Manuel Rivera

About me

I am an Assistant Professor at 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. More specifically, I am interested in the applications of the homotopy theory of algebraic structures to problems in topology and geometry. This had led me to think about abstract homotopy theory in general, homological algebra, higher category theory, geometric topology, string topology, symplectic topology, among other topics.

I am also interested in sharing, discussing and developing initiatives and ideas that promote diversity in mathematics and make quality research and education accesible to all. I am particularly interested in promoting research and higher education in mathematics, as well as general mathematical culture, in Latin America and among underrepresented groups in the US.

You can contact me at manuelr at

Publications and preprints:

  • The Tate-Hochschild complex of a cyclic A-infinity algebra,

M. Rivera, Z. Wangin preparationM. Rivera, F. Wierstra, M. ZeinaliansubmittedarXiv:2006.05362M. Rivera, Z. WangsubmittedarXiv:1912.13267M. RiverasubmittedarXiv:1910.08455 M. Rivera, F. Wierstra, M. Zeinalianto appear in Algebraic and Geometric Topology (2020)arXiv:1906.03655M. Rivera, M. Zeinalianto appear in Fundamenta Mathematicae (2020)arXiv:1807.06410M. Rivera, M. ZeinalianHigher Structures, 4(1) (2020) 33-56.arXiv:1805.01264M. Rivera, F. Wierstra, M. ZeinalianProc. Amer. Math. Soc. (2019)doi: 10.1090/proc/14555 arXiv:1808.10237M. Rivera, Z. WangJ. Noncommut. Geom. 13 (2019), 297-361. doi: 10.4171/JNCG/325 arXiv:1703.03899M. Rivera, M. ZeinalianAlgebr. Geom. Topol. 18:7 (2018), 3789-3820arXiv:1612.04801M. Rivera, S. SaneblidzeBull. London Math. Soc. (2018) doi:10.1112/blms.12202, arXiv:1712.02644M. Rivera, S. SaneblidzeJ. Homotopy Relat. Struct. (2018) doi:10.1007/s40062-018-0216-4,arXiv:1706.00983F. Dorais, S. Gubkin, D. McDonald, M. Rivera Order 30 (2013), 415–426 arXiv:1202.4092

Expository notes:

M. Rivera,The Harvard College Mathematics Review 3 (2011) 24-27