I am interested in topics of geometric group theory, geometric and algebraic topology, low dimensional topology and applications of representation theory to problems in topology.
Preprints and Publications
A spine for the decorated Teichmüller space of a punctured non-orientable surface (arXiv) (pdf) with Nestor Colin, Porfirio L. León Álvarez y Luis Jorge Sánchez Saldaña. Submitted (2025).
The proper geometric dimension of the mapping class group of an orientable surface with punctures (arXiv) (pdf)
Torsion at the threshold for mapping class groups (arXiv) (pdf)
On the dimension of Harer's spine for the decorated Teichmüller space (arXiv) (pdf) with Nestor Colin, Porfirio L. León Álvarez y Luis Jorge Sánchez Saldaña.
On the virtually cyclic dimension of normally poly-free groups (arXiv) (pdf)
with Porfirio L. León Álvarez.
On the large scale geometry of big mapping class groups of surfaces with a unique maximal end (arXiv) (pdf)
with Israel Morales.
Periodicity of the pure mapping class group of non-orientable surfaces (arXiv) (pdf)
with Nestor Colin and Miguel A. Xicoténcatl.
Commensurators of abelian subgroups and the virtually abelian dimension of mapping class groups (arXiv) (pdf)
with Porfirio L. León Álvarez. and Luis Jorge Sánchez Saldaña.
Presentando al toro y sus simetrías Outreach paper (in Spanish) written with Juanita Claribel Santiago.
Stability properties of moduli spaces (arXiv) (pdf) Survey paper written with Jennifer C.H. Wilson.
On the non-vanishing of the powers of the Euler class for mapping class groups (pdf) Other My research has been supported by DGAPA-UNAM through PAPIIT Grants IA100816, IA104010 and IA106923 and a PASPA fellowship. It has also been supported by CONAHCyT through Grants CB-2017-2018-A1-S-30345 and CF-2019-217392. Collaborators:
Mauricio Bustamente,
Nestor Colin, Marinés de la Peña-Domene, Jason Fulman, Ruben A. Hidalgo,
Solomon Jekel, Rolando Jiménez Benítez,
Porfirio L. León Álvarez, César Lozano Huerta, Joaquín Maya Duque, Israel Morales,
Luis Jorge Sánchez Saldaña, Juanita Claribel Santiago, Saúl Quispe, Manuel Valdespino,
Jennifer C.H. Wilson, Miguel A. Xicoténcatl. IMUNAM-Oaxaca topology group :
Bruno A. Cisneros de la Cruz, Rolando Jiménez Benítez, Carlos Segovia, Porfirio León, Nestor Colin.
with Nestor Colin, Porfirio L. León Álvarez y Luis Jorge Sánchez Saldaña.
Journal of Group Theory. Ahead of Print DOI 10.1515/jgth-2024-0227 (2025).
with Solomon Jekel.
To appear in Transactions of the American Mathematical Society.
To appear in Homology, Homotopy and Applications.
Boletín de la Sociedad Matemática Mexicana. Volume 31, Number 5 (2025).
Michigan Mathematical Journal. Advance Publication 1 - 18, 2025.
Proceedings of the American Mathematical Society. Volume 152, Number 7 (2024).
Journal of Pure and Applied Algebra. Volume 228, Issue 6 (2024).
Miscelánea Matemática 75 (Agosto 2022 - Enero 2023) pp. 35-54.
Notices of the American Mathematical Society Vol. 69 No. 4 (2022) pp. 522-533.
with Solomon Jekel.
Arnold Math J. 7, 159-168 (2021).
Linear representation stable bounds for the integral cohomology of pure mapping class groups (arXiv) (pdf)
Bull. Belg. Math. Soc. Simon Stevin Vol. 26, Number 5 (2019) pp. 641-658.
Configuration spaces and braid groups Outreach paper (in English) written with Miguel A. Xicoténcatl.
Snapshots of modern mathematics from Oberwolfach 11 (2019) pp. 1-17.
Stability for hyperplane complements of type B/C and statistics on squarefree polynomials over finite fields (arXiv) (pdf)
with Jennifer C.H. Wilson.
The Quarterly Journal of Mathematics Vol. 70 Issue 2 (2019), no. 2, 565-602.
Configuraciones, trenzas y el teorema de Abel-Ruffini Outreach paper (in Spanish) written with Manuel Valdespino.
Miscelánea Matemática 67 (2018) pp. 23-41.
Generating functions and statistics on spaces of maximal tori in classical Lie groups (arXiv) (pdf)
with Jason Fulman and Jennifer C.H. Wilson.
New York Journal of Mathematics Vol. 23 (2017) pp.165--191.
Convergence criteria for FIW-algebras and polynomial statistics on maximal tori in type B/C (arXiv) (pdf)
with Jennifer C.H. Wilson.
Advances in Mathematics Vol. 310 (2017) pp.121--158.
Representation stability for the pure cactus group (arXiv) (pdf)
with Joaquín Maya Duque.
Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics,
Contemp. Math., vol. 709, Aportaciones Mat., Amer. Math. Soc., Providence, RI, 2018, pp. 53-67.
The cohomology of M_0^n as an FI-module (arXiv) (pdf)
Configuration Spaces: Geometry, Topology and Representation Theory, Springer INdAM Series (2016).
On the cohomology of pure mapping class groups as FI-modules (arXiv) (pdf)
Journal of Homotopy and Related Structures (2015).
Representation stability for the cohomology of the moduli space M_g^n (arXiv) (pdf)
Algebraic and Geometric Topology (2011).
Breve historia de la Unidad Oaxaca del Instituto de Matemáticas
Historical review (in Spanish) written with Rolando Jiménez Benítez
for the paper El Instituto de Matemáticas de la UNAM cumplió 80 años.
Miscelánea Matemática 77 (Agosto 2023 - Enero 2024) pp. 97--100.
Topology of Arrangements and Representation Stability Report of the MFO workshop organized in January 2018 with Graham Denham, Giovanni Gaiffi and Alex Suciu.
Oberwolfach Rep. 15 (2018), no. 1 pp. 43-123.
Seed to seedling transitions in successional habitats across a tropical landscape with Marinés de la Peña-Domene, Henry F. Howe, Emiliano Cruz-León, César Lozano-Huerta, Cristina Martínez.
Oikos Volume126, Issue 3 (2017) Pages 410-419.
My PhD Thesis: Examples of Representation Stability Phenomena
My Topic Proposal: Studying the mapping class group of a surface through its actions
My Master's Thesis: Harer-Ivanov's Stability Theorem
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