José Manuel Gómez Guerra

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

Academic Background

Associate Profesor. Universidad Nacional de Colombia, sede Medellín. January 2014-Present.

J. J. Sylvester Assitant Professor. Johns Hopkins University. July 2011-December 2013.

Postdoctoral Fellow. University of British Columbia. August 2008-July 2011.

PhD Mathematics. Adviser Igor Kriz. University of Michigan. August 2008.

Masters of Science Mathematics. University of Cincinnati. September 2004.

Bachelor´s degree in Mathematics. Universidad Nacional de Colombia, sede Medellín. December 2002.

studEnts

PhD

• Johana Ramírez Gaviria. Current student.

• Mauricio Cepeda Dávila. Thesis: Transitionally commutative bundles and characteristic classes. (2020).

Masters degree

• Valentina Zapata Castro. Thesis: Atiyah-Segal completion theorem. (2020). Received the award: Tesis meritoria.

• Julián Uribe Castañeda. Thesis: Campos vectoriales linealmente independientes sobre esferas. (2019).

• César Leandro Higuita Pérez. Thesis: Espacios moduli de conexiones planas en G-fibrados principales. (2018).

• Santiago Hernández Torres. Thesis: La sucesión espectral de Atiyah-Hirzebruch para K-teoría. (2018).

• Tomás Mejía Gómez. Thesis: On the topological proof of the Mumford conjeture. (2018). Received the award: Tesis meritoria.

• Leonardo Antonio Aguirre Morales. Thesis: Teorías generalizadas de cohomología. (2017).

• Niny Johanna Arcila Maya. Thesis: Cohomología de productos semidirectos. (2016).

Undergraduate

• Pablo Toro Sánchez. Thesis: Espacios clasificantes y homología de grupos. (2019).

• Jefferson Andrés García Ortiz. Thesis: Curvatura y conexiones en variedades Riemannianas. (2015).

• César Leandro Higuita Pérez. Thesis: Cohomología de de Rham en grupos de Lie compactos. (2015).

• Santiago Hernández Torres. Thesis: Clases características y K-teoría. (2015).