Manuel Rivera

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

From 2016- 2019 I held a joint Research Assistant Professorship between University of Miami and CINVESTAV (Mexico City). From 2015-2016 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 using homotopical and homological techniques to study problems in geometry, topology, and algebra.

I am also interested in discussing and developing initiatives 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.




  • A detailed look at the Szczarba map, E. Minichiello, M. Rivera, M. Zeinalian, arXiv:2305.13638



  • 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

Expository notes

Videos and slides

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Some seminars