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Alessandro Carlotto: Katalogdaten im Herbstsemester 2016

NameHerr Prof. Dr. Alessandro Carlotto
LehrgebietMathematik
Adresse
Professur für Mathematik
ETH Zürich, HG G 61.2
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 633 81 10
E-Mailalessandro.carlotto@math.ethz.ch
DepartementMathematik
BeziehungAssistenzprofessor

NummerTitelECTSUmfangDozierende
401-4831-66LMathematical Themes in General Relativity I4 KP2VA. Carlotto
KurzbeschreibungFirst part of a one-year course offering a rigorous introduction to general relativity, with special emphasis on aspects of current interest in mathematical research. Topics covered include: initial value formulation of the Einstein equations, causality theory and singularities, constructions of data sets by gluing or conformal methods, asymptotically flat spaces and positive mass theorems.
LernzielAcquisition of a solid and broad background in general relativity and mastery of the basic mathematical methods and ideas developed in such context and successfully exploited in the field of geometric analysis.
InhaltLorentzian geometry; geometric review of special relativity; the Einstein equations and their basic classes of special solutions; the Einstein equations as an initial-value problem; causality theory and hyperbolicity; singularities and trapped domains; Penrose diagrams; asymptotically flat spaces: ADM invariants, positive mass theorems, Penrose inequalities, geometric properties.
SkriptLecture notes written by the instructor will be provided to all enrolled students.
Voraussetzungen / BesonderesThe content of the basic courses of the first three years at ETH will be assumed. In particular, enrolled students are expected to be fluent both in Differential Geometry (at least at the level of Differentialgeometrie I, II) and Functional Analysis (at least at the level of Funktionalanalysis I, II). Some background on partial differential equations, mainly of elliptic and hyperbolic type, (say at the level of the monograph by L. C. Evans) would also be desirable.
401-5350-00LAnalysis Seminar Information 0 KP1KM. Struwe, A. Carlotto, D. Christodoulou, F. Da Lio, A. Figalli, N. Hungerbühler, T. Ilmanen, T. Kappeler, T. Rivière, D. A. Salamon
KurzbeschreibungResearch colloquium
Lernziel