Research

I am interested in topics of geometric group theory, geometric and algebraic topology, and applications of representation theory to problems in topology. In particular, the study of homological properties of mapping class group and homological and representation stability phenomena.

Preprints and Publications

On the non-vanishing of the powers of the Euler class for mapping class groups (pdf)
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).

Other

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.

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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