About Me
I am a fourth-year math Ph.D. candidate at Boston College, advised by Ian Biringer. I am originally from Mexicali, Mexico.
My mathematical interests are related to the algebra and geometry of (big) mapping class groups.
I earned my bachelor’s degree at Universidad Autonoma de Nuevo Leon, and wrote an undergraduate thesis on the Birman-Hilden Theorem under the supervision of Rita Jimenez Rolland.
Places we may have met
- June 8 - 12, 2026. Vanderbilt, Nashville: Topology Students Workshop. I highly recommend attending this workshop!
- March 28 - 29, 2026. Boston College: AMS Spring sectional.
- January 26 - 30, 2026. SL Math, Berkeley: Topological and Geometric Structures in Low Dimensions & Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups.
- November 8, 2025. Brown, Providence: GATSBY.
- January 06 – 10, 2025. IMPA, Rio de Janeiro: Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups.
Research interests
I am currently thinking about normal subgroups of mapping class groups and surface braid groups on infinitely many strands. To be more specific, problems and techniques involving completions of infinite braid groups, normal closures of mapping classes, large-scale geometry of big mapping class groups, and congruence subgroups.
Writing
- Tame braid groups and a Birman exact sequence for infinite type surfaces (In preparation.)
Expository talks
Boston College’s graduate student seminar:
- Large-scale geometry of uncountable groups.
- Algebraic simplicity of homeomorphism groups.
- Coxeter, Artin and the Salvetti complex. Notes.
- Braid Groups. Notes.
- The Mapping Class Groups of a genus 2 surface.
HyperboliciTea (informal geometry/topology seminar at Boston College):
- Topologized fundamental groups. Notes.
- Normal subgroups of mapping class groups. Notes.
- The normal closure of classical braid groups in torus braid groups. Notes.
- The congruence subgroup problem. Notes.
- Purely pseudo-Anosov normal subgroups of mapping class groups.
Boston College’s undergraduate colloquim
- Groups and puzzles.
- Patterns and symmetry: demystifying group theory.
Teaching
Instructor of record, Boston College
- MATH4453 Euclid’s Elements, Spring 2027
- MATH1100 Calculus 1, Fall 2026
- MATH1100 Calculus 1, Fall 2025
Service
- Graduate Student Association, Vicepresident.
- I’m co-organizing HyperboliciTea this year with Katerina Stuopis.
- TA/TF Orientation (Fall 2026): STEM TA panelist.
- TA/TF Orientation (Fall 2025): International student panelist.
- Directed Reading Program (Spring 2026), Mentor. Projects: Introduction to mapping class groups, mentee Adam Wright. Surface braid groups, mentee Angie Wu.
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