# 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 purdue.edu.

## Publications and preprints:

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

*in preparation*M. Rivera, F. Wierstra, M. Zeinalian

*submitted*arXiv:2006.05362M. Rivera, Z. Wang

*submitted*arXiv:1912.13267M. Rivera

*submitted*arXiv:1910.08455 M. Rivera, F. Wierstra, M. Zeinalian

*to appear in*

**Algebraic and Geometric Topology**(2020)arXiv:1906.03655M. Rivera, M. Zeinalian

*to appear in*

**Fundamenta Mathematicae**(2020)arXiv:1807.06410M. Rivera, M. Zeinalian

**Higher Structures,**4(1) (2020) 33-56.arXiv:1805.01264M. Rivera, F. Wierstra, M. Zeinalian

**Proc. Amer. Math. Soc.**(2019)doi: 10.1090/proc/14555 arXiv:1808.10237M. Rivera, Z. Wang

**J. Noncommut. Geom.**13 (2019), 297-361. doi: 10.4171/JNCG/325

*arXiv:1703.03899M. Rivera, M. Zeinalian*

**Algebr. Geom. Topol.**

*18:7 (2018), 3789-3820arXiv:1612.04801M. Rivera, S. Saneblidze*

**Bull. London Math. Soc.**(2018) doi:10.1112/blms.12202, arXiv:1712.02644M. Rivera, S. Saneblidze

**J. 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

## Videos:

Talk at Purdue Topology Seminar June 2020

Colloquium talk at Stony Brook University January 2019

Talk at the IAS, Princeton, NJ May 2017

Talk at "Algebraic Geometry in Mexico 2017" November 2017

Talk at "Algebraic Geometry in Mexico 2016" November 2016

## Teaching:

## Links:

Lists of math conferences: MathMeetings.net, Conference-Service

Einstein Chair Seminar at CUNY Graduate Center and its video collection.