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Current term events in the Department of Mathematics

This week:


  • May 6, 2008 at 12:00, in Gilkey 115: (Topology Seminar) Aaron Leeman, University of Oregon, Generating Spaces for K-Theory Acyclics

    I will consider a functor L_H(-) from the category of nice topological spaces to itself. This functor satisfies several important qualities, but one of them is that it turns maps that induce an isomorphism with respect to integral homology into homotopy equivalences. In fact, I will call the above functor localization with respect to integral homology. It’s intended to be analogous to localization in a ring, instead of inverting certain elements we invert certain maps. It turns out one can do such a thing for any generalized homology theory, but I’ll be considering mainly L_K(-), which is localization with respect to complex K-theory. To investigate such a thing, it’s natural to ask which spaces are sent by this functor to something contractible. I’ll discuss a result by Emmanuel Dror-Farjoun along these lines and work I’ve been doing in this area.

  • May 7, 2008 at 16:00, in TBA (at UO): (UO - Moursund Lecture) William Fulton, University of Michigan, Equivariant cohomology of homogeneous varieties I

    The cohomology of Grassmannians and flag varieties has a rich structure which has been studied geometrically, algebraically, and combinatorially since the 19th century. It grew with the development of enumerative geometry, and influenced the development of intersection theory in algebraic geometry. Equivariant cohomology, which has been available for half a century, further enriches this structure and gives powerful new tools for studying it. These lectures will define and describe these equivariant cohomology rings, and discuss some of the recent developments.

  • May 8, 2008 at 14:00, in Kidder 364: Probability Seminar

  • May 8, 2008 at 16:00, in TBA (at UO): (UO - Moursund Lecture) William Fulton, University of Michigan, Equivariant cohomology of homogeneous varieties II

    see previous

  • May 9, 2008 at 12:00, in Gilkey 113: (Applied Mathematics and Computation Seminar) Kenneth Kennedy, (Student presentation): Application of the 2DSVD to Gappy Images

    The 2DSVD is presented with an application to incomplete data. It has been shown that the SVD (with many other names) may be used to approximate missing data in images. The techniques are extended to the 2DSVD and comparisons are made between the computational efficiency, storage, and results from the SVD and the 2DSVD.

  • May 9, 2008 at 12:00, in Gilkey 113: (Applied Mathematics and Computation Seminar) Viviane Klein, (Student presentation, part II) A-posteriori error estimate for FE methods with non-smooth coefficients

    An a-posteriori estimate by Bernardi/Verfuerth as well as an interesting regularity result for solutions to problems with non-smooth coefficients in fractional order Sobolev spaces will be presented. An example demonstrating the application will be shown.

  • May 9, 2008 at 16:00, in Kidd 364: (Colloquium) Jeremiah Heller, University of Western Ontario, Interactions of geometry and topology in cohomology

    Given a complex algebraic variety one can associate to it a variety of interesting cohomological invariants. For example the "classical" topological invariants such as singular cohomology or complex K-theory or more geometric invariants such as motivic cohomology or algebraic K-theory. In between there are also invariants such as morphic cohomology defined by Friedlander-Lawson and semi-topological K-theory defined by Friedlander-Walker. In this talk we will discuss these invariants and some interesting relations between them.

  • May 9, 2008 at 16:00, in TBA (at UO): (UO - Moursund Lecture) William Fulton, University of Michigan, Equivariant cohomology of homogeneous varieties III

    see previous

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