Research

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, spaces of homomorphisms in Lie groups and problems in twisted K-theory and orbifold theory.

Publications

A stable splitting for spaces of commuting elements in unitary groups.  With A. Adem and S. Gritschacher. ArXiv:2404.09229. (2024). 

On the second homotopy group of spaces of commuting elements in Lie groups. With A. Adem and S. Gritschacher. International Mathematical Research Notices,  Vol 2022, No. 24, pp. 19617-19689.

A decomposition of twisted equivariant K-theory. With J. Ramírez. SIGMA 17 (2021), 041, 20 pages.

Twisted equivariant K-theory of comapct Lie group actions with maximal rank isotropy.  With A. Adem and J. Cantarero. Journal of Mathematical Physics 59, 113502 (2018).

Equivariant complex bundles, fixed points and equivariant unitary bordism. With A. Angel and B. Uribe. Journal of Alg. & Geo. Topology. 18, (2018), 4001-4035.

A decomposition of equivariant K-theory in twisted equivariant K-theories. With B. Uribe. International Journal of Math. 28, (2017), no. 2.

Infinite loop spaces and nilpotent K-theory With A. Adem, J. A. Lind and U. Tillmann. Journal of Alg. & Geo. Topology. 17, (2017), 869-893.

A classifying space for commutativity in Lie groups. With A. Adem. Journal of Alg. & Geo. Topology 15, (2015), 493-535.

A basis for the diagonally signed-symmetric polynomials. The electronic journal of combinatorics. Vol 20, Issue 4 (2013), P36

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, (2013), 1-26.

Actions of K(π,n) spaces on K-theory and uniqueness of twisted K-theory. With B. Antieau and D. Gepner. Trans. Amer. Math. Soc. 366, (2014), 3631-3648.

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. Proc. Edinb. Math. Soc. (2), 56, (2013), no. 1, 112.

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