Home Page of Mario Andrés Velásquez

Of: 52-512
Email: mario.velasquez at javeriana dot edu dot co

About me

I am an Assistant Professor at Departamento de Matemáticas of the Pontificia Universidad Javeriana in Bogotá.

I am mainly interested in algebraic topology, currently I am working on the different models for (twisted) equivariant K-theory and K-homology as for example configuration spaces or Drinfeld doubles and on computational methods for the Isomorphism Conjectures, and its connections with non-commutative geometry and orbifolds invariants. Here my CV.

I got my PhD at Universidad de los Andes with Bernardo Uribe and in an initial phase with Thomas Schick (Here my thesis).
I was a postdoc at the Centro de Ciencias Matemáticas of the Universidad Nacional Autónoma de México, Campus Morelia. In Morelia I worked with Daniel Juan.

Research Papers
  • Twisted K-theory for the orbifold [*/G], (j.w. E. Becerra and H. Martínez), Pacific Journal of Mathematics, Vol. 264 (2013), No. 2, 471-490. arxiv.
  • Twisted  Equivariant  K-Theory and K-Homology of Sl_3(Z), (j.w. N. Bárcenas), Algebraic and Geometric Topology, Vol. 14 (2014), 823-852. arxiv.
  • A configuration space for equivariant connective K-homology, Journal of Noncommutative Geometry, Vol. 9 (2015), No. 4, 1343-1382. arxiv.
  • Equivariant K-Theory of Central Extensions and Twisted Equivariant K-theory: Sl3(Z) and St3(Z), Homology, Homotopy and Applications, Vol. 18 (2016), 49-70. arxiv.
  • Multiplicative Structures and the Twisted Baum-Connes Assembly map, Transactions of the American Mathematical Society, Vol. 369 (2017), No. 7,  5241--5269.  DOI: 10.1090/tran/7024. arxiv
Preprints
  • Segal's spectral sequence in twisted equivariant K-theory for proper actions, (j.w. N. Bárcenas, J. Espinoza and B.Uribe), to appear in Proceedings of the Edinburg Mathematical Society. arxiv
  • Bredon Cohomology, K-theory and K-homology of Pullbacks of groups, (j.w. N. Bárcenas and D. Juan). arxiv.
  • The Completion Theorem in twisted equivariant $K$-Theory for proper and discrete actions, submitted. arxiv
  • A Kunneth formula for Bredon cohomology of pullbacks and twisted K-theory of some 6-dimensional orbifolds, (j. w. G. Combariza). arxiv
  • A description of the assembly map for the Baum-Connes conjecture with coefficients, submitted. arxiv
  • The algebraic and topological K-theory of the Hilbert Modular Group, (j. w. L. Sánchez), submitted. arxiv
Teaching
  • Differential Geometry (curves and surfaces)
  • Vector Calculus
  • Representation theory (finite groups)
Contact

Address:

Departamento de Matématicas
Cra. 7 No. 43-82
Edificio Carlos Ortíz 5o piso
Tel: (571) 320 8320 ext: 4032
Bogotá D.C, Colombia