# Suchergebnis: Katalogdaten im Frühjahrssemester 2021

Nummer Titel Typ ECTS Umfang Dozierende Mathematik Master  KernfächerFür das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 15 KP der erforderlichen 28 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen.  Kernfächer aus Bereichen der reinen Mathematik 401-3002-12L Algebraic Topology II W 8 KP 4G P. Biran Kurzbeschreibung This is a continuation course to Algebraic Topology I. The course will cover more advanced topics in algebraic topology including:cohomology of spaces, operations in homology and cohomology, duality. Lernziel Literatur 1) G. Bredon, "Topology and geometry",Graduate Texts in Mathematics, 139. Springer-Verlag, 1997.2) A. Hatcher, "Algebraic topology",Cambridge University Press, Cambridge, 2002.The book can be downloaded for free at:http://www.math.cornell.edu/~hatcher/AT/ATpage.html3) E. Spanier, "Algebraic topology", Springer-Verlag Voraussetzungen / Besonderes General topology, linear algebra, singular homology of topological spaces (e.g. as taught in "Algebraic topology I").Some knowledge of differential geometry and differential topologyis useful but not absolutely necessary. 401-3226-00L Symmetric Spaces W 8 KP 4G A. Iozzi Kurzbeschreibung * Generalities on symmetric spaces: locally and globally symmetric spaces, groups of isometries, examples* Symmetric spaces of non-compact type: flats and rank, roots and root spaces* Iwasawa decomposition, Weyl group, Cartan decomposition* Hints of the geometry at infinity of SL(n,R)/SO(n). Lernziel Learn the basics of symmetric spaces 401-3532-08L Differential Geometry II W 10 KP 4V + 1U W. Merry Kurzbeschreibung This is a continuation course of Differential Geometry I.Topics covered include:- Connections and curvature,- Riemannian geometry,- Gauge theory and Chern-Weil theory. Lernziel Skript I will produce full lecture notes, available on my website: https://www.merry.io/courses/differential-geometry/ Literatur There are many excellent textbooks on differential geometry. A friendly and readable book that contains everything covered in Differential Geometry I is:John M. Lee "Introduction to Smooth Manifolds" 2nd ed. (2012) Springer-Verlag.For Differential Geometry II, the textbooks:- S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volume I (1963) Wiley,- I. Chavel, "Riemannian Geometry: A Modern Introduction" 2nd ed. (2006), CUP,are both excellent. The monograph- A. L. Besse "Einstein Manifolds", (1987), Springer,gives a comprehensive overview of the entire field, although it is extremely advanced. (By the end of the course you should be able to read this book.) Voraussetzungen / Besonderes Familiarity with all the material from Differential Geometry I will be assumed (smooth manifolds, Lie groups, vector bundles, differential forms, integration on manifolds, principal bundles and so on). Lecture notes for Differential Geometry I can be found on my website. 401-3462-00L Functional Analysis II W 10 KP 4V + 1U A. Carlotto Kurzbeschreibung Sobolev spaces, weak solutions of elliptic boundary value problems, basic results in elliptic regularity theory (including Schauder estimates), maximum principles. Lernziel Acquire fluency with Sobolev spaces and weak derivatives on the one hand, and basic elliptic regularity on the other. Apply these methods for studying elliptic boundary value problems. Literatur Michael Struwe. Funktionalanalysis I und II. Lecture notes, ETH Zürich, 2013/14.Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.Luigi Ambrosio, Alessandro Carlotto, Annalisa Massaccesi. Lectures on elliptic partial differential equations. Springer - Edizioni della Normale, Pisa, 2018. David Gilbarg, Neil Trudinger. Elliptic partial differential equations of second order. Classics in Mathematics. Springer, Berlin, 2001.Qing Han, Fanghua Lin. Elliptic partial differential equations. Second edition. Courant Lecture Notes in Mathematics, 1. Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2011.Michael Taylor. Partial differential equations I. Basic theory. Second edition. Applied Mathematical Sciences, 115. Springer, New York, 2011.Lars Hörmander. The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis. Classics in Mathematics. Springer, Berlin, 2003. Voraussetzungen / Besonderes Functional Analysis I plus a solid background in measure theory, Lebesgue integration and L^p spaces. 401-8142-21L Algebraic Geometry II (University of Zurich)Der Kurs muss direkt an der UZH belegt werden.UZH Modulkürzel: MAT517Beachten Sie die Einschreibungstermine an der UZH: https://www.uzh.ch/cmsssl/de/studies/application/deadlines.html W 9 KP 4V + 1U Uni-Dozierende Kurzbeschreibung We continue the development of scheme theory. Among the topics that will be discussed are: properties of schemes and their morphisms (flatness, smoothness), coherent modules, cohomology, etc. Lernziel
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