Brooke Shipley

Professor

Contact Information

• My cv is available.
Updated 6/13.  

Information for students:

• In Fall 2012, I taught MATH 589.


• Here is a somewhat random list of lists of grants and fellowships for graduate school.


• Here is a collection of somewhat random thoughts on mentoring.

Slides for various mathematical talks:

• BIRS, Banff, Canada, June 2011
  Rigidity and algebraic models for rational equivariant stable homotopy theory
  


• Three lectures for Young Women in Topology workshop,
  Hausdorff Research Institute for Mathematics, Bonn, Germany, June, 2010
  An introduction to stable homotopy theory
  An introduction to equivariant homotopy theory
  Algebraic models for rational equivariant stable homotopy theory
  


• A monoidal algebraic model for free rational torus-equivariant spectra (joint with John Greenlees)
  Talk at Complex Cobordism in Homotopy Theory, Baltimore, March 2007
  .pdf version.
  


• Derived equivalences of rings and DGAs (joint work with Dan Dugger)
  Talk at BCAT, July, 2002
  .dvi version, .pdf version.
  


• K-theory and derived equivalences (joint work with Dan Dugger)
  Talk at Northwestern 1/03, similar talk 10/02 at Newton Institute, Cambridge
  .dvi version, .pdf version. .ps version.
  Another version of this talk, given in Arolla, Switzerland 8/04
  .pdf version.
  


• Topological equivalences of DGAs (joint work with Dan Dugger)
  Talk at MSRI 2/03 at MSRI conference on
  Interactions between commutative algebra, homological algebra and representation theory
  .dvi version, .pdf version. .ps version.


• Bernhard Keller's "On differential graded categories"
  An expository paper mentioning the above work, at the ArXiv.
  

Slides for various non-mathematical talks:

• "Tips for writing an NSF Career proposal" part of a panel presentation for a workshop at UIC. .pdf version.
  



• "UIC WISEST (Women in Science and Engineering System Transformation)," .pdf version.
  Panel presentation on NSF Advance Grants, Joint Math Meetings, January 2011;
  Slide contributors: pp. 1 - 14: M. Khare, D. Marker, B. Shipley, L. Siebert, M. Tam; pp. 15 - 28: C. Megaridis, S. Laxpati, C. Jameson, L. Nitsche

Research

Preprints:

• An algebraic model for free rational G-spectra
with John Greenlees; arXiv:1101.4818, January 2011.


• An algebraic model for rational torus-equivariant spectra
with J. P. C. Greenlees , 72 pp; arXiv:1101.2511, January 2011.

Publications:

• The cellularization principle for Quillen adjunctions
  with J. P. C. Greenlees , arXiv:1301.5583,
  to appear in Homology, Homotopy and Applications, 2013.


• The homotopy theory of coalgebras over a comonad
with Kathryn Hess, arXiv:1205.3979,
to appear in Proceedings of the London Mathematical Society, 2013.


• An algebraic model for free rational G-spectra for compact connected Lie groups G
  with J. P. C. Greenlees ,
  Mathematische Zeitschrift 269 (2011), no. 1-2, 373-400.
  
  
• A curious example of triangulated-equivalent model categories which are not Quillen equivalent
  with D. Dugger,
  Algebraic and Geomtric Topology 9 (2009), no. 1, 135-166.
  
  
• Enriched model categories and an application to additive endomorphism spectra
with D. Dugger, PDF
(Previously known as: "Enrichments of additive model categories")
34 pp; Theory and applications of categories 18 (2007) 400--439.


• Interactions between homotopy theory and algebra (Chicago 2004)
  L. L. Avramov, J. D. Christensen, W. G. Dwyer, M. A. Mandell and B. Shipley (Eds.)
  Contemporary Math. 436 (2007) 334pp.
  Amer. Math. Soc., Providence, RI
  
  Conference home page with links to preprints and notes based on the talks.
  

• HZ-algebra spectra are differential graded algebras
PDF
American Journal of Mathematics 129 (2007) 351-379.
© 2007 The Johns Hopkins University Press


• Topological equivalences of differential graded algebras
with D. Dugger, PDF
Advances in Mathematics 212 (2007) 37-61.


• Morita theory in stable homotopy theory
PS, and PDF,
Handbook of Tilting Theory (eds. Angeleri Huegel, Happel, Krause)
London Math. Soc. Lecture Notes Series. 332 (2007) 393-409.


• Postnikov extensions of ring spectra
with D. Dugger, PDF
Algebraic and Geometric Topology 6 (2006) 1785-1829.


• K-theory and derived equivalences
with D. Dugger, PS, PDF, and abstract
Duke Math. J. 124 (2004), no.3, 587--617.
© 2005 Duke University Press


• A convenient model category for commutative ring spectra
PS, PDF, and abstract
Contemp. Math. 346 (2004), 473--483.
© 2004 American Mathematical Society


• Equivalences of monoidal model categories
with S. Schwede, PS, PDF, and abstract
Algebraic and Geometric Topology 3 (2003), 287-334.
© 2003 Geometry and Topology Publications


• Stable model categories are categories of modules.
  with S. Schwede, 44pp., PDF, PS, abstract
  Topology 42 (2003), 103-153.
  This circulated as a preprint under the title Classification of stable model categories.
  © 2003 Elsevier Science Ltd.
  


• A uniqueness theorem for stable homotopy theory
  with S. Schwede, PS, PDF, abstract
  Mathematische Zeitschrift 239 (2002), 803-828.
  © 2002 Springer-Verlag.
  


• An algebraic model for rational $S^1$-equivariant stable homotopy theory
PS, PDF, abstract
Quarterly Journal of Mathematics; 53 (2002), 87-110
© 2002 Oxford University Press


• A telescope comparison lemma for THH
  with M. Mandell,
  Topology and its Applications; 117 (2002), 161-174
  abstract © 2002 Elsevier Science
  
  
• Simplicial structures on model categories and functors
  with C. Rezk and S. Schwede,
  Amer. J. of Math. 123 (2001), 551-575
  abstract and PDF © 2001 The Johns Hopkins University Press
  


• Monoidal uniqueness of stable homotopy theory
  Advances in Mathematics 160 (2001), 217-240
  abstract and PDF © 2001 Academic Press
  


• Model categories of diagram spectra
  with M. Mandell, J. P. May and S. Schwede,
  Proc. London Math. Soc. 82 (2001), 441-512
  abstract and PDF © 2001 London Mathematical Society
  

• Symmetric spectra
  with M. Hovey and Jeff Smith,
  J. of the Amer. Math. Soc. 13 (2000), 149-209
  abstract and PDF © 1999 American Mathematical Society
  
  
• Algebras and modules in monoidal model categories
  with S. Schwede, Proc. London Math. Soc. 80 (2000), 491-511
  abstract and PDF © 2000 London Mathematical Society
  

• Symmetric spectra and topological Hochschild homology
  K-theory 19(2) (2000), 155-183
  abstract and PDF © 2000 Kluwer Academic Publishers

• Convergence of the homology spectral sequence of a cosimplicial space (PDF)
  Amer. J. of Math. 118 (1996), 179-207
  abstract © 1996 The Johns Hopkins University Press
  
  
• Pro-isomorphisms of homology towers
  Mathematische Zeitschrift 220 (1995), 257-271
  abstract © 1995 Springer Berlin
   

   
   

  One of my favorite things:
   

  
   

  Here are some of my bookmarks:

  • Math at the University of Illinois at Chicago
  • Math at Purdue University
  • Math at the University of Chicago
  • Hopf Archive