Dr. Elio E. Espejo's research lies at the intersection of pure and applied mathematics, with a particular focus on the theory of partial differential equations (PDEs) and their applications to real-world phenomena. His work spans several key areas of mathematical analysis, including:

• Regularity Theory of PDEs: Investigating the smoothness and behavior of solutions to nonlinear partial differential equations, with applications in fluid dynamics, materials science, and biological systems.

• Global Existence and Blow-Up Phenomena: Developing rigorous mathematical frameworks to determine when solutions to PDEs exist globally or exhibit finite-time blow-up, particularly in systems modeling chemotaxis, fluid flow, and pattern formation.

• Mathematical Modeling for Data Analysis: Constructing innovative mathematical models to analyze and interpret complex datasets, with applications in biology, engineering, and beyond. This includes the development of predictive models for biological processes such as cell motility, tumor growth, and chemotaxis.

• Chemotaxis and Biological Systems: Exploring the mathematical foundations of chemotaxis—the movement of organisms in response to chemical gradients—and its role in biological processes such as cell aggregation, fertilization, and tumor dynamics.

• Variational Analysis and Pattern Formation: Applying variational methods to study the emergence of patterns in physical and biological systems, with a focus on understanding the underlying mechanisms driving self-organization and structure formation.

Dr. Espejo's research is characterized by a deep commitment to both theoretical rigor and practical applications. By combining advanced mathematical techniques with interdisciplinary approaches, he aims to uncover fundamental insights into complex systems and contribute to solving real-world challenges.

Dr. Elio E. Espejo is a member of the Department of Mathematical Sciences at the University of Nottingham Ningbo China (UNNC), where he specializes in the theory of partial differential equations (PDEs), with a focus on regularity theory, global existence, and blow-up phenomena. His research also extends to the construction of mathematical models for data analysis, bridging the gap between theoretical mathematics and real-world applications.

Dr. Espejo holds a Ph.D. in Mathematics from the University of Leipzig and the Max Planck Institute for Mathematics in the Sciences, Germany, complemented by a Master’s and Bachelor’s degree from the National University of Colombia. His academic journey includes prestigious research fellowships at the Israel Institute of Technology (Technion) in Haifa, Israel, and at Osaka University and Kyushu University in Japan. In 2015, he was awarded a US$50,000 repatriation grant by the Colombian government, which supported his advanced research at the National University of Colombia for two years.

With a strong international research profile, Dr. Espejo has made significant contributions to the field of nonlinear PDEs, particularly in the areas of chemotaxis, pattern formation, and variational analysis. His work on global existence and blow-up techniques has provided critical insights into the behavior of complex systems, while his expertise in mathematical modeling has enabled innovative approaches to data analysis in biological and physical systems.

Currently, Dr. Espejo is deeply engaged in advancing the mathematical understanding of regularity in PDEs and developing robust frameworks for global existence and blow-up phenomena. He is also actively involved in constructing mathematical models to analyze and interpret complex datasets, with applications ranging from biological systems to engineering and beyond. At UNNC, he is committed to fostering a vibrant research environment and mentoring the next generation of mathematicians.

UNNC

Mathematical Medicine and Biology, Differential Equations and Fourier Analysis, Mathematics Groups Projects, Applied Mathematics, Modelling with Differential Equations, Calculus, Advanced Mathematical Methods for Civil Engineering.

Past (other campuses)

Ring theory, Functional analysis, Mathematical Analysis I, II and III, abstract algebra, vectorial geometry, differential equations, linear algebra, introduction to elliptic equations, partial differential equations, Euclidean geometry, and differential calculus.