# Omar Antolín Camarena

## Table of Contents

## Contact

Institute of Mathematics

UNAM (National Autonomous University of Mexico)

Mexico City

`omar@matem.unam.mx`

`www.matem.unam.mx/~omar`

## Work

- 2017–present
- Assistant Professor

Institute of Mathematics, UNAM

Mexico City - 2015–2017
- Postdoctoral Fellow

Department of Mathematics, University of British Columbia

Vancouver, Canada

## Education

- 2010–2015
- Ph.D.

Department of Mathematics, Harvard University

Cambridge, MA, USA

*Thesis*: The mod 2 homology of free spectral Lie algebras

*Advisor*: Jacob Lurie - 2006–2007
- M.Sc.

Department of Mathematics, University of Toronto

Toronto, Canada - 1998–2006
- B.Sc.

Faculty of Science, UNAM

Mexico City

*Tesis*: Critically Connected Matroids (in Spanish)

*Advisor*: Jorge Luis Arocha Pérez

## Research Papers

### Published

- with Daniel Sheinbaum.
*Crystallographic Interacting Topological Phases and Equivariant Cohomology: To assume or not to assume*, Journal of High Energy Physics (2021). (https://doi.org/10.1007/JHEP07(2021)139,`arXiv:2007.06595 [math-ph]`

) - with Simon Gritschacher, Bernardo Villareal.
*Higher generation by abelian subgroups in Lie groups*, Transformation Groups (2021). (https://doi.org/10.1007/s00031-021-09659-8/,`arXiv:2009.12257 [math.AT]`

) - with Bernardo Villarreal.
*Nilpotent \(n\)-tuples in \(SU(2)\)*, Proceedings of the Edinburgh Mathematical Society (2020). (https://doi.org/10.1017/S0013091520000309,`arXiv:1611.05937 [math.AT]`

) *The mod 2 homology of free spectral Lie algebras*, Transactions of the American Mathematical Society (2020). (https://doi.org/10.1090/tran/8131,`arXiv:1611.08771 [math.AT]`

)- with Tobias Barthel.
*A simple universal property of Thom ring spectra*, Journal of Topology 12.1 (2019), pp. 56–78. (https://doi.org/10.1112/topo.12084,`arXiv:1411.7988 [math.AT]`

). - with Simon Gritschaher, Bernardo Villareal.
*Commutative classifying spaces of some low-dimensional Lie groups*, Mathematical Proceedings of the Cambridge Philosophical Society (2019). (https://doi.org/10.1017/S0305004119000240,`arXiv:1802.03632 [math.AT]`

). - with Alejandro Adem, Gordon W. Semenoff, Daniel Sheinbaum.
*Topology of Fermi Surfaces and Anomaly Inflows*, Journal of High Energy Physics (2016) 2016:83. (https://doi.org/10.1007/JHEP11(2016)083,`arXiv:1509.01635 [cond-mat.mes-hall]`

). - with Endre Csóka, Tamás Hubai, Gábor Lippner, László Lovász.
*Positive Graphs*, European Journal of Combinatorics (2016). (https://doi.org/10.1016/j.ejc.2015.07.007,`arXiv:1205.6510 [math.CO]`

) - with Ronald Brown.
*Erratum to “Groupoids, the Phragmen-Brouwer Property, and the Jordan Curve Theorem”*, J. Homotopy and Related Structures (2015). (https://doi.org/10.1007/s40062-014-0089-0,`arXiv:1404.0556 [math.AT]`

)

### Refereed book chapters

- with Tobias Barthel,
*Chromatic Fracture Cubes*, Equivariant Topology and Derived Algebra (edited by S. Balchin, D. Barnes, M. Kędziorek, & M. Szymik.), pages 100–118, London Mathematical Society Lecture Note Series, Cambridge University Press, 2021. https://doi.org/10.1017/9781108942874 - with Gregory R. Maloney, Roland K. W. Roeder.
*Computing arithmetic invariants for hyperbolic reflection groups*, Complex Dynamics: Families and Friends (D. Schleicher, editor), a volume commemorating J. H. Hubbard’s 60th birthday, pages 597–631, A.K. Peters, 2008.

### Pre-prints

- with Bernardo Villarreal.
*The Complex of Affinely Commutative Sets*.`arXiv:1906.07205 [math.AT]`

. - with Balázs Szegedy.
*Nilspaces, nilmanifolds and their morphisms*.`arXiv:1009.3825 [math.DS]`

.

## Expository papers

### Refereed

*A Whirlwind Tour of the World of \((\infty,1)\)-categories*, Mexican Mathematicians Abroad: Recent Contributions. Contemporary Mathematics, 657. American Mathematical Society, 2016. (`arXiv:1303.4669 [math.CT]`

)- with Sarah Kock.
*On a theorem of Kas and Schlessinger*, Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces, AMS Special Session in Honor of Clifford J. Earle. Contemporary Mathematics, 575. American Mathematical Society, 2012.

### Non-refereed, in Spanish

- La jerarquía de conmutatividad, Motivos Matemáticos (2019).
- La obra matemática de Jacob Lurie, universo.math (2014).

## Thesis Supervision

These are listed by the date of the defense. All theses titles are in the original Spanish.

### Undergraduate theses at UNAM

- July 2020
- Félix Almendra Hernández,
*Una prueba del teorema de la cota superior*

### Masters theses at UNAM

- September 2020
- Holger Ludwig Moysen Cortés,
*Equivalencia entre dos modelos de (∞,1)-categorías*

## Recent talks

### Research Talks

- January 2021
*Higher generation of compact Lie groups by abelian subgroups*Purdue Topology Seminar, Purdue University.

- November 2020
*Higher generation of compact Lie groups by abelian subgroups*Pure Math Seminar, University of Leicester

- October 2020
*Higher generation of compact Lie groups by abelian subgroups*Colloquium of the Center for Mathematical Sciences, UNAM, Morelia

- October 2020
*Conjuntos afínmente conmutativos y clases laterales de subgrupos abelianos*Algebra and Geometry Seminar, Institute of Mathematics, UNAM, Cuernavaca

- November 2019
*Commutativity in Lie Groups*Mathematics Seminar, ITAM

- October 2019
*A space that measure non-abeliannes of a group*Colloquium of the Institute of Mathematics, UNAM, Oaxaca

- October 2019
*The complex of affinely commuting sets*Algebra and Topology Seminar, Institute of Mathematics, UNAM, Oaxaca

- March 2019
*A space that measure non-abeliannes of a group*CIMAT Colloquium

- February 2019
*Topología de superficies de Fermi*Seminario Guillermo Torres, Instituto de Matemáticas, UNAM

- December 2018
*Thom ring spectra from \(n\)-fold loop maps*,Algebraic Geometry in Mexico, Puerto Escondido, Oaxaca. (Event jointly organized by Cinvestav and the University of Miami.)

### Mini-courses

- December 2020
*An introduction to stable homotopy theory*. Four and a half hour mini-course in the online CIMPA Pre-school, an event held in preparation for the*Algebraic Methods in Topology*CIMPA School that will take place in El Salvador in 2022.- March–April 2018
*Derived Algebraic Geometry*. Fourteen hour mini-course at the Institute of Mathematics, UNAM, Mexico City- October 2017
*Classifying spaces for commutativity*. Three hour mini-course during the Geometry and Topology Workshop at the Institute of Mathematics, UNAM, Oaxaca

### Expository Talks

- March 2022
*Puzzles with rectangular pieces*Mathematics Colloquium, UACJ, Ciudad Juárez

- April 2021
*Group extensions from a categorical point of view*Colloquium of the Institute of Mathematics, UNAM, Cuernavaca

- March 2021
*Counting with symmetries*Talk cycle

*Matematices*. Aimed at high school students.- September 2019
*Derivatives of regular expressions*Engineering Week, UACJ, Ciudad Juárez

- September 2019
*Searching infinite sets in a finite amount of time*Engineering Week, UACJ, Ciudad Juárez

## Recent teaching

Courses marked with † are graduate courses.

### UNAM (in Spanish)

- 2022-1
- Introduction to Avanced Geometry
- 2022-1
- Introduction to Recursive Functions and Computability
- 2021-1
- † Homotopy Theory
- 2021-1
- Differential Topology I
- 2020-1
- Linear Algebra I
- 2020-1
- Convex Sets
- 2019-2
- † The theory of \(\infty\)-categories
- 2019-1
- † Spectral sequence calculations
- 2018-2
- Groupoids in Topology

## Mathematical Software

- with Gregory R. Maloney, Roland K. W. Roeder.
*SNAP-HEDRON: computer program for computing arithmetic invariants of polyhedral reflection groups*(written in PARI/GP). Available at http://www.math.iupui.edu/~rroeder/SNAP-HEDRON/.

## Service

- September 2021
- Co-organizer of the online workshop
*Spaces of Homomorphisms and Classifying Spaces 2021*. (website) - April 2018–present
- Examiner for 11 undergraduate theses, 7 Master’s theses and 1 PhD thesis.
- March 2021
- Co-organizer of
*Sixth Days of Geometry, Topology and Dinamics*, online event. - February 2021–present
- Co-organizer of the online
*Algebraic Topology Seminar*of the Institute of Mathematics, UNAM. - October 2020–May 2021
- Co-organizer of the
*UNAM Category Theory Seminar*, online seminar, CCM–IM-UNAM. - December 2019
- Co-organizer of the
*Fifth Day of Geometry, Topology and Dynamics*at the Institute of Mathematics, UNAM, Mexico City. - October 2019
- Coordinator of the
*Algebraic and Geometric Topology Session*of the*52*, Monterrey, Mexico.^{nd}National Meeting of the Mexican Mathematical Society - Mayo 2019
- Co-organizer of the
*Algebra and Topology Session*of the*X Topology Days*conference, Durango, Mexico. - Abril 2019
- Co-organizer of the
*Fourth Day of Geometry, Topology and Dynamics*at the Center for Mathematicial Sciences, UNAM, Morelia. - November 2018
- Co-organizer of the
*Third Day of Geometry, Topology and Dynamics*at the Samuel Gitler Center for Collaboration in Mathematics. - September 2018
- Referee report for UNAM’s
*Vínculos Matemáticos*series. - 2015
- Co-organized the Topology seminar at UBC with Ben Williams.

## Awards

- 2021–2023
- Level 1 Member of Mexico’s National System of Researchers (Conacyt-SNI, Nivel 1)
- 2018–2020
- Candidate for membership in Mexico’s National System of Researchers (Conacyt-SNI, Candidato)
- 2012
- Certificate of Distintion in Teaching from Harvard’s Derek Bok Center for Teaching and Learning
- 2010
- Daniel B. DeLury Teaching Award, given by the University of Toronto for outstanding performance as a teaching assistant
- 2007
- Sotero Prieto Prize, an annual prize given in MExico to the best undergraduate thesis in mathematics
- 1999
- Silver Medal, International Mathematical Olympiad
- 1998
- Bronze Medal, International Mathematical Olympiad