Affiliated Faculty

Jack Morava

Professor, Department of Mathematics, Johns Hopkins University

Address:
3400 N. Charles St.
218 Krieger Hall
Baltimore, MD 21218

Phone: (410) 516-7409
Fax: (410) 516-5549
E-mail: jack@math.jhu.edu
Website: http://mathnt.mat.jhu.edu/mathnew/Faculty/HomePages/jmorava.html

CV

Research Interest Statement

My principal interests are algebraic topology and global analysis, and I try to work on questions where they overlap. In recent years I have concentrated on applications of homotopy theory to modern quantum field theory.  More specifically, this usually involves techniques from cobordism and K -theory, applied to problems from equivariant topology (e.g. free loopspaces, orbifolds, Tate cohomology of spectra), or to the theory of operads and configuration spaces (with applications to moduli spaces of Riemann surfaces). Some of my earlier work involved questions in number theory, e.g. unit groups in division algebras, which are some kind of motivic groups for the stable homotopy category; I try to keep up with that subject as best I can. I am currently trying to catch up with recent developments in the study of four-manifolds and Goodwillie calculus.

In terms of mathematical physics, my main interests are conformal field theory and Donaldson theory, and related (semi-infinite) cohomology theories. I am currently trying (without great success) to learn about relations between Seiberg-Witten and integrable systems theory. I have a long-term interest in questions involving the Yamabe problem, expansionary cosmologies, and bubbling, and I'd like to know more about the current big brane theories.

Current Projects

 

Publications

Topological gravity in Minkowski space: notes from a talk at the Second Congress of Latin-
American Mathematicians, Cancun (July 2004); available at math.AT/0407104

(with Nitu Kitchloo): Thom prospectra for loop group representations, submitted to Communications in Mathematical Physics, available at math.AT/0404541

The motivic Thom isomorphism: talk at the Newton Institute (December 2002); Proceedings
of the conference on chromatic phenomena in homotopy theory (Cambridge University
Press); available at math.AT/0306151

Heisenberg groups in algebraic topology: to appear in the Segal Festschrift (Cambridge
University Press), available at math.AT/0305250

HKR characters and higher twisted sectors: talk at the ChengDu ICM satellite conference
on orbifolds (August 2002); to appear in Contemporary Mathematics; available at
math.AT/0208235

more>>

Presentations

Cold Spring Harbor / Wellcome Trust meeting on Interactome Networks, Aug 31 – Sep 4, 2005

Biomolecular networks: properties and evolution, DIMACS Special Focus on Information Processing in Biology, May 13, 2005

Wistar Institute Seminar, April 13, 2005

Workshop on Emerging Genomic Technologies and Data Integration Problems, Feb 21, 2005