Paul Goerss

Courses 2010-12

This year I have taught advanced graduate courses on complex orientable cohomology theories, including elliptic cohomology. This quarter I'm running a weekly review session for the Geometry and Topology prelim. Here are some suggested review problems:

• Review Questions Geometry and Topology

Courses 2010-11

• Math 360-2 MENU Applied Analysis (Winter 2011)

• Math 360-1 MENU Applied Analysis (Fall 2010)

Midwest Topology Seminar

• Midwest Topology Seminar (March 10, 2012.)

Journals

I am currently editor of two journals:

• Geometry and Topology
  

• Topology and Its Applications
  

Presentations

• Topological Algebraic Geometry: A workshop at the University of Copenhagen June 16--20, 2008.

Manuscripts

• Picard groups for the prime 3 and chromatic level 2 with Hans-Werner Henn, Mark Mahowald, and Charles Rezk

• The rational homotopy of the K(2)-local sphere and the chromatic splitting for the prime 3 and level 2 with Hans-Werner Henn and Mark Mahowald

• The Kervaire invariant in homotopy theory with Mark Mahowald

• The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres (Notes from lectures at IRMA Strasbourg, May 7-11, 2007)

• Model categories and simplicial methods (Notes from lectures given at the University of Chicago, August 2004)

• A resolution of the K(2)-local sphere (with Hans-Werner Henn, Mark Mahowald, and Charles Rezk)

• The realization space of a Pi-algebra (with David Blanc and Bill Dwyer)

• Homotopy and homology for simplicial abelian Hopf algebras (with James Turner)

• Homotopy theory of simplicial abelian Hopf algebras(with James Turner)

• The homology of homotopy inverse limits

• Localization theories for simplicial presheaves (with J.F. Jardine)

• A homotopy operation spectral sequence for the computation of homotopy groups (with H.-J. Baues)

• Hopf rings, Dieudonne modules, and $E_\ast \Omega^2 S^3$

• Brown-Gitler Spectra (Entry for Kluwer Mathematics Encyclopedia)

The Multiplicative Ring Spectra Project, with Mike Hopkins

• Quasi-coherent sheaves on the moduli stack of formal groups (Revised April 2, 2008)

• Moduli spaces of commutative ring spectra
  This is a greatly revised version of "Realizing commutative ring spectra as E_\ifty ring spectra".

• Moduli problems for structured ring spectra
  This contains all of the proofs (and much more) promised by the paper "Moduli spaces of commutative ring spectra" above.

• Andre-Quillen(co-)homology for simplicial algebras over simplicial operads

• (Pre-)sheaves of ring spectra over the moduli stack of formal group laws
  Notes from a talk given at the Isaac Newton Institute, September 2002.

• Realizing families of Landweber exact homology theories
  Notes from a talk given at the BIRC March 2008

• Topological Modular Forms [after Hopkins, Miller, and Lurie]
  Article to accompany Bourbaki presentation of March 14, 2009.