ULL Topology Seminar, Spring 2008

webpage last modified: 5/20/08

  • Note: The seminar meets on Mondays at 3 p.m., in MDD 214.
  • Note: This seminar is being offered to graduate students as Math 591. Here is Math 591's Course Information sheet.
  • January 28: "Inverse limits of spaces and their homotopy limits, with an eye on examples in continuum theory," Daniel Davis.
  • February 11: "Beginning steps in understanding the relationship between algebraic geometry and complex-oriented cohomology theories," Daniel.
  • February 18: "Quandles, racks, and related knot invariants," Maciej Niebrzydowski.
  • February 25: "Quandle homology theories and their connection with geometry of knots," Maciej.
  • March 3: "Topological groups," Vic Schneider.
  • March 10: "Topological groups, part two," Vic.
  • March 17: "The homological algebra of the continuous cohomology of topological groups increases as one restricts to profinite groups," Daniel.
  • March 24: no seminar (Spring break).
  • March 31: "Three basic examples employing inverse limits, Part I," Thelma West. Inverse limits have appeared in various ways in the seminar, but no speaker has yet really dug into the interior of an inverse limit of topological spaces and really unpacked its meaning in a particular situation. One of the purposes of this talk (and the sequel on April 21st) is to give graduate students a better feel for inverse limits.
  • April 7: "The Fixed Point Property," Roger Waggoner.
  • April 14: "The Nielsen number," Roger.
  • April 21: "Three basic examples employing inverse limits, Part II," Thelma. (This talk is a continuation of the March 31st seminar.)
  • April 28: "Higher Grothendieck-Witt groups in Algebra and Topology," Marco Schlichting (Louisiana State University). Abstract: I will motivate the study of higher Grothendieck-Witt groups (alias hermitian K-groups) of rings and schemes with two examples from topology-- cobordism categories of certain 4 manifolds (due to Giansiracusa) and an algebraic reinterpretation of 8-fold real Bott periodicity (due to Karoubi). Then I will explain a recent result of mine concerning the local-global behavior of those groups.
  • May 5: Part one: a brief statement of the definition of elliptic spectrum (related to Q(2) - from the last result of Daniel's colloquium), Daniel, 5 minutes; Part two: "Elliptic curves, their associated abelian groups, and points of finite order," Matthew Lennon (graduate student), a 25-minute talk; Part three: "The Nielsen number and the Jiang subgroup," Roger Waggoner, a 35-minute talk.
  • Other seminar activity: on May 9, Anne Vakarietis (graduate student) gave a one-hour talk to Daniel on the topic of Morita equivalence in ring theory. Note: there is a version of Morita theory that has been worked out in the context of commutative ring spectra.
  • Note: The next-to-last entry above marks our last meeting for this semester. There will be a new edition of the Topology seminar in the fall semester.