we distinquish, using, say, the singular chain complex, spaces whose cohomology rings are isomorphic?" With this motivation, I will introduce the higher-order cohomology operations known as Massey products. At the end I will relate these to the more general A-infinity structures on a graded algebra, defined last Friday by Professor Harvey. First-year grad students are welcome, but having seen cup-product and cohomology would be a prerequisite to getting a lot out of the talk. Host Department: Rice University-Mathematics
Submitted by cochran@rice.edu

4:00 pm Wednesday, September 30, 2009
Geometry-Analysis: Rectifiable and Flat G-Chains in a Metric Space
by Robert Hardt in HB 227

Rectifiability and compactness properties for Euclidean-space chains having coefficients in a finite group G were studied by W.Fleming(1966). This allowed for the modeling of unorientable least-area surfaces including a minimal Mobius band in 3-space. These properties were optimally extended by Brian White (1999) to any complete normed abelian group which contains no nonconstant Lipschitz curves. The new proofs of basic theorems from Geometric Measure Theory involved slicing to reduce to questions about 0 dimensional chains (which are finite or countable sums of weighted point masses). Independently L.Ambrosio and B.Kirchheim (2000) also generalized some basic rectifiability theorems of Federer and Fleming to currents in a general metric space. Our current work with T. De Pauw shares features and results with all these works, includes new definitions of a flat G chain in a metric space, and a proof that such a chain is determined by its 0 dimensional slices. Host Department: Rice University-Mathematics
Submitted by hardt@rice.edu

2:30 pm Thursday, October 1, 2009
Current Math Seminar: An Introduction to Cellular Homology, Covering Spaces
by James Cooper, Derek Goto (Rice University) in HB 227

James Cooper: Homology is a tool that we use to find the higher dimensional holes that the fundamental group fails to find. This provides us another topological invariant we may use to distinguish between spaces. I define a cellular complex and n-chains on that complex. With a boundary operator, we form a chain of abelian groups of these chains. We then use this sequence of groups to define homology. I will end with examples of computing homology and, time permitting, the statement of the Mayer–Vietoris sequence. Derek Goto: The correspondence between covering spaces and deck groups is basically Galois theory in another category. I will talk about this and go over some relevant examples. If there is time, I will say a bit about Cayley complexes.Host Department: Rice University-Mathematics
Submitted by sm29@rice.edu