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 Andrés Carnero Bravo, Homotopy type through homology, Boletín de
la Sociedad Matemática Mexicana (2024). (doi:10.1007/s40590-024-00605-8,
arXiv:2212.07509 [math.AT]). - with Hugo Flores-Arguedas, Serguei Saavedra, Marco Tulio Angulo, Assembly archetypes in ecological communities, Journal of the Royal Society Interface (2023). (doi:10.1098/rsif.2023.0349)
- with Daniel Sheinbaum. Crystallographic Interacting Topological
Phases and Equivariant Cohomology: To assume or not to assume,
Journal of High Energy Physics (2021).
(doi: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).
(doi: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).
(doi:10.1017/S0013091520000309,
arXiv:1611.05937 [math.AT]) - The mod 2 homology of free spectral Lie algebras, Transactions of
the American Mathematical Society (2020). (doi: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.
(doi: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). (doi: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. (doi: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).
(doi: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). (doi: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. doi: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 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.
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