Fall 2009 Topology Seminar
Fridays at 1:00 in MDD 207

• 11 September 2009:
  Graph embeddings and chromatic numbers
  Maciej Niebrzydowski
• 18 September 2009:
  More on graph embeddings
  Maciej Niebrzydowski
• 25 September 2009:
  Sheaves of sets on a Grothendieck site
  Daniel Davis
• 9 October 2009:
  Limits and sheaves of sets on a site
  Daniel Davis
• 16 October 2009:
  Crossing numbers of graphs
  Maciej Niebrzydowski
• 23 October 2009:
  What is the Dimension of R(n)?
  Roger Waggoner
• 30 October 2009:
  Lloyd Roeling Conference
• 6 November 2009:
  Representing graphs
  Jake Sundberg
• 13 November 2009:
  Representing graphs, part two
  Jake Sundberg
• 20 November 2009:
  Path connectedness
  Vic Schneider

• January 21st:
  Introduction to span
  Thelma West
• January 28th:
  Span, pt. II: a consideration of 'an atriodic tree-like continuum with positive span' (after Ingram)
  Thelma West
• February 6th:
  Sheaves of abelian groups on topological spaces
  Daniel Davis
• February 13th:
  Regular Sequences in unstable algebras over the Steenrod algebra
  Mara Neusel (Texas Tech)
• February 20th:
  Connections between graph theory and knot theory
  Maciej Niebrzydowski
• February 27th:
  Defining sheaves with equalizer diagrams and Grothendieck sites
  Daniel Davis
• March 6th:
  Fibered products, sieves, and pretopologies on categories
  Daniel
• March 13th:
  Connections between graph theory and knot theory, Part II
  Maciej Niebrzydowski
• March 20th:
  Obtaining Grothendieck sites via bases
  Daniel
• March 27th:
  Topological quandles
  Maciej
• April 3rd:
  Introduction to hyperspaces
  Thelma West
• April 24th:
  An Application of the snake and horseshoe lemmas to the functors Hom( - , G) and Ext( - , G), in the category Ab
  Chris Ryan (graduate student)
• May 1st:
  Size levels of arcs, continued
  Thelma West

• September 5:
  Introduction to Khovanov homology I
  Maciej Niebrzydowski
• September 12:
  No seminar due to Hurricane Ike
• September 19:
  Introduction to Khovanov homology II
  Maciej Niebrzydowski
• September 26:
  Introduction to simplicial sets
  Daniel Davis
• October 3:
  No seminar due to Fall break
• October 10:
  No seminar due to Hurricane Ike makeup classes
• October 17:
  Homotopy theory and simplicial sets
  Daniel Davis
• October 24:
  Gram determinants in Knot Theory: skein module motivation
  Jozef Przytycki (The George Washington University)
• October 31:
  The lattice of topologies on the set
  Vic Schneider
• November 7:
  The lattice of topologies on the set, part 2
  Vic Schneider
• November 14:
  No seminar
• November 21:
  Dimension theory 101
  Roger Waggoner
• December 5:
  Elementary open problems in knot theory
  Maciej Niebrzydowski

• 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 Davis.
• February 18:
  Quandles, racks, and related knot invariants,
  Maciej Niebrzydowski.
• February 25:
  Quandle homology theories and their connection with geometry of knots,
  Maciej Niebrzydowski.
• March 3:
  Topological groups,
  Vic Schneider.
• March 10:
  Topological groups, part two,
  Vic Schneider.
• March 17:
  The homological algebra of the continuous cohomology of topological groups increases as one restricts to profinite groups,
  Daniel Davis.
• 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 Waggoner.
• April 21:
  Three basic examples employing inverse limits, Part II,
  Thelma West. (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 Davis, 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.