Harmonic Maps Between Surfaces - Jürgen Jost

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Résumé :
Geometric considerations.- Conformal mappings.- Existence theorems for harmonic maps between surfaces.- Uniqueness theorems.- A-priori C1,?-estimates.- A-priori estimates from below for the functional determinant of harmonic diffeomorphisms.- The existence of harmonic diffeomorphisms which solve a Dirichlet problem.- C1, ? - a priori estimates for arbitrary domains. Non-variational existence proofs.- Harmonic coordinates. C2, ? - a - priori estimates for harmonic maps.- The existence of harmonic diffeomorphisms between surfaces.- Applications of harmonic maps between surfaces.

Biographie:
Parvaneh Joharinad received her PhD in mathematics from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran in March 2013. She worked as an assistant professor in the geometry group at the Institute for Advanced Studies in Basic Sciences (IASBS) in Zanjan, Iran, for seven years. She is interested in the use of geometry in data science and machine learning, and in particular in dimensionality reduction, a fundamental problem in topological and geometric data analysis. Her collaboration with J?rgen Jost began in 2017, via a project on a generalization of the concept of sectional curvature to datasets. In 2020, she received a grant from the Max-Planck society to continue her collaboration at the Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany. As of August 2022, she started a new position at the Center for Scalable Data Analytics and Artificial Intelligence, as a senior postdoc. J?rgen Jost worked as a Professor of Mathematics at Ruhr University Bochum from 1984 to 1996 and since 1996 has been director and a permanent member of the Max Planck Institute for Mathematics in the Sciences, Leipzig. In 1998 he became an Honorary Professor at the University of Leipzig. He is also an external member of the Santa Fe Institute for the Sciences of Complexity, New Mexico. He pursues both topical research in different fields of pure mathematics and theoretical physics (Riemannian and algebraic geometry, geometric analysis, calculus of variations, partial differential equations, dynamical systems, graph and hypergraph theory) and interdisciplinary research in complex systems, including evolutionary and theoretical molecular biology, mathematical and theoretical neuroscience, nonlinear dynamics and statistical physics, economics and social sciences, strategy science, history and philosophy of science. He directs a group of about 40 scientists, postdocs and PhD students, and has manyinternational cooperation partners....

Sommaire:
J?rgen Jost studierte von 1975 bis 1980 Mathematik, Physik, Volkswirtschaftslehre und Philosophie an der Universit?t Bonn. Er promovierte 1980 in der Mathematik und wurde nach verschiedenen internationalen Forschungsaufenthalten 1984 als Professor f?r Mathematik an die Ruhruniversit?t Bochum und 1996 als Direktor an das neu zu gr?ndende Max-Planck-Institut f?r Mathematik in den Naturwissenschaften in Leipzig berufen. Er ist auch Honorarprofessor an der Universit?t Leipzig und externes Fakult?tsmitglied des Santa Fe Institute for the Sciences of Complexity in den USA. 1993 erhielt er den Gottfried-Wilhelm-Leibniz-Preis der DFG und 2010 einen Advanced Grant des European Research Council. Er ist Autor von mehr als 20 Forschungsmonographien und Lehrb?chern und von ?ber 400 wissenschaftlichen Fachpublikationen. In seinen Forschungen verbindet er eine Vielzahl von mathematischen Disziplinen und Methoden mit einer allgemeinen Theorie komplexer Systeme und vielf?ltigen Anwendungen in der mathematischen und theoretischen Biologie und Neurobiologie....