# 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 Bernardo Villarreal.
*Nilpotent \(n\)-tuples in \(SU(2)\)*, Proceedings of the Edinburgh Mathematical Society (2020). (10.1017/S0013091520000309, arXiv:1611.05937/math.AT) *The mod 2 homology of free spectral Lie algebras*, Transactions of the American Mathematical Society (2020). (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. (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). (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. (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). (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). (10.1007/s40062-014-0089-0, arXiv:1404.0556/math.AT)

### Refereed book chapters

- 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.

### Submitted

- with Simon Gritschaher, Bernardo Villareal.
*Higher generation by abelian subgroups in Lie groups*. arXiv:2009.12257/math.AT - with Daniel Sheinbaum.
*Crystallographic Interacting Topological Phases and Equvariant Cohomology: To assume or not to assume*. arXiv:2007.06595/math-ph

### Pre-prints

- with Bernardo Villarreal.
*The Complex of Affinely Commutative Sets*. arXiv:1906.07205/math.AT. - with Tobias Barthel.
*Chromatic fracture cubes*. arXiv:1410.7271/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).

## Talks

### Research Talks

- 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*- 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.)

- October 2018
*Thom spaces from a categorical viewpoint*Invited talk in the

*Algebraic and Geometric Topolgoy*session of the LI Annual Meeting of the Mexican Mathematical Society, Villahermosa, Tabasco- October 2018
*An introduction to Higher Order Fourier Analysis**Seminario Preguntón*, Institute of Mathematics, UNAM, Juriquilla- June 2018
*A simple universal property of Thom ring spectra*Encounter of the Columbian and Mexican Mathematical Societies, Barranquilla, Colombia

- May 2018
*Thom ring spectra and orientations*In the BIRS workshop

*\(\infty\)-Categories, \(\infty\)-Operads, and their Applications*, Casa Matemática Oaxaca- February 2018
*Commutativity in Lie Groups*Colloquium of the Institute of Mathematics, UNAM, Cuernavaca

- February 2018
*Commutativity in Lie Groups*Colloquium of the Center for Matematical Sciences, UNAM, Morelia

- October 2017
*Classifying spaces for commutativity and nilpotency in low-dimensional Lie groups*L Annual meeting of the Mexican Mathematical Society, Mexico City

- October 2015
*A simple universal property of Thom ring spectra*UBC Topology Seminar, Vancouver

- December 2014
*A universal property of the multiplicative structure of Thom spectra*Topology Seminar, Cinvestav, Mexico City

- November 2014
*Nilspaces for Higher Order Fourier Analysis*MIT Combinatorics Seminar.

- October 2014
*The universal property of the multiplicative structure of Thom spectra*University of Michigan Topology Seminar

- October 2014
*The universal property of the multiplicative structure of Thom spectra*University of Chicago Topology Seminar

- October 2014
*The universal property of the multiplicative structure of Thom spectra*Northwestern University Topology Seminar

- October 2014
*The multiplicative structure of Thom spectra*University of Massachusetts Boston Mathematics Colloquium

- January 2009
*Reflection positive hypergraph parameters*Workshop on Graph limits, Homomorphism and Structures held at Hraniční Zámeček, Czech Republic.

### Mini-courses

- 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

- 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

- January 2019
*The hierarchy of commutativity for monoidal structures*CINVCAT’s Third Coloquium of Categories, Algebra and Related Topics, Oaxaca

- January 2019
*All ways of measuring a convex set*Orientation Colloquium, FC-UNAM, Mexico City

- September 2018
*Mixing Algebraic Geometry with Homotopy Theory I: Motivic Homotopy*Recent Perspectives in Algebraic Geometry, ESFM–IPN, Mexico City

- September 2018
*Mixing Algebraic Geometry with Homotopy Theory II: Derived Algebraic Geometry*Recent Perspectives in Algebraic Geometry, ESFM–IPN, Mexico City

- April 2018
*Integral Geometry in Higher Dimensions*Physics and Math Days, UACJ, Ciudad Juárez

- April 2018
*Integral Geometry in the Plane*Physics and Math Days, UACJ, Ciudad Juárez

- April 2018
*Buffon’s needle: Probability in Geometry*Physics and Math Days, UACJ, Ciudad Juárez

- April 2018
*Can you divide a square into an odd number of triangles of equal area?*Talk cycle “Speaking of Mathematics”, Institute of Mathematics, UNAM, Mexico City

- January 2018
*Operads in Topology and Algebra*2

^{nd}National Encounter of Young Researchers in Mathematics, Institute of Mathematics, UNAM, Mexico City- January 2018
*Basic homotopy theory from an (∞,1)-categorical viewpoint*CINVCAT’s Second Coloquium of Categories, Algebra and Related Topics, Institute of Mathematics, UNAM, Mexico City

- October 2017
*Integral Geometry in the Plane*Second Mathematics Colloquium, FES Acatlán, Mexico City

- October 2017
*The Taylor series of a topological functor*Colloquium of the Institute of Mathematics, UNAM, Mexico City

- December 2014
*A glance at the theory of ∞-categories*Student Seminar, Cinvestav, Mexico City

- August 2012
*Why would we expect étale homotopy theory to work?*MIT Summer Topology Seminar

- December 2011
*What is Derived Algebraic Geometry and why do we want it?*Geometry and Topolgoy Seminar, Institute of Mathematics, UNAM, Mexico City

- October 2000
*Filling spaces with circles and spheres*, joint presentation with Juan José Alba GonzálezXXXIII Annual Meeting of the Mexican Mathematical Society, Saltillo

- November 1998
*The dark side of Josiah Willard Gibbs*XXXI Annual Meeting of the Mexican Mathematical Society, Hermosillo

## Teaching

Courses marked with † are graduate courses.

### UNAM (in Spanish)

- 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

### UBC

- Spring 2017
- † MATH 427/527, Algebraic Topology I
- Fall 2016
- MATH 340, Linear Programming
- Spring 2016
- MATH 340, Linear Programming
- Fall 2015
- MATH 102, Differential Calculus with Applications to Life Sciences

### Harvard University

- Spring 2015
- MATH 21b, Linear Algebra and Differential Equations
- Spring 2014
- MATH 21b, Linear Algebra and Differential Equations
- Fall 2013
- MATH 1a, Introduction to Calculus
- Fall 2012
- MATH Ma, Introduction to Functons and Calculus I
- Spring 2012
- MATH 99r, Tutorial: Grupoids in Topology

### University of Toronto

- Summer 2010
- MAT235, Calculus II, multivariable calculus for engineering students

## 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/.

## Thesis Supervision

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

### Undergraduate theses at UNAM

- June 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*

## Thesis Examination

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

### Examiner for Masters theses at UNAM

- September 2020
- José Juan López Alvarado,
*Severidad en categorías monoidales: una vista hacia las súper álgebras* - October 2019
- Anayeli Tomás Alvarez,
*Rigidez topológica del Grafo de Schmutz* - September 2019
- Alberto Alcalá Alvarez,
*Algunas aplicaciones de la sucesión espectral de Leray-Serre* - September 2019
- Iván Antonio Hernández Lizárraga,
*El teorema de Estratificación de Mumford* - March 2019
- Andrés Carnero Bravo,
*Dominación total y homología* - January 2019
- Miguel Ángel Cadena Negrete,
*Algebroide de Lie asociado a una variedad de Poisson*

### Examiner for Masters theses elsewhere

- August 2019
- Angel Rolando Jiménez Cruz,
*Invariantes de espacios de configuraciones de k-tuplas que conmutan*, Universidad Autónoma de Yucatán

### Examiner for undergraduate theses at UNAM

- September 2020
- Luis Daniel Ramos Trejo,
*Una introducción a los topos de Grothendieck mediante la equivalencia de Giraud* - September 2019
- David Ernán Huerta Guerrero,
*Un acercamiento a los enteros algebraicos mediante el último teorema de Fermat* - August 2019
- Luis Alberto Macías Barrales,
*Una introducción al teorema de Dold–Kan y sus aplicaciones* - April 2019
- Carlos Enrique Gómez Vlichis,
*Representaciones lineales y cohomología de grupos finitos. Un acercamiento a las representaciones proyectivas de grupos finitos y sus aplicaciones* - March 2019
- Daniel Green Tripp,
*Modificación de Nash en variedades tóricas* - August 2018
- César Ernesto Rodríguez Angón,
*La función Tau de Ramanujan* - August 2018
- Juan Andrés Orozco Gutiérrez,
*Caracterización de Grothendieck de la categoría de acciones continuas de un grupo profinito* - April 2018
- Jerónimo García Mejía,
*Construcciones de espacios clasificantes*

### Examiner for undergraduate theses elsewhere

- June 2020
- Alain Chavarri Villarello,
*El retículo de particiones de enteros positivos y su contexto estándar*, ITAM

## Service

- 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.
- 2012
- Co-organized the Trivial Notions student seminar at Harvard with Eric Riedl.
- 2009
- Refereed a paper for the Electronic Journal of Combinatorics.
- Fall 2008–Spring 2010
- Organized the Informal Algebraic Topology Seminar, the Homotopical Algebra Seminar and the Infinity Seminar at the University of Toronto. These are really a single seminar that changed name every term.
- Fall 2008
- Organized the Basic Notions Seminar and the Algebraic Topology Seminar at the University of Toronto.
- 2005
- Acted as Chief Coordinator at the International Mathematical Olympiad held, that year, in Mérida, Yucatán, México. (The Chief Coordinator organizes and supervises the marking of the contestants exams, and also mediates marking disputes.)
- 1999–2005
- Was a member of the Mexican Mathematical Olympiad Organizing Committee. I helped train the Mexican teams competing in the International Mathematical Olympiad, I helped invent and select the problems for the Mexican Mathematical Olympiad Exam, and I co-wrote the annual problem booklet.

## Awards

- 2018
- Candidate for membership in Mexico’s National System of Researchers (Conacyt-SNI)
- 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