Manuel Rivera

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 different initiatives and ideas that promote diversity in mathematics and make quality research and education accesible to all.

You can contact me at manuelr at purdue.edu

Publications and preprints:

- Adams' cobar construction revisited,

M. Rivera

submitted

arXiv:1910.08455

- Rational homotopy equivalences and singular chains,

M. Rivera, F. Wierstra, M. Zeinalian

submitted

arXiv:1906.03655

- Singular chains and the fundamental group,

M. Rivera, M. Zeinalian

submitted

arXiv:1807.06410

- The functor of singular chains detects weak homotopy equivalences,

M. Rivera, F. Wierstra, M. Zeinalian

Proc. Am. Math. Soc. (2019)

doi: 10.1090/proc/14555

arXiv:1808.10237

- The colimit of an infinity local system as a twisted tensor product,

M. Rivera, M. Zeinalian

Higher Structures, 3 (2) 1-24 (2019)

arXiv:1805.01264

- Singular Hochschild cohomology and algebraic string operations,

M. Rivera, Z. Wang

J. Noncommut. Geom. 13 (2019), 297-361.

doi: 10.4171/JNCG/325

arXiv:1703.03899

- Cubical rigidification, the cobar construction, and the based loop space,

M. Rivera, M. Zeinalian

Algebr. Geom. Topol. 18:7 (2018), 3789-3820

arXiv:1612.04801

- A combinatorial model for the free loop space fibration,

M. Rivera, S. Saneblidze

Bull. London Math. Soc. (2018)

doi:10.1112/blms.12202,

arXiv:1712.02644

- A combinatorial model for the path fibration,

M. Rivera, S. Saneblidze

J. Homotopy Relat. Struct. (2018)

doi:10.1007/s40062-018-0216-4,

arXiv:1706.00983

- Automorphism groups of countably categorical linear orders are extremely amenable,

F. Dorais, S. Gubkin, D. McDonald, M. Rivera

Order 30 (2013), 415–426

arXiv:1202.4092

Expository notes:

- Chen's Power Series Connection

- Summary of Chen's theory of iterated integrals and the (co)homology of the based loop space

- The Toronto Space Problem,

M. Rivera,

The Harvard College Mathematics Review 3 (2011) 24-27

Videos:

- Colloquium talk at Stony Brook University January 2019

- Talk at the IAS, Princeton, NJ May 2017

- Talk at "Algebraic Geometry in Mexico 2017"

- Talk at "Algebraic Geometry in Mexico 2016"

Slides:

- Cubical rigidification, cobar construction, and based loop space- Slides for a talk given at the Topology Ecuador conference in Galápagos on August 2017

- Slides for a talk given at the ICM 2018 Satellite Conference at University of Miami

- Slides for a talk given at the Short Communications Session at ICM 2018 in Rio de Janeiro, Brazil

Links:

- Purdue Topology Seminar

- List of math conferences: MathMeetings.net

- Midwest Topology Seminar

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

- Simons Center for Geometry and Physics