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José Manuel Gómez Guerra


J. J. Sylvester Assistant Professor Department of Mathematics Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218 USA Office : 222 Krieger Hall Phone : 410 516 5132 Email : jgomez@math.jhu.edu

Research Interests

My research in mathematics concerns algebraic topology. More specifically, stable and unstable homotopy theory, infinite loop spaces and K-theory. I am especially interested in applying homotopy theory to problems arising from different areas of mathematics such as geometry, topology and algebraic geometry and also to problems arising in the mathematical aspects of string theory. With this point of view, in the past few years I have been trying to understand moduli spaces of flat connections over surfaces and problems in twisted K-theory and orbifold theory.

Academic Background

J.J. Sylvester Assistant Professor. Johns Hopkins University. July 2011-Present.
Postdoctoral Fellow under the supervision of Alejandro Adem. University of British Columbia. August 2008-July 2011.
PhD Mathematics. Adviser Igor Kriz. University of Michigan. August 2008.
Masters of Science in Mathematics. University of Cincinnati. July 2004.
Bachelor's degree in Mathematics. Universidad Nacional de Colombia sede Medellin. December 2002.

Publications

A basis for the diagonally signed-symmetric polynomials. Arxiv 1303.3491.

On the structure of the spaces of commuting elements in compact Lie groups. With A. Adem. Configuration spaces: Geometry, Combinatorics and Topology. Publications of the Scuola Normale Superiore, Vol. 14

Actions of K(π,n) spaces on K-theory and uniqueness of twisted K-theory. With B. Antieau and D. Gepner. Accepted for publication in Trans. Amer. Math. Soc. Arxiv.1006.5099

Equivariant K-theory of compact Lie group actions with maximal rank isotropy. With A. Adem. Journal of Topology 5 (2012) 431–457.

On the fundamental group of Hom(Zk,G). With A. Pettet and J.Souto. Math. Zeitschrift 271 (2012) 33-44.
Cohomology of toroidal orbifold quotients. With A. Adem and A. N. Duman. Journal of Algebra 344 (2011) 114-136.
Stable splittings, spaces of representations and almost commuting elements in Lie Groups . With A. Adem and F. Cohen. Math. Proc. Camb. Phil. Soc. 149 (2010) 455-490.

Commuting elements in central products of special unitary groups. With A. Adem and F. Cohen. Proceedings of the Edinburgh Mathematical Society. First View Article, October 2012, pp 1 12 DOI: 10.1017/S0013091512000144

On the nonexistence of higher twistings over a point for Borel cohomology of K-theory. Journal of Geometry and Physics 60 (2010) 678-685.

From fibered symmetric bimonoidal categories to symmetric spectra. Preprint.

Stringy bundles and infinite loop space theory. With P. Hu and I. Kriz. Preprint.