Suchergebnis: Katalogdaten im Frühjahrssemester 2021

Nummer	Titel	Typ	ECTS	Umfang	Dozierende
Mathematik Master
Kernfächer Für 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.html 3) 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 topology is 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: MAT517 Beachten 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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