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Seminar on Potential Theory on the Berkovich Projective Line SemesterSoSe 2018 Lecturer Prof. Dr. Klaus Kuennemann Type of course (Veranstaltungsart) Seminar Contents The Berkovich projective line is the easiest non-trivial example of a non-archimedean analytic space in the sense of Berkovich. The aim of the seminar is to get a better understanding of this example by developing the foundations to do analysis on the Berkovich projective line. The motivation is more precisely to develop a non-archimedean analog of classical potential theory in the complex plane. After recalling basic facts about the Berkovich projective line, we introduce the Hsia kernel, the fundamental kernel for potential theory. We develop a theory of capacities, define a Laplacian operator and harmonic functions, and develop the theory of subharmonic functions. Of course we will only be able to cover a part of the book by Baker and Rumely. Literature M. Baker, R. Rumely: Potential Theory and Dynamics on the Berkovich Projective Line, Mathematical Surveys and Monographs Volume: 159; AMS 2010. The ebook is with a university IP available at http://www.ams.org/books/surv/159/surv159.pdf A preliminary version of this book is available at: https://arxiv.org/abs/math/0407433 Recommended previous knowledge The seminar aims at students of my courses on non-archimedean geometry. However the book by Baker and Rumely is self-contained and can be read without previous knowledge about non-archimedean analytic geometry. Time/Date Mon 14h15-15h45 Location M103 Registration
BSem, MV, MSem, LA-GySem ECTS Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16 |