María Fernanda Espinal
Ph.D. in Mathematics
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About me
I am currently a postdoctoral fellow at the CMM-Center for Mathematical Modeling in Santiago - Chile. I completed my PhD in Mathematics at the Pontificia Universidad Católica de Chile, under the supervision of Prof. Mariel Sáez with co-advise of Prof. María del Mar González. My main area of research is Geometric Analysis. I am interested in the study of problems in elliptic/parabolic nonlinear equations arising from conformal geometry. Before coming to Chile I obtained my Master and Bachelor degrees in Mathematics from Universidad de Valle, under the guidance of Prof. Gonzalo García and Prof. Heber Mesa. Beside doing math, like all caleña, I love to dance salsa! :D
Research interests: Conformal Geometry. Fully Nonlinear Analysis. Geometric Flows. Singularity Analysis.
Publications
M. F. Espinal and M. Sáez. On the existence and classification of k-Yamabe solitons. The Journal of Geometric Analysis, Vol. 35, No. 07, 2025.
Preprints
M. d. M. González and M. F. Espinal. A gluing construction of singular solutions for a fully non-linear equation in conformal geometry, arXiv:2404.05965 (submitted).
Work in progress
R. Caju and M. F. Espinal. An end-to-end construction for the sigma_k-curvature equation .
M. F. Espinal, M. Andrade, A. Silva-Santos and R. Caju. Uniqueness and differentiability in the space of \sigma_2-metrics.
Activities
Co-organizer of the congress WoMaths: "Congreso de Mujeres Matemáticas".
From October 5th 2022 to May 3rd 2023 I was a visiting student at the Universidad Autónoma de Madrid working in the PDEs group of UAM-ICMAT.
Talks
Existence of k-Yamabe Gradient Solitons. VII Congreso Latinoamericano y del Caribe de Matemática 2024 CLAM. Joao Pessoa, Brazil. 26.08.2024.
On the existence and Classification of k-Yamabe Gradient Solitons. XCI Encuentro Anual de la Sociedad Matemática Chilena (SOMACHI), Universidad de Chile. 19.12.23.
Métricas con singularidades no aisladas y σ2 curvatura constante. Seminario de Estudiantes de Postgrado, Pontificia Universidad Católica de Chile. 30.06.23.
Una introducción al σk problema de Yamabe. Seminario de Estudiantes Coloquio Junior, Universidad Autónoma de Madrid. 01.02.23.
Geometric flows and k-Yamabe problem. Seminario de Estudiantes de Postgrado, Universidad de Chile (DIM). 07.06.22.
Conformal invariance and Yamabe-type flows. Seminario de Egresados CONVImaTE, Universidad del Valle, Colombia. 20.01.21.
Problema de Yamabe: Desarrollo histórico. Seminario de Egresados CONVImaTE, Universidad del Valle, Colombia. 15.12.16.
Skew loops and quadric surfaces. Congreso Colombiano de Matemáticas, Universidad Industrial de Santander. 11.07.11.
Thesis
M. F. Espinal. Conformal invariance and Yamabe-type flows. Pontificia Universidad Católica de Chile PhD Thesis. August 2024.
M. F. Espinal. Conformal deformation of metrics over a manifold with two connected components boundary (in spanish). Universidad del Valle M.Sc. Thesis. January 2016.
M. F. Espinal. Skew loops and quadric surfaces (in spanish). Universidad del Valle B.Sc. Thesis. April 2013.
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