Research interests
I did my doctorate studies at the University of Southampton. I hold a BSc in Mathematics by the National Autonomous University of Mexico. My current research in pure maths includes problems in algebraic topology, differential geometry and metric geometry. In particular, I’m interested in the unstable homotopy theory of mapping spaces, the topology of fibre bundles and moduli spaces of Riemannian metrics, actions of Lie groups on metric spaces and the topology and geometry of orbifolds and Alexandrov spaces. I am also interested in theoretical problems related to persistent homology.
Research papers
- K. Gittins, C. Gordon, M. Khalile, I. Membrillo Solis, M. Sandoval and .Stanhope. Do the Hodge spectra distinguish orbifolds from manifolds? Part 1. Mich. Math. J. (2023) 1(1), 1-28.
- D. Kishimoto, I. Membrillo Solis, S. Theriault. The homotopy types of SO(4)-gauge groups. Eur. J. Math. (2021) 7(3), 1245-1252.
- I. Membrillo Solis, S. Theriault. The homotopy types of U(n)-gauge groups over Lens Bol. Soc. Mat. Mex. (2021) 27, 1-12.
- I. Membrillo-Solis. Homotopy types of gauge groups related to $S^3$-bundles over $S^4$. Topol. Appl., 255(2019), 56-85.
Preprints
- Do the Hodge spectra distinguish orbifolds from manifolds? Part 2 (joint with Katie Gittins, Carolyn Gordon, Magda Khalile, Juan Pablo Rossetti, Mary Sandoval and Liz Stanhope).
- Basic metric geometry of the bottleneck distance (joint with Mauricio Che, Fernando Galaz-García, Luis Guijarro and Motiejus Valiunas).
- Metric geometry of spaces of persistence diagrams (joint with Mauricio Che, Fernando Galaz-García and Luis Guijarro).
- I.Membrillo-Solis. On gauge group over high dimensional manifolds and self-equivalences on $H$-spaces. Preprint, available here.
In preparation
- Moduli spaces of flat Riemannian metrics (joint with Ana Karla García and Motiejus Valiunas).
Ingrid Membrillo Solis 