John E. Harper Visiting Assistant Professor Department of Mathematics Purdue University West Lafayette, Indiana 47907 USA Web: http://www.math.purdue.edu/~harper20/ Email: john.edward.harper@gmail.com Email: harper20@math.purdue.edu Phone: 765-494-1952 Office: MATH 728

About my research

• Research statement --- last updated on February 8, 2013


• Curriculum vitae --- last updated on February 27, 2013


• Long and detailed version of an old research statement

Publications and preprints

• Homotopy theory of modules over operads in symmetric spectra.
  Algebr. Geom. Topol., 9(3):1637--1680, 2009. pdf / journal
  


• Bar constructions and Quillen homology of modules over operads.
  Algebr. Geom. Topol., 10(1):87--136, 2010. pdf / journal
  


• Homotopy theory of modules over operads and non-Sigma operads in monoidal model categories.
  J. Pure Appl. Algebra, 214(8):1407--1434, 2010. pdf / journal
  


• Homotopy completion and topological Quillen homology of structured ring spectra. (with K. Hess)
  To appear in Geometry & Topology. arXiv:1102.1234, 67 pages, 2012. pdf / arXiv
  


• TQ-completion of structured ring spectra. (with M. Ching)
  In preparation.


• Nilpotent structured ring spectra and a generalized TQ Whitehead theorem. (with M. Ching)
  In preparation.

Projects

• TQ-localization. In progress.


• Nilpotency conditions and TQ-completion. (with M. Ching). In progress.


• Pro-TQ-completion. In progress.


• TQ-homology spectral sequence of a cosimplicial structured ring spectrum.
  (with E. Finster). In progress.


• Non-Sigma structured ring spectra over H(Z). In progress.


• Goodwillie towers and structured ring spectra. (with K. Hess). In progress.


• Obstruction theory and homotopy spectral sequences for cosimplicial spaces.
  This is a longer term project that is in its earliest stages.

Extended research visits (1+ months)

• Massachusetts Institute of Technology, Department of Mathematics, July -- August 2011. Invited by M. Behrens and H.R. Miller.


• Universität Bonn, Mathematisches Institut, June -- July 2010. Invited by J. Hornbostel and S. Schwede.


• Fields Institute for Research in Mathematical Science, Toronto, May -- June 2007. Thematic Program on Geometric Applications of Homotopy Theory. Invited by the organizers: G. Carlsson, D. Christensen, and J.F. Jardine.


• Hebrew University of Jerusalem, Einstein Institute of Mathematics, March -- April 2006. Invited by E. Dror Farjoun.

Education

• University of Notre Dame (August 2003 -- May 2008)
  Ph.D. in Mathematics, May 2008, Advisor: W.G. Dwyer

  Before going full-time into mathematics in 2003, I studied rocket science at MIT and Rensselaer:

• Massachusetts Institute of Technology
  S.M. in Aeronautics and Astronautics, June 1999


• Rensselaer Polytechnic Institute
  B.S. in Aeronautical Engineering, December 1995, Magna Cum Laude

Mentoring: Undergraduate and Graduate

• Master's thesis: Varvara Karpova. Thesis title: Why HZ-algebra spectra are differential graded algebras, fall 2009, École Polytechnique Fédérale de Lausanne. Thesis supervisor.


• Mini project: Cyril Becker and Rosalie Chevalley. Project title: Notion de propriété universelle dans le langage de la théorie des catégories, spring 2009, École Polytechnique Fédérale de Lausanne. Project supervisor.


• Semester project: Lev Kiwi. Project title: Algébres de Hopf, fall 2008, École Polytechnique Fédérale de Lausanne. Project supervisor.


• Semester project: Florent Mayencourt. Project title: Noeuds et invariants de Vassiliev, fall 2008, École Polytechnique Fédérale de Lausanne. Project supervisor.


• Semester project: Jean-Paul Wenger. Project title: Braid theory, fall 2008, École Polytechnique Fédérale de Lausanne. Project supervisor.

Teaching: Undergraduate and Graduate

• Math 35300: Section 162. Linear algebra II, spring 2013, Purdue University. Instructor.


• Math 35300: Section 161. Linear algebra II, spring 2013, Purdue University. Instructor.


• Math 35300: Section 002. Linear algebra II, fall 2012, Purdue University. Instructor.


• Math 35300: Section 001. Linear algebra II, fall 2012, Purdue University. Instructor.


• Calc 1000A: Section 011. Calculus I, fall 2011, University of Western Ontario. Instructor.


• Calc 1000A: Section 007. Calculus I, fall 2011, University of Western Ontario. Instructor.


• Calc 1000A: Section 008. Calculus I, fall 2010, University of Western Ontario. Instructor.


• Algebraic topology (topics course), spring 2010, École Polytechnique Fédérale de Lausanne. Instructor.


• Theory of knots, fall 2009, École Polytechnique Fédérale de Lausanne. Assistant.


• Homology and cohomology, spring 2009, École Polytechnique Fédérale de Lausanne. Assistant.


• Elements of homotopy, fall 2008, École Polytechnique Fédérale de Lausanne. Assistant.


• Math 10560: Calculus II, fall 2007, University of Notre Dame. Instructor.


• Math 10560: Calculus II, fall 2006, University of Notre Dame. Instructor.


• Math 20550: Calculus III, fall 2005, University of Notre Dame. Instructor.


• Math 10560: Calculus II, spring 2005, University of Notre Dame. Teaching assistant.


• Math 20550: Calculus III, fall 2004, University of Notre Dame. Teaching assistant.

Selected invited talks

• Ohio State University, Topology Seminar, February 12, 2013: ``Completions in topology and homotopy theory''.


• Purdue University, Topology Seminar, January 24, 2013: ``Coalgebras and TQ-complete structured ring spectra''.


• University of Illinois at Urbana-Champaign, Topology Seminar, December 11, 2012: ``TQ-homology completion of nilpotent structured ring spectra''.


• University of Massachusetts Amherst, Valley Geometry Seminar, December 7, 2012: ``Completions in topology and homotopy theory''.


• Indiana University, Topology Seminar, November 28, 2012: ``TQ-homology completion of nilpotent structured ring spectra''.


• Purdue University, Topology Seminar, September 6, 2012: ``Localization and completion of nilpotent structured ring spectra''.


• Purdue University, Topology Seminar, August 30, 2012: ``Structured ring spectra and TQ-homology''.


• University of Virginia, Virginia Conference on Algebraic Topology, June 14, 2012: ``TQ-completion, homotopy functor calculus, and nilpotent operadic algebras in modules over a ring spectrum''.


• Hunter College of the City University of New York, Colloquium, May 22, 2012: ``Homology, completions, and localizations of structured ring spectra''.


• University of Western Ontario, Algebra Seminar, January 20, 2012: ``Localization and completion of nilpotent structured ring spectra''.


• Boston, Massachusetts, AMS Special Session on Homotopy Theory, January 7, 2012: ``Localization and completion with respect to topological Quillen homology''.


• University of Western Ontario, Geometry and Topology Seminar, September 19, 2011: ``Completion with respect to topological André-Quillen homology''.


• Wesleyan University, Topology Seminar, August 17, 2011: ``Completion with respect to topological André-Quillen homology''.


• Universität Hamburg, Conference on Structured Ring Spectra, August 2, 2011: ``On a finiteness theorem and Quillen homology completion for algebras over operads in symmetric spectra''.


• Massachusetts Institute of Technology, Topology Seminar, July 19, 2011: ``Quillen homology completion and strong convergence of the associated homotopy spectral sequence''.


• University of Georgia, Topology Seminar, April 11, 2011: ``Homology completion, homotopy completion, and a finiteness theorem for operadic algebras in symmetric spectra''.


• University of Calgary, PIMS Voyageur Colloquium, March 22, 2011: ``Homotopy completion, homology completion, and a finiteness theorem for operadic algebras''.


• Massachusetts Institute of Technology, Topology Seminar, February 7, 2011: ``On a finiteness theorem and Quillen homology completion for algebras over operads in symmetric spectra''.


• University of Minnesota, Topology Seminar, November 8, 2010: ``On a homotopy completion tower for algebras over operads in symmetric spectra''.


• University of Virginia, Topology Seminar, October 28, 2010: ``On a homotopy completion tower for algebras over operads in symmetric spectra''.


• University of Western Ontario, Algebra Seminar, October 15, 2010: ``On a homotopy completion tower for algebras over operads''.


• Wayne State University, Topology Seminar, October 12, 2010: ``On a Whitehead theorem for topological Quillen homology of algebras over operads''.


• University of California Los Angeles, AMS Special Session on Homotopy Theory and K-theory, October 9, 2010: ``On a Whitehead theorem for topological Quillen homology of algebras and modules over operads''.


• University of Western Ontario, Geometry and Topology Seminar, October 4, 2010: ``On a Whitehead theorem for topological Quillen homology of algebras over operads''.


• Université Lille 1, Workshop on Operads and Homotopy Theory, August 26, 2010: ``On a Whitehead theorem for topological Quillen homology of algebras over operads''.


• Universität Bonn, Topology Seminar, July 13, 2010: ``On a Whitehead theorem for topological Quillen homology of algebras and modules over operads''.


• University of Copenhagen, Algebra and Topology Seminar, June 7, 2010: ``On a Whitehead theorem for topological Quillen homology of algebras and modules over operads''.


• Université Lille 1, Séminaire de Topologie, March 26, 2010: ``On a Whitehead theorem for topological Quillen homology of algebras and modules over operads''.


• Université Paris 13, Séminaire de Topologie Algébrique, January 28, 2010: ``On a Whitehead theorem for topological Quillen homology of modules and algebras over operads''.


• Isle of Skye, Scotland, Conference on Algebraic Topology, Group Theory and Representation Theory, June 11, 2009: ``Bar constructions and Quillen homology of modules over operads''.


• Le Châtelard, Switzerland, Topology in the Swiss Alps, Young Topologists' Meeting, April 26, 2009: ``Bar constructions and Quillen homology of modules over operads''.


• North Carolina State University, AMS Special Session on Homotopical Algebra with Applications to Mathematical Physics, April 4, 2009: ``Bar constructions and Quillen homology of modules over operads''.


• Massachusetts Institute of Technology, Topology Seminar, March 2, 2009: ``Bar constructions and Quillen homology of modules over operads''.


• Université Lille 1, Séminaire de Topologie, December 12, 2008: ``Bar constructions and Quillen homology of modules over operads''.


• École Polytechnique Fédérale de Lausanne, Séminaire de Topologie, November 27, 2008: ``E_infinity algebras and p-adic homotopy theory''.


• University of Copenhagen, Workshop on E_n Operads in Differential Graded Algebra, November 18, 2008: ``E_infinity algebras and p-adic homotopy theory''.


• Universität Bonn, Topology Seminar, October 21, 2008: ``Bar constructions and Quillen homology of modules over operads''.


• École Polytechnique Fédérale de Lausanne, Séminaire de Topologie, July 1, 2008: ``Bar constructions and Quillen homology of modules over operads''.


• Wayne State University, Topology Seminar, April 15, 2008: ``Quillen homology of modules over operads''.


• University of Chicago, Algebraic Topology Seminar, January 22, 2008: ``Quillen homology of modules over operads''.


• University of Notre Dame, Topology Seminar, October 11, 2007: ``Co-operations on Quillen homology''.


• University of Chicago, Graduate Student Topology Conference, April 21, 2007: ``Quillen homology, homotopy algebras, and Koszul duality for operads''.


• Hebrew University of Jerusalem, Graduate Homotopy Seminar, April 2006: ``Delooping iterated loop spaces, quasifibrations, and bar constructions''.


• Hebrew University of Jerusalem, Graduate Homotopy Seminar, March 2006: ``Detecting loop spaces, monads from adjunctions, and a bar construction''.


• Hebrew University of Jerusalem, Graduate Homotopy Seminar, March 2006: ``Algebras over topological A_infinity operads, E_infinity operads, and the little n-cubes operads''.


• Hebrew University of Jerusalem, Graduate Homotopy Seminar, March 2006: ``Symmetric sequences, circle products, and modules over operads''.

Selected informal talks

• University of Western Ontario, Topics in Homotopy Theory, Fall 2011: ``Connections between topology and algebra: Homotopy theory, André-Quillen homology, and iterated suspensions of commutative rings''.


• École Polytechnique Fédérale de Lausanne, Working Group on the Stable h-Cobordism Theorem, Spring 2009: ``Spaces of thickenings''.


• École Polytechnique Fédérale de Lausanne, Working Group on the Stable h-Cobordism Theorem, Spring 2009: ``Algebraic K-theory of spaces II''.


• École Polytechnique Fédérale de Lausanne, Working Group on the Stable h-Cobordism Theorem, Spring 2009: ``Algebraic K-theory of spaces I''.

Conference participation

• Midwest Topology Seminar, February 2013, organized by M. Ando, M. Frankland, R. McCarthy, and C. Rezk, at the University of Illinois at Urbana-Champaign.


• Midwest Topology Seminar, October 2012, organized by T. Gerhardt and M. Hedden, at Michigan State University.


• The Legacy of Daniel Quillen: K-theory and Homotopical Algebra, October 2012, organized by C. Barwick, M. Behrens, J. Cuntz, E. Friedlander, M.J. Hopkins, J.-L. Loday, H.R. Miller, A. Ranicki, G. Segal, and I. Singer, at the Massachusetts Institute of Technology.


• Stanford Symposium on Algebraic Topology: applications and new directions---a conference to celebrate the birthdays of Gunnar Carlsson, Ralph Cohen, and Ib Madsen, July 2012, organized by S. Galatius, D. Sinha, and U. Tillmann, at Stanford University.


• West Coast Algebraic Topology Summer School: advances in K-theory, July 2012, organized by A. Adem, R. Cohen, and D. Sinha, at Stanford University.


• Virginia Conference on Algebraic Topology, June 2012, organized by G. Arone, W.G. Dwyer, M. Hill, N. Kuhn, K. Lesh, and V. Turchin, at the University of Virginia.


• Midwest Topology Seminar, March 2012, organized by A.M. Bohmann, A. Elmendorf, and P. Goerss, at Northwestern University.


• AMS Special Session on Homotopy Theory, January 2012, organized by M. Behrens, M.W. Johnson, H.R. Miller, J. Turner, and D. Yau, in Boston, Massachusetts.


• AMS Special Session on Calculus of Functors and Its Applications, January 2012, organized by B. Munson and I. Volic, in Boston, Massachusetts.


• Midwest Topology Seminar, October 2011, organized by S. Chebolu and G. Seelinger, at Illinois State University.


• Conference on Structured Ring Spectra, August 2011, organized by A. Baker and B. Richter, at the Universität Hamburg.


• Geometric and Algebraic Structures in Mathematics: a conference to celebrate Dennis Sullivan's 70th birthday, May--June 2011, organized by A. Bonifant, J. Bowman, M. Lyubich, and S. Sutherland, at Stony Brook University.


• Functor Calculus and Operads Workshop, March 2011, organized by M. Ching, N. Kuhn, and V. Turchin, at the Banff International Research Station, Alberta.


• Midwest Topology Seminar, October 2010, organized by R. Bruner, P. Hu, D. Isaksen, and J. Klein, at Wayne State University.


• AMS Special Session on Homotopy Theory and K-theory, October 2010, organized by J. Bergner and C. Haesemeyer, at the University of California Los Angeles.


• Conference on Homotopy Theory and Derived Algebraic Geometry, September 2010, organized by P. Goerss and J.F. Jardine, at the Fields Institute for Research in Mathematical Science, Toronto.


• Workshop on Operads and Homotopy Theory, August 2010, organized by D. Chataur, B. Fresse, and B. Vallette, at the Université Lille 1.


• Georgia Topology Conference: Goodwillie-Weiss embedding calculus and its application to spaces of knots, May 2010, organized by M. Ching and N. Johnson, at the University of Georgia.


• Mayday 2009---New Contexts in Homotopy Theory: a conference in honor of Peter May on the occasion of his 70th birthday, October 2009, organized by M. Basterra, M. Behrens, A. Blumberg, J. McClure, and M. Mandell, at the University of Chicago.


• p-Adic Geometry and Homotopy Theory Conference, August 2009, organized by J. Rognes, in the Nordfjord region of Loen, Norway.


• Conference on Algebraic Topology, Group Theory and Representation Theory, June 2009, organized by D. Benson, C. Broto, I. Capdeboscq, R. Kessar, K. Lesh, R. Levi, and A. Libman, in Isle of Skye, Scotland.


• Topology in the Swiss Alps, Young Topologists' Meeting, April 2009, organized by P. Müller, in Le Châtelard, Switzerland.


• AMS Special Session on Homotopical Algebra with Applications to Mathematical Physics, April 2009, organized by T. Lada and J. Stasheff, at North Carolina State University.


• Workshop on E_n Operads in Differential Graded Algebra, November 2008, organized by A. Berglund, B. Vallette, and N. Wahl, at the University of Copenhagen.


• Workshop on Higher Structures in Mathematics and Physics, November 2008, organized by A. Alekseev, A. Cattaneo, and P. Xu, at the École Polytechnique Fédérale de Lausanne.


• Arolla Conference on Algebraic Topology, August 2008, organized by C. Ausoni, K. Hess, and J. Scherer, in Arolla, Switzerland.


• Homotopical Group Theory and Topological Algebraic Geometry: a conference in honor of Haynes R. Miller on the occasion of his 60th birthday, June 2008, organized by M. Ando, C.F. Bodigheimer, J. Grodal, G. Laures, and B. Shipley, at the Max Planck Institute, Bonn.


• Homotopical Group Theory and Topological Algebraic Geometry Workshop, June 2008, organized by J. Grodal, I. Madsen, J. Moller, E. Pedersen, and N. Wahl, at the University of Copenhagen.


• Midwest Topology Seminar, May 2008, at Northwestern University.


• Graduate Student Topology Conference, March 2008, organized by D. Zaharapol and C. Wendler, at the University of Illinois at Urbana-Champaign.


• Midwest Topology Seminar, February 2008, at the University of Notre Dame.


• Midwest Topology Seminar, October 2007, at the University of Illinois at Urbana-Champaign.


• Workshop on Stacks in Geometry and Topology, May 2007, organized by K. Behrend, P. Goerss, and B. Toën, at the Fields Institute for Research in Mathematical Science, Toronto.


• Graduate Student Topology Conference, April 2007, organized by M. Abouzaid, B. Guillou, and K. Ponto, at the University of Chicago.


• Midwest Topology Seminar, February 2007, at the University of Illinois at Chicago.


• Topics in Homotopy Theory Graduate Summer School, August 2005, organized by K. Bauer and L. Scull, at the University of Calgary.


• Summer School on the Interactions between Homotopy Theory and Algebra, July -- August 2004, organized by L. Avramov, D. Christensen, W.G. Dwyer, M. Mandell, and B. Shipley, at the University of Chicago.

Service to the profession

• Referee for: Algebraic & Geometric Topology, Journal of Pure and Applied Algebra.


• International Peer Reviewer for: Shota Rustaveli National Science Foundation, Tbilisi, Georgia.

Seminars organized

• Geometry and Topology Seminar. University of Western Ontario, fall 2011, spring 2012, co-organizer.


• Séminaire de Topologie. École Polytechnique Fédérale de Lausanne, spring 2009, co-organizer.


• Graduate Topology Seminar, University of Notre Dame, fall 2007, spring 2008, organizer.

Honors, prizes, and memberships

• Ricketts Prize, Rensselaer Polytechnic Institute: ``In recognition of demonstrated outstanding ability in academic work and promise for outstanding professional success''.


• American Mathematical Society (2003 -- present).

Languages (reading)

• French, German.

Extracurricular

• I enjoy running several times a week.

Useful links

• Google
• Mathscinet
• arXiv
• Hopf archive
• K-theory archive
• Bielefeld SFB 343 preprints
• NUMDAM archives
• ALGTOP-L Algebraic topology listserve
• AMS
• SMS
• EMS
• Topology conferences
• Mathematics departments
• Mathematics genealogy project