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PhD in Mathematics (advisor: Luis Guijarro) at Maths Department in Universidad Autónoma de Madrid

Born in Madrid in 1995, I pursued my Bachelor’s degree in Mathematics from 2013 to 2017, followed by a Master’s degree from 2017 to 2018 at the Universidad Autónoma de Madrid.

During my PhD, my research initially focused on the collapse of sequences of Riemannian manifolds with totally bounded sectional curvature and intermediate k-Ricci curvature. Subsequently, I shifted my focus to studying Gromov’s invariant Filling Radius and the reach (in the sense of Federer) of isometric embeddings into Wasserstein-type spaces. Additionally, I explored applications of the Wasserstein distance, particularly in addressing the problem of uniformly distributing points on a compact manifold.

Throughout this period, I also delved into Topological Data Analysis (TDA), engaging in both theoretical and applied research in this field. TDA has now become a cornerstone of my research endeavors.

Research interests: TDA (Topological Data Analysis). Metric Geometry. Optimal Transport.

Contact details:

• Email: manuel.mellado@cunef.edu (Send Email)
• Office E-6.11.
  Department of Quantitative Methods, CUNEF.
  C/ Leonardo Prieto Castro 2, 28040, Madrid, Spain.