Kristine Bauer * Department of Mathematics and Statistics University of Calgary 2500 University Dr. NW Calgary, AB T2N 1N4 Contact Information Office: MS 578 Office Tel: (403) 220-7675 e-mail: kristine@math.ucalgary.ca

Research

• Ph. D. 2001 University of Illinois Urbana-Champaign, "On Hopf Algebra Type and Rational Calculus Decompositions". Supervised by Randy McCarthy.
  
  Abstract: We show that the Goodwillie tower of homotopy functors to spectra split rationally as a product of their homogeneous layers when evaluated on objects which behave like Hopf algebras in the source category. In particular, functors from spaces to (rational) spectra split when evaluated on suspensions: On vanishing Tate cohomology and decompositions in Goodwillie calculus , joint with Randy McCarthy. As an example, we provide a decomposition of higher Hochschild homology and show that the decomposition occurs as the splitting of a Goodwillie tower: Higher Order Hochschild Homology and Its Decompositions .


• Calculus and cotriples: joint work with Brenda Johnson and Randy McCarthy.
  
  Abstract: We extend the derivation of Goodwillie calculus as a cotriple construction to homotopy functors from unbased model categories to spectra. We show that this model agrees with Goodwillie's construction of the tower of n-excisive approximations to a homotopy functor. We use this model to explain how two proposed models of DeRham cohomology for spectra are homotopy equivalent.


• Operads and spectral sequences: joint work with Laura Scull.
  
  Abstract: Given a spectral sequence whose E^2 page consists of algebras over an operad, we give conditions guaranteeing that the spectral sequence converges as an operad algebra.
  Spectral sequences of operad algebras.
  

Courses

• Math 205, Mathematical Explorations (Winter 2008, Winter 2009)
• Math 251, Calculus I (Fall 2003, Fall 2004, Winter 2007)
• Pmat 315, Abstract Algebra (Winter 2004, Winter 2006)
• Math 349, Calculus III (Fall 2004, Fall 2005, Fall 2007)
• Math 353, Calculus IV (Winter 2005, WInter 2007)
• Math 211/221, Linear Algebra I (Fall 2005, Fall 2007, Fall 2008)
• Math 273, Honour Math I: Numbers and Proofs (Fall 2008, Fall 2009) (I was involved in the creation of this course and it is one of my pet projects.)
• Math 213, Honours Linear Algebra I (Winter 2011) (This is another one of my pet projects.)
• PMAT 505, Topology I (Fall 2006)
• PMAT 607, Topology II (Winter 2008, Winter 2009, Winter 2011)

Links

• MathSciNet Mathematical Reviews on the Web.
• XXX Mathematics Archives of online "e-prints".
• Hopf Topology Archives.
• Midwest Topology Seminar Websight.
• Algebraic Topology Discussion List
• XY-Pic User's guide