Manuel Rivera

I am an Assistant Professor in the Department of Mathematics at Purdue University. 

From September 2016 to August 2019 I held a joint Research Assistant Professorship between University of Miami and CINVESTAV (Mexico City). From September 2015 to August 2016 I was a postdoc at Institut de Mathématiques de Jussieu- Paris Rive Gauche.  I completed my PhD in mathematics at CUNY Graduate Center in 2015 under the supervision of Dennis Sullivan.  From 2006-2010 I was an undergraduate at MIT.  I am originally from San Juan, Puerto Rico

My research is in algebraic topology. I am interested in understanding different kinds of structures from the lens of homotopy theory. This had led me to think about homological and homotopical algebra, category theory, geometric topology, string topology, non-commutative geometry, symplectic topology, among other topics.

I am also interested in sharing, discussing, and developing initiatives and ideas that promote research and higher education, as well as general mathematical culture, in Latin America and among underrepresented groups in academia.

You can contact me at manuelr at  

My research is supported by the NSF Grant DMS 210554 Algebraic structures in topology and geometry.


Publications and preprints

Expository notes

Videos and slides



I am currently one of the organizers for:

  • Purdue Topology Seminar
  • Cibercoloquio Latinoamericano de Matemáticas: See the following article at the Notices for more on this initiative: Cibercoloquio Latinoamericano de Matemáticas, Campos, Daniel; Rivera, Manuel; Salazar, María Amelia; Samper, José Alejandro; Simental, José; Villar, Soledad. Notices Amer. Math. Soc. 68 (2021), no. 5, 793–797

Links to other seminars: