Macarena Arenas

Macarena
[Covadonga Robles]
Arenas

arXiv, MathSciNet, ORCID, zbMATH, MGP

About

I am the Denman Baynes Fellow at Clare College, Cambridge, and a member of the Department of Pure Mathematics and Mathematical Statistics (DPMMS). I completed my PhD at the DPMMS, supervised by Henry Wilton. Before that, I did my Master's in the Department of Mathematics and Statistics at McGill University, under the supervision of Dani Wise, and my Bachelor's Degree at UNAM, in Mexico City, under the supervision of Max Neumann-Coto.

DPMMS CV Thesis

Interests

I am mainly interested in geometric group theory and geometric/low dimensional topology. Some keywords include: non-positively curved cube complexes, hyperbolic and non-positively curved groups, finiteness properties of groups, combinatorial properties of curves on surfaces.

Papers

The Cohen-Lyndon property, coherence, and immersions, with Henry Wilton. In preparation.

Cubulating Artin groups via small-cancellation, with Alexandre Martin. In preparation.
Cubical small-cancellation quotients of non-products, with Kasia Jankiewicz and Daniel T. Wise. Submitted. Available here.
Filling cubulated relatively hyperbolic groups, with Mahan Mj and Daniel T. Wise. In preparation.
Asphericity of cubical presentations: the general case. Submitted. arXiv version.
Taut smoothings of arcs and curves, with Max Neumann-Coto. Submitted. arXiv version.
The Cohen-Lyndon property in non-metric small-cancellation. Accepted at Groups, Geometry, and Dynamics. arXiv version.

Hyperbolicity in non-metric cubical small cancellation with Kasia Jankiewicz and Daniel T. Wise, Bull. Lond. Math. Soc.. Journal version, arXiv version.
Asphericity of cubical presentations: the 2-dimensional case, IMRN. Journal version, arXiv version.
A cubical Rips construction, Alg. Geom. Top., Journal version, arXiv version
- Slides for a talk I gave on the topic at GaTO (Warwick's online seminar), and slides in spanish for a talk I gave at the University of Buenos Aires' Topology seminar.
Linear isoperimetric functions for surfaces in hyperbolic groups with Daniel T. Wise. Submitted. arXiv version.
- Slides in spanish for a talk I gave on the topic at the National Congress of the Mexican Mathematical Society, and slides in english for a talk at Queens' Geometry & Dynamics Seminar.
Measuring complexity of curves on surfaces with Max Neumann-Coto, Geometriae Dedicata. Available here.
- Slides for a talk I gave on the topic at the Topology Students Workshop in 2020.

Teaching

In Lent 2024 (i.e., the winter term), I lectured the Part III (i.e., Master's level) course Cubulating spaces and groups at Cambridge.

In July 2022, I taught a minicourse at the Escuela de Teoría Geométrica de Grupos in Morelia, Michoacan.
Based on the lecture notes for the minicourse, I wrote a survey paper (in spanish!) which is available here and on the arXiv.

Some things I've been involved in:

Summer school: Homological aspects of groups and their classifying spaces.

I organise Cambridge's Geometric Group Theory Seminar.

During my PhD, I co-organised the Junior Geometry Seminar at Cambridge.

In 2020, Sami Douba, Robbie Lyman, Abdul Zalloum, and I organised the virtual summer school Geometric Group Theory without Boundaries. In 2021 we organised the second iteration.

While at McGill, I co-organised the Geometric Group Theory Seminar.

During my undergrad, I was involved in the organisation of the Festival Matemático.

Some other things:

Cambridge's Differential Geometry and Topology Seminar.

GGT people at Cambridge: Henry Bradford, Jack Button, Ewan Cassidy, William Cohen, Francesco Fournier-Facio, Ana Isakovic, Monika Kudlinska, Liam Hanany, Jakub Tucker, Gareth Wilkes, Henry Wilton, Owain Wiliams, Jacob Willis, Julian Wykowski.

This is how space begins, with words only, signs traced on the blank page. To describe space: to name it, to trace it, like those portolano-makers who saturated the coastlines with the names of harbours, the names of capes, the names of inlets, until in the end the land was only separated from the sea by a continuous ribbon of text.

- Georges Perec