The theory of Banach spaces is one of the basic pillars of functional analysis and finds wide application in modern mathematics. It deals with the structure and properties of these spaces, whose significance goes beyond pure mathematics and extends to areas such as numerical analysis and optimization theory. Dr. Dantas's habilitation talk focused on key aspects of this theory, including norm reachability, smoothness and linearity. He will first introduce the basic ideas of Banach spaces and then focus on their deeper analytical properties, which are crucial for the further development of the field. During the talk, the audience will learn not only classical results, but also the latest insights provided by his research.
Dr. Sheldon Miriel Gil Dantas received his bachelor's degree in mathematics in 2011 from the Federal University of Paraíba and his master's degree in mathematics from the University of São Paulo in 2013. He received his PhD in Mathematics from the University of Valencia in 2017 after successfully defending his PhD thesis entitled "On the Bishop-Phelps-Bollobás type theorems". He is now an assistant professor at the University of Valencia, where he teaches advanced mathematical analysis. Previously, he has worked at several prestigious universities around the world, including Pohang University of Science and Technology in South Korea, Czech Technical University in Prague, and University of Tartu in Estonia. He has authored or co-authored more than 30 technical papers and has actively contributed to the development of functional analysis internationally. In addition to research and teaching, he participates in the organization of international mathematical conferences and regularly reviews articles for prestigious professional journals.
Dr. Dantas's habilitation thesis entitled Norm-attainment, smoothness and linearity was very positively evaluated by his opponents, including renowned experts - Prof. Gilles Lancien (University of Franche-Comté Besancon, France), Prof. Gustavo Adolfo Munoz Fernandez (Complutense University of Madrid, Spain) and Prof. Oscar Blasco de La Cruz (University of Valencia, Spain). All three experts agreed that the thesis fulfilled all the requirements for a habilitation thesis and that its author had made a significant contribution to the development of the field.
