HOME

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

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

2nd 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 González

XXXIII 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

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 52nd National Meeting of the Mexican Mathematical Society, Monterrey, Mexico.
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

Omar Antolín Camarena