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. *

Outreach paper (in Spanish) written with Manuel Valdespino.

with Jason Fulman and Jennifer C.H. Wilson.

with Jennifer C.H. Wilson.

with Joaquín Maya Duque.

Contemp. Math., vol. 709, Aportaciones Mat., Amer. Math. Soc., Providence, RI, 2018, pp. 53-67.

**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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