Spring 2012 Topology Seminar
Fridays at 11:00 in MDD 203

• 27 January 2012
  Introduction to Haar integrals
  Vic Schneider
• 3 February 2012
  Introduction to Haar integrals, part 2
  Vic Schneider
• 10 February 2012
  Title to be announced
  Maciej Niebrzydowski

Fall 2011 Topology Seminar
Fridays at 1:00 in MDD 214

• 2 September 2011
  On some Cayley type theorems
  Maciej Niebrzydowski
• 9 September 2011
  On some Cayley type theorems, part 2
  Maciej Niebrzydowski
• 16 September 2011
  Selfcoincidences of Mappings between Spheres
  Duane Randall (Loyola University, New Orleans)
  Abstract: The concepts of loose and also loose by small deformation are defined for mappings between spheres. The relationship in certain dimensions between mappings which are loose, but not loose by small deformation, with the existence or non-existence of Kervaire invariant one elements will be explained.
• 23 September 2011
  Discrete groups and manifolds in S²xR
  Jozsef Z. Farkas
  Abstract: Thurston's geometrization conjecture played a crucial role for example in proving the Poincare conjecture. There are eight homogeneous simply connected geometries which give rise to compact three-manifolds. One of the simplest of the non-constant curvature ones is the space S²xR, which as its name suggests, is the direct product of the sphere with the real line. Similarly to the "Euclidean strategy" we classify the crystallographic groups in S²xR. We find 134 equivalence classes of space groups up to similarity. These in turn give rise to the 4 well-known compact manifolds admitting S²xR geometry.
• 30 September 2011
  Obstruction theory for E_infty maps
  Niles Johnson (University of Georgia)
  Abstract: We take an obstruction-theoretic approach to the question of algebraic structure on spectra. At its heart, this is an application of the Bousfield-Kan spectral sequence adapted for general operadic structure in a range of topological categories. This talk will focus on examples from rational homotopy theory which illustrate the obstructions to rigidifying homotopy algebra maps between differential graded algebras to strict algebra maps. In the topological context, these provide explicit examples of H_infty maps which cannot be rigidified to E_infty maps.
• 7 October 2011
  An introduction to operads and algebras over operads
  Daniel Davis
  
• 14 October 2011
  Algebras over operads and some canonical examples
  Daniel Davis
  
• 28 October 2011
  S²xR space groups: generalized Coxeter groups and ball packings
  Jozsef Farkas
  
• 4 November 2011
  Fibered categories, fibers, and groupoids
  Daniel Davis
  
• 11 November 2011
  Categories fibered in groupoids, monoids, and classifying spaces
  Daniel Davis
  
• 2 December 2011
  Profinite Groups and Discrete G-Sets
  Brian Hill (graduate student)
  Abstract: Some interactions between profinite groups and discrete G-sets will be explored. In addition, we will examine the sets of morphisms between discrete G-sets, as well as the Hom-set functor.

Spring 2011 Topology Seminar
Wednesdays at 2:00 in MDD 311

• 19 January 2011
  Schubert polynomials and cohomology of flag manifolds
  Leonardo Mihalcea
• 26 January 2011
  Inverse limits with subsets of IxI
  Thelma West
• 2 February 2011
  Inverse limits with subsets of IxI, Part 2
  Thelma West
• 16 February 2011
  Inverse limits with subsets of IxI, Part 3
  Thelma West
• 23 February 2011
  Inverse limits of upper semi-continuous set valued functions
  Thelma West
• 2 March 2011
  Schubert varieties revisited
  Leonardo Mihalcea
• 16 March 2011
  Towards Schubert polynomials
  Leonardo Mihalcea
• 23 March 2011
  Towards Schubert polynomials, part 2
  Leonardo Mihalcea
• 30 March 2011
  Spatial graphs and their invariants
  Maciej Niebrzydowski
• 6 April 2011
  Areas of certain quadrilaterals
  Vic Schneider
• 13 April 2011
  Areas of certain quadrilaterals, part 2
  Vic Schneider
• 27 April 2011
  Continuous group cohomology for towers of discrete G-modules
  Daniel Davis

Fall 2010 Topology Seminar
Fridays at 1:00 in MDD 207

• 17 September 2010
  Knotted surfaces
  Maciej Niebrzydowski
• 24 September 2010
  Knotted surfaces, part 2
  Maciej Niebrzydowski
• 8 October 2010
  A Tale of Six Atriodic Continua, Part 1
  Thelma West
• 15 October 2010
  No seminar this week due to the Roeling Conference.
  
• 22 October 2010
  A Tale of Six Atriodic Continua, Part 2
  Thelma West
• 29 October 2010
  postponed
• 5 November 2010
  Introduction to inverse limits
  Thelma West
• 12 November 2010
  Quantum Schubert Calculus
  Leonardo Mihalcea
  This will be a gentle introduction to main definitions and ideas of Schubert Calculus and its "quantum" version for Grassmannians.
• 19 November 2010
  An introduction to model categories
  Daniel Davis
• 3 December 2010
  An introduction to model categories, part 2
  Daniel Davis

Spring 2010 Topology Seminar
Fridays at 1:00 in MDD 306

• January 29th:
  Kan complexes and categories
  Daniel Davis
• February 5th:
  Kan complexes and $\infty$-categories
  Daniel Davis
• February 19th:
  $\infty$-categories and composition through horns
  Daniel Davis
• February 26th:
  Introduction to digital topology
  Maciej Niebrzydowski
• March 12th:
  Axiomatic digital topology
  Maciej Niebrzydowski
• March 19th:
  'Composition' and joins for $\infty$-categories
  Daniel Davis
• March 26th:
  Equivalent metrics and the spans of graphs, Part I
  Thelma West
• April 16th:
  Equivalent metrics and the spans of graphs, Part II
  Thelma West
• April 23rd:
  Equivalent metrics and the spans of graphs, Part III
  Thelma West
• April 30th (ROOM 208):
  $A^1$-Representability of Hermitian $K$-theory
  Girja Shanker Tripathi (graduate student, LSU)
  Abstract: I will discuss my result that in the $A^1$-homotopy category of smooth schemes over a field of characteristic not equal to 2, the Hermitian $K$-theory is representable by "orthogonal Grassmannians." This result is the Hermitian analogue of the corresponding result for algebraic $K$-theory. I will introduce some ideas (parallel to the ones in topology) from the $A^1$-homotopy theory developed by Morel and Voevodsky (1999).

Fall 2009 Topology Seminar

• 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 (graduate student)
• 13 November 2009:
  Representing graphs, part two
  Jake Sundberg (graduate student)
• 20 November 2009:
  Path connectedness
  Vic Schneider
• 4 December 2009:
  Path connectedness, part 2
  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.