Research

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Topology Seminar
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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.

Publications

On the structure of the spaces of commuting elements in compact Lie groups. With A. Adem. Accepted for publication in the proceedings of the conference Configuration spaces: Geometry, Combinatorics and Topology. C.R.M. Ennio De Giorgi.

Actions of Eilenberg-MacLane spaces on K-theory spectra and uniqueness of twisted K-theory. With B. Antieau and D. Gepner. Submitted. Arxiv.1006.5099

Equivariant K-theory of compact Lie group actions with maximal rank isotropy. With A. Adem. Accepted for publication in the Journal of Topology.

On the fundamental group of Hom(Zk,G). With A. Pettet and J.Souto. To appear in Math. Zeitschrift. Arxiv.1006.3055
Cohomology of toroidal orbifold quotients. With A. Adem and A. N. Duman. J. 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. To appear in the Proceedings of the Edinburgh Mathematical Society.

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.

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Topology Seminar

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Topology
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