Mark W. Johnson's Research
Professor of Mathematics
Penn State Altoona
 Homepage

Conference Information Link
 I was an organizer of a conference to held at the
University of Illinois (at UrbanaChampaign) July 17 to 21,
2017.
 Old Conference Information

 I was an organizer of an American Mathematical Society
special session at the Jan. 2014 Joint
Mathematics meetings in Baltimore, along with a
satellite conference at Johns Hopkins
 I was an organizer of an American Mathematical Society
special session at the Jan. 2012 Joint Mathematics meetings
in Boston, along with a satellite conference at MIT.
 I was corresponding organizer of a special session
at the Fall 2009 AMS Eastern Section Meeting in State College, PA,
October 24 and 25, as well as an associated miniconference
at Penn State Altoona on October 23.
Session details
 I was corresponding organizer of an
American Mathematical Society special session at
the Jan. 2009 Joint Mathematics meetings in Washington, D. C.
 I was corresponding organizer of a
special session
at the Fall 2007 AMS Southeastern Section Meeting in Murfreesboro,
TN, November 3 and 4.

Topology/Geometry Seminar
 The Penn State Topology/Geometry Seminar meets almost exclusively
in Altoona these days, but used to have occassional meetings at
University Park. If you are
interested in giving a talk, feel free to contact me.
 PROPs book
 This is a research monograph, with
Donald Yau,
attempting to provide a unified
treatment of all kinds of operational structure (operads, properads,
dioperads, wheeled PROPs, etc.) and the things they naturally
act upon (i.e. algebras and modules).
Nearly final pdf file.
 Publications in Print

An alternative, often more uptodate for preprints, is to look through my submissions to the arXiv or with
their atom feed. This
arxiv list excludes only the last three items below.

Higher homotopy operations and AndreQuillen cohomology,
Advances in Mathematics, 230 (2012) 777817,
with
David Blanc of
the University of
Haifa and James M. Turner of Calvin College.

Factoring the BeckerGottlieb Transfer Through the Trace Map,
Pure and Applied Mathematics Quarterly, 8 no. 1 (2012)
(the FarrellJones proceedings), with
Wojciech Dorabiala also of Penn State Altoona.
 On
modified Reedy and modified projective model structures,
Theory and Applications of Categories, 24 (2010) 179208.

Higher homotopy operations and cohomology,
Journal of Ktheory 5 (2010) 167200,
with
David Blanc of
the University of
Haifa and James M. Turner of Calvin College.

On homotopy invariance for algebras over colored PROPs,
Journal of Homotopy and Related Structures 4 (2009) 275315,
with
Donald Yau of
the Ohio State University at Newark.

Localtoglobal spectral sequences for the cohomology
of diagrams,
Journal of Pure and Applied Algebra 213 (2009) 3453,
with
David Blanc of
the University of
Haifa and James M. Turner of Calvin College.

On Realizing Diagrams of Pialgebras,
Algebraic and Geometric Topology 6 (2006) 763807,
with
David Blanc
of the University of Haifa and James M. Turner of Calvin College.

Realizing Kasparov's KKtheory Groups as the Homotopy Classes of Maps
of a Quillen Model Category,
in Contemporary Mathematics, Volume 399 (2006)
An Alpine Anthology of Homotopy Theory,
Dominique Arlettaz and Kathryn Hess (Editors),
with
Michael Joachim
of Universitaet Muenster.

The product theorem for parametrized homotopy Reidemeister torsion,
Journal of Pure and Applied Algebra, 196 (2005) 5390 with
Wojciech Dorabiala also of Penn State Altoona.

Model structures on the category of exspaces,
Topology and its Applications, 119 (2002) 325353,
with
Michele Intermont of
Kalamazoo College.

A sheaftheoretic view of loop spaces,
Theory and Applications of Categories, 8 (2001) 490508.
 Preprints in progress

Once again, you can see my arXiv listing or the atom feed to see if any have been posted.
 On higher Segal maps and internal categories.
 On describing Waldhausen's S. construction using adjoints.
 Ideals in categories and Cech cohomology for diagrams, with
David Blanc and James Turner.
 Generalized metrics, diameters and onesided enrichments, with
Hossein MovahediLanakarani and Bob Wells.
 Foundations of the Theory of PROPs, a research monograph in progress with
Donald Yau.
 Current Research Collaborations

 David Blanc, Jim Turner and I received a
grant supporting our ongoing work
with diagrams of Pialgebras, AndreQuillen cohomology, and
higher homotopy operations in Quillen model categories. We have
been gradually shifting our focus toward the last of these.
Here are slides
from a 20minute talk I gave in March 2008
on this project. We hope to finish the ideals SS article this summer
and hopefully use it to study higher homotopy operations.
 Wojciech Dorabiala and I are continuing to talk about things
related to Walhausen's algebraic Ktheory of spaces. Most recently,
we have been discussing an approach to the Additivity Theorem which
would generalize to an adjoint functors approach to Atheory.
 Tom Fiore is telling me about double categories (e.g. internal categories
in Cat), and we're talking about generalizing various constructions
to them. With luck, this may eventually lead to a
version of Waldhausen's Ktheory functor for double categories.
 Donald Yau has been discussing various model category constructions
with me, mostly for extending our article on colored PROPs into a
research monograph. The content of the monograph is to be a careful
discussion of graph substitution, Markl's notion of pasting scheme,
generalized PROPs which include things like properads and halfPROPs
in the same theory, and the appropriate notions of algebra or module.
As a related side project, we hope to work with Terry Bisson to
adapt his recent model category of graphs techniques to our
version of colored wheeled graphs.
 Hossein MovahediLankarani, Bob Wells, and I are talking about various
constructions for generalized metric spaces, particularly
trying to build the machinery of Lipschitz topology in this context.
The nominal goal is to understand HausdorffGromov limits in a quite
general context.
 Research Collaborators (Past, Present, and Future)

 Terry Bisson 
Canisius College
 David Blanc  U. Haifa
 Wojciech Dorabiala  Penn State Altoona
 Tom Fiore 
U. MichiganDearborn
 Michele Intermont 
Kalamazoo College
 Michael Joachim
 U. Munster
 Hossein MovahediLankarani  Penn State Altoona
 Jonathan Scott  Cleveland State University
 Jim Turner  Calvin College
 Robert Wells  Penn State (University Park) Emeritus
 Donald Yau  Ohio State Newark
 Recent Presentations

 "On Minimal Higher Homotopy Operations", Topology Seminar,
Johns Hopkins University, October 2011. Also at
Union College Mathematics Conference, April 2011.
 "Deconstructing Waldhausen's S_\bullet construction", American
Mathematical Society Eastern Sectional Meeting, Ithaca NY, September 2011.
 "Quillen's Language of Model Categories", Mathematics Colloquium,
University of Haifa, Israel, May 2011.
 "Stable Homotopy and the Language of Sheaves", Topology Student Seminar,
Hebrew University of Jerusalem, Israel, May 2011.
 "Minimal Higher Homotopy Operations and Realizing Resolutions",
Deformation Theory Seminar, University of Pennsylvania, February 2011.
 "On Homotopy Invariance for Algebras over Colored PROPs", Geometry and
Physics Seminar, Penn State, November 2010.
 "Thoughts on higher Segal maps and internal categories",
Topology/Geometry Seminar, Penn State, February 2010.
 "Spec of a category and a Tot spectral sequence",
Topology/Geometry Seminar, Penn State, October 2009.
 "On homotopy invariance for algebras
over colored PROPs",
Mathematics Colloquium, University of Haifa, June 2009.
 "Pialgebras and higher homotopy operations", Topology Seminar,
City University of New York, May 2009.
 "On homotopy invariance for algebras over colored PROPs",
Topology/Geometry Seminar, Penn State, April 2009.
 "On modified Reedy structures", Topology Seminar,
Wayne State University, November 2008.
 "Homotopy theory of colored PROPs", Homotopy Theory special session
of the Fall 2008 AMS Central Section Meeting, organized by
Michele Intermont (Kalamazoo), John Martino (Western Michigan),
and Jeff Strom (Western Michigan).
 "Pialgebras and higher homotopy operations," Topology Seminar,
Ohio State University, May 2008.

"On obstructions to realizing diagrams of Pialgebras," Geometric
Topology special session of the Spring 2008 AMS Eastern Section Meeting,
organized by David Rosenthal (St. John's)
and Marco Varisco (Binghamton).
 "A localtoglobal approach to AndreQuillen cohomology of diagrams,"
Topology Seminar, University of Chicago, May 2007.
 "A localtoglobal approach to AndreQuillen cohomology of diagrams,"
Deformation Theory Seminar, University of Pennsylvania, May 2007.
 "Factoring the BeckerGottlieb transfer through the trace map,"
Topology Seminar, MIT, October 2006.
 "A different view of the algebraic Ktheory of a model category,"
Topology/Geometry Seminar, Penn State, September 2006.
 "Factoring the BeckerGottlieb transfer through the trace map,"
Topology Proseminar, University of Chicago, March 2006.
 "Factoring the BeckerGottlieb transfer through the trace map,"
Topology Seminar, Northwestern University, March 2006.
 "Realizing diagrams of Pialgebras," Union College Mathematics
Conference, Contributed Talks in Algebraic Topology, December 2005.
 "Toward the AndreQuillen cohomology of diagrams,"
Topology/Geometry Seminar, Penn State, September 2005.
 "Realizing generalized Pialgebras," Special Session at
AMS Eastern Section Meeting, April 2005.
 "Resolution Model Categories," Topology/Geometry Seminar,
Penn State, March 2005.