Suchergebnis: Katalogdaten im Herbstsemester 2017

Mathematik Master Information
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
NummerTitelTypECTSUmfangDozierende
401-3225-00LIntroduction to Lie GroupsW8 KP4GA. Iozzi
KurzbeschreibungTopological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups.
LernzielThe goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it.
LiteraturA. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser)
A. Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73)
F. Warner: "Foundations of differentiable manifolds and Lie groups" (Springer)
H. Samelson: "Notes on Lie algebras" (Springer, '90)
S. Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78)
A. Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press)
Voraussetzungen / BesonderesTopology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester.

Course webpage: https://metaphor.ethz.ch/x/2017/hs/401-3225-00L/
401-3001-61LAlgebraic Topology I Information W8 KP4GW. Merry
KurzbeschreibungThis is an introductory course in algebraic topology. Topics covered include: the fundamental group, covering spaces, singular homology, cell complexes and cellular homology and the Eilenberg-Steenrod axioms. Along the way we will introduce the basics of homological algebra and category theory.
Lernziel
SkriptI will produce full lecture notes, available on my website at

www.merry.io/algebraic-topology
Literatur"Algebraic Topology" (CUP, 2002) by Hatcher is excellent and covers all the material from both Algebraic Topology I and Algebraic Topology II. You can also download it (legally!) for free from Hatcher's webpage:

www.math.cornell.edu/%7ehatcher/AT/ATpage.html

Another classic book is Spanier's "Algebraic Topology" (Springer, 1963). This book is very dense and somewhat old-fashioned, but again covers everything you could possibly want to know on the subject.
Voraussetzungen / BesonderesYou should know the basics of point-set topology (topological spaces, and what it means for a topological space to be compact or connected, etc).

Some (very elementary) group theory and algebra will also be needed.
401-4147-67LAlgebraic Geometry IIW10 KP4V + 1UR. Pink
KurzbeschreibungQuasicoherent sheaves, cohomology, Serre duality, Riemann-Roch theorem, algebraic curves, moduli schemes
Lernziel
LiteraturPrimary reference:
* Robin Hartshorne: Algebraic Geometry, Graduate Texts in Mathematics, Springer.
* Ulrich Görtz and Torsten Wedhorn: Algebraic Geometry I, Advanced Lectures in Mathematics, Springer.

Secondary reference:
* Qing Liu: Algebraic Geometry and Arithmetic Curves, Oxford Science Publications.
* Siegfried Bosch: Algebraic Geometry and Commutative Algebra (Springer 2013).

Other good textbooks and online texts are:
* David Eisenbud, Joe Harris: The Geometry of Schemes, Graduate Texts in Mathematics, Springer.
* Ravi Vakil, Foundations of Algebraic Geometry, http://math.stanford.edu/~vakil/216blog/
* Jean Gallier and Stephen S. Shatz, Algebraic Geometry http://www.cis.upenn.edu/~jean/algeom/steve01.html

"Classical" Algebraic Geometry over an algebraically closed field:
* Joe Harris, Algebraic Geometry, A First Course, Graduate Texts in Mathematics, Springer.
* J.S. Milne, Algebraic Geometry, http://www.jmilne.org/math/CourseNotes/AG.pdf

Further readings:
* Günter Harder: Algebraic Geometry 1 & 2
* I. R. Shafarevich, Basic Algebraic geometry 1 & 2, Springer-Verlag.
* Alexandre Grothendieck et al.: Elements de Geometrie Algebrique EGA
* Saunders MacLane: Categories for the Working Mathematician, Springer-Verlag.
Voraussetzungen / BesonderesAlgebraic Geometry I Spring 2017
401-3132-00LCommutative Algebra Information W10 KP4V + 1UP. D. Nelson
KurzbeschreibungThis course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry.
LernzielWe shall cover approximately the material from
--- most of the textbook by Atiyah-MacDonald, or
--- the first half of the textbook by Bosch.
Topics include:
* Basics about rings, ideals and modules
* Localization
* Primary decomposition
* Integral dependence and valuations
* Noetherian rings
* Completions
* Basic dimension theory
LiteraturPrimary Reference:
1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969)
Secondary Reference:
2. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013)
Tertiary References:
3. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995)
4. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989)
5. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer)
Voraussetzungen / BesonderesPrerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory).
401-3581-67LSymplectic GeometryW8 KP4V + 1UA. Cannas da Silva
KurzbeschreibungThis course is an introduction to symplectic geometry -- the geometry of manifolds equipped with a closed non-degenerate 2-form.
We will discuss symplectic manifolds and transformations, the relation of symplectic to other geometries and some of the interplay with dynamics, eventually in the presence of symmetry groups.
Guided homework assignments will complement the exposition.
LernzielIntroduction to symplectic geometry
Kernfächer aus Bereichen der angewandten Mathematik ...
vollständiger Titel: Kernfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten
NummerTitelTypECTSUmfangDozierende
401-3651-00LNumerical Methods for Elliptic and Parabolic Partial Differential Equations (University of Zurich)
Course audience at ETH: 3rd year ETH BSc Mathematics and MSc Mathematics and MSc Applied Mathematics students.
Other ETH-students are advised to attend the course "Numerical Methods for Partial Differential Equations" (401-0674-00L) in the CSE curriculum during the spring semester.

Der Kurs muss direkt an der UZH belegt werden.
UZH Modulkürzel: MAT802

Beachten Sie die Einschreibungstermine an der UZH: https://www.uzh.ch/cmsssl/de/studies/application/mobilitaet.html
W10 KP4V + 1U + 1PS. Sauter
KurzbeschreibungThis course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems, related eigenvalue problems and linear, parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods. Practical exercises include MATLAB implementations of finite element methods.
LernzielParticipants of the course should become familiar with
* concepts underlying the discretization of elliptic and parabolic boundary value problems
* analytical techniques for investigating the convergence of numerical methods for the approximate solution of boundary value problems
* methods for the efficient solution of discrete boundary value problems
* implementational aspects of the finite element method
InhaltA selection of the following topics will be covered:

* Elliptic boundary value problems
* Galerkin discretization of linear variational problems
* The primal finite element method
* Mixed finite element methods
* Discontinuous Galerkin Methods
* Boundary element methods
* Spectral methods
* Adaptive finite element schemes
* Singularly perturbed problems
* Sparse grids
* Galerkin discretization of elliptic eigenproblems
* Non-linear elliptic boundary value problems
* Discretization of parabolic initial boundary value problems
SkriptCourse slides will be made available to the audience.
LiteraturS. C. Brenner and L. Ridgway Scott: The mathematical theory of Finite Element Methods. New York, Berlin [etc]: Springer-Verl, cop.1994.

A. Ern and J.L. Guermond: Theory and Practice of Finite Element Methods,
Springer Applied Mathematical Sciences Vol. 159, Springer,
1st Ed. 2004, 2nd Ed. 2015.

R. Verfürth: A Posteriori Error Estimation Techniques for Finite Element Methods, Oxford University Press, 2013

Additional Literature:
D. Braess: Finite Elements, THIRD Ed., Cambridge Univ. Press, (2007).
(Also available in German.)

D. A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, vol. 69 SMAI Mathématiques et Applications,
Springer, 2012 [DOI: 10.1007/978-3-642-22980-0]

V. Thomee: Galerkin Finite Element Methods for Parabolic Problems,
SECOND Ed., Springer Verlag (2006).
Voraussetzungen / BesonderesPractical exercises based on MATLAB
401-3621-00LFundamentals of Mathematical Statistics Information W10 KP4V + 1US. van de Geer
KurzbeschreibungThe course covers the basics of inferential statistics.
Lernziel
401-4889-00LMathematical FinanceW11 KP4V + 2UJ. Teichmann
KurzbeschreibungAdvanced introduction to mathematical finance:
- absence of arbitrage and martingale measures
- option pricing and hedging
- optimal investment problems
- additional topics
LernzielAdvanced level introduction to mathematical finance, presupposing knowledge in probability theory and stochastic processes
InhaltThis is an advanced level introduction to mathematical finance for students with a good background in probability. We want to give an overview of main concepts, questions and approaches, and we do this in both discrete- and continuous-time models. Topics include absence of arbitrage and martingale measures, option pricing and hedging, optimal investment problems, and probably others.
Prerequisites are probability theory and stochastic processes (for which lecture notes are available).
SkriptCourse homepage: https://metaphor.ethz.ch/x/2017/hs/401-4889-00L/
-Lecture notes
-Exercise sheets
-A list of relevant literature
Voraussetzungen / BesonderesPrerequisites are probability theory and stochastic processes (for which lecture notes are available).
401-3901-00LMathematical Optimization Information W11 KP4V + 2UR. Weismantel
KurzbeschreibungMathematical treatment of diverse optimization techniques.
LernzielAdvanced optimization theory and algorithms.
Inhalt1) Linear optimization: The geometry of linear programming, the simplex method for solving linear programming problems, Farkas' Lemma and infeasibility certificates, duality theory of linear programming.

2) Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization.

3) Integer optimization: Ties between linear and integer optimization, total unimodularity, complexity theory, cutting plane theory.

4) Combinatorial optimization: Network flow problems, structural results and algorithms for matroids, matchings, and, more generally, independence systems.
Literatur1) D. Bertsimas & R. Weismantel, "Optimization over Integers". Dynamic Ideas, 2005.

2) A. Schrijver, "Theory of Linear and Integer Programming". John Wiley, 1986.

3) D. Bertsimas & J.N. Tsitsiklis, "Introduction to Linear Optimization". Athena Scientific, 1997.

4) Y. Nesterov, "Introductory Lectures on Convex Optimization: a Basic Course". Kluwer Academic Publishers, 2003.

5) C.H. Papadimitriou, "Combinatorial Optimization". Prentice-Hall Inc., 1982.
Voraussetzungen / BesonderesLinear algebra.
Bachelor-Kernfächer aus Bereichen der reinen Mathematik
Nebst weiteren Einschränkungen gilt:
Die Anrechnung von 401-3531-00L Differentialgeometrie I / Differential Geometry I im Master-Studiengang ist nur dann zulässig, wenn 401-3532-00L Differentialgeometrie II / Differential Geometry II nicht für den Bachelor-Studiengang angerechnet wurde.
Ebenso für:
401-3461-00L Funktionalanalysis I / Functional Analysis I - 401-3462-00L Funktionalanalysis II / Functional Analysis II
401-3001-61L Algebraische Topologie I / Algebraic Topology I - 401-3002-12L Algebraische Topologie II / Algebraic Topology II
401-3132-00L Kommutative Algebra / Commutative Algebra - 401-3146-12L Algebraische Geometrie / Algebraic Geometry
401-3371-00L Dynamische Systeme I / Dynamical Systems I - 401-3372-00L Dynamische Systeme II / Dynamical Systems II
Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (www.math.ethz.ch/studiensekretariat).
NummerTitelTypECTSUmfangDozierende
401-3461-00LFunctional Analysis I Information
Höchstens eines der drei Bachelor-Kernfächer
401-3461-00L Funktionalanalysis I / Functional Analysis I
401-3531-00L Differentialgeometrie I / Differential Geometry I
401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory
ist im Master-Studiengang Mathematik anrechenbar.
E-10 KP4V + 1UA. Carlotto
KurzbeschreibungBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
LernzielAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
SkriptLecture Notes on "Funktionalanalysis I" by Michael Struwe
LiteraturA primary reference for the course is the textbook by H. Brezis:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

Other useful, and recommended references are the following:

Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Voraussetzungen / BesonderesSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).
401-3531-00LDifferential Geometry I Information
Höchstens eines der drei Bachelor-Kernfächer
401-3461-00L Funktionalanalysis I / Functional Analysis I
401-3531-00L Differentialgeometrie I / Differential Geometry I
401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory
ist im Master-Studiengang Mathematik anrechenbar.
E-10 KP4V + 1UD. A. Salamon
KurzbeschreibungSubmanifolds of R^n, tangent bundle,
embeddings and immersions, vector fields, Lie bracket, Frobenius' Theorem.
Geodesics, exponential map, completeness, Hopf-Rinow.
Levi-Civita connection, parallel transport,
motions without twisting, sliding, and wobbling.
Isometries, Riemann curvature, Theorema Egregium.
Cartan-Ambrose-Hicks, symmetric spaces, constant curvature,
Hadamard's theorem.
LernzielIntroduction to Differential Geometry.
Submanifolds of Euclidean space, tangent bundle,
embeddings and immersions, vector fields and flows,
Lie bracket, foliations, the Theorem of Frobenius.
Geodesics, exponential map, injectivity radius, completeness
Hopf-Rinow Theorem, existence of minimal geodesics.
Levi-Civita connection, parallel transport, Frame bundle,
motions without twisting, sliding, and wobbling.
Isometries, the Riemann curvature tensor, Theorema Egregium.
Cartan-Ambrose-Hicks, symmetric spaces, constant curvature,
nonpositive sectional curvature, Hadamard's theorem.
LiteraturJoel Robbin and Dietmar Salamon "Introduction to Differential Geometry",
https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf
Bachelor-Kernfächer aus Bereichen der angewandten Mathematik ..
Nebst weiteren Einschränkungen gilt:
Die Anrechnung von 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory im Master-Studiengang ist nur dann zulässig, wenn weder 401-3642-00L Brownian Motion and Stochastic Calculus noch 401-3602-00L Applied Stochastic Processes für den Bachelor-Studiengang angerechnet wurde.
Neu ist 402-0205-00L Quantenmechanik I als angewandtes Kernfach anrechenbar, aber nur unter der Bedingung, dass 402-0224-00L Theoretische Physik (letztmals im FS 2016 angeboten) nicht angerechnet wird oder wurde (weder im Bachelor- noch im Master-Studiengang).
Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (www.math.ethz.ch/studiensekretariat).
NummerTitelTypECTSUmfangDozierende
401-3601-00LProbability Theory
Höchstens eines der drei Bachelor-Kernfächer
401-3461-00L Funktionalanalysis I / Functional Analysis I
401-3531-00L Differentialgeometrie I / Differential Geometry I
401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory
ist im Master-Studiengang Mathematik anrechenbar.
E-10 KP4V + 1UA.‑S. Sznitman
KurzbeschreibungBasics of probability theory and the theory of stochastic processes in discrete time
LernzielThis course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned:
Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
InhaltThis course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned:
Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
Skriptavailable, will be sold in the course
LiteraturR. Durrett, Probability: Theory and examples, Duxbury Press 1996
H. Bauer, Probability Theory, de Gruyter 1996
J. Jacod and P. Protter, Probability essentials, Springer 2004
A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006
D. Williams, Probability with martingales, Cambridge University Press 1991
402-0205-00LQuantum Mechanics I Information W10 KP3V + 2UC. Anastasiou
KurzbeschreibungEinführung in die nicht-relativistische Einteilchen-Quantenmechanik. Diskussion grundlegender Ideen der Quantenmechanik, insbesondere Quantisierung klassischer Systeme, Wellenfunktionen und die Beschreibung von Observablen durch Operatoren auf einem Hilbertraum, und die Analyse von Symmetrien. Grundlegende Phänomene werden analysiert und durch generische Beispiele illustriert.
LernzielEinführung in die Einteilchen Quantenmechanik. Beherrschung grundlegender Ideen (Quantisierung, Operatorformalismus, Symmetrien, Störungstheorie) und generischer Beispiele und Anwendungen (gebunden Zustände, Tunneleffekt, Streutheorie in ein- und dreidimensionalen Problemen). Fähigkeit zur Lösung einfacher Probleme.
InhaltStichworte: Schrödinger-Gleichung, Formalismus der Quantenmechanik (Zustände, Operatoren, Kommutatoren, Messprozess), Symmetrien (Translation, Rotationen), Quantenmechanik in einer Dimension, Zentralkraftprobleme, Potentialstreuung, Störungstheorie, Variations-Verfahren, Drehimpuls, Spin, Drehimpulsaddition, Relation QM und klassische Physik.
LiteraturJ.J. Sakurai: Modern Quantum Mechanics
Lectures on Quantum Mechanics, S. Weinberg
Wahlfächer
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.
Wahlfächer aus Bereichen der reinen Mathematik
Auswahl: Algebra, Topologie, diskrete Mathematik, Logik
NummerTitelTypECTSUmfangDozierende
401-3034-00LAxiomatische MengenlehreW8 KP3V + 1UL. Halbeisen
KurzbeschreibungEs werden ausführlich die Axiome der Mengenlehre besprochen und parallel dazu wird die Theorie der Ordinal- und Kardinalzahlen aufgebaut. Zudem werden Ultrafilter untersucht und es wird das Martinaxiom eingeführt.
Lernziel
InhaltEs werden ausführlich die Axiome der Mengenlehre besprochen und parallel dazu wird die Theorie der Ordinal- und Kardinalzahlen aufgebaut. Insbesondere wird die Kontinuumshypothese behandelt und einige Konsequenzen besprochen. Zudem werden Ultrafilter untersucht und die Existenz gewisser Ultrafilter diskutiert. Im letzten Teil der Vorlesung wird das Martin-Axiom eingeführt, mit dessen Hilfe sich interessante Konsistenzresultate in Topologie und Masstheorie, sowie Resultate über Ultrafilter, beweisen lassen.
SkriptIch werde mich weitgehend an mein Buch "Combinatorial Set Theory" (2nd ed., erscheint im Herbst 2017) halten.
Literatur"Combinatorial Set Theory: with a gentle introduction to forcing" (Springer-Verlag 2012)

http://www.springer.com/mathematics/book/978-1-4471-2172-5
401-3118-67LClassical Modular FormsW8 KP4GI. N. Petrow
Kurzbeschreibung
Lernziel
401-3129-67LDifferential Galois TheoryW4 KP2VP. S. Jossen
KurzbeschreibungAlgebraic theory of linear differential equations, Picard-Vessiot theory, Differential Galois groups, local theory of differential equations, the Frobenius method, Newton polygons, Connections and local systems, Riemann-Hilbert correspondence on ℙ¹.
LernzielWe introduce differential Galois theory and mathematical concepts surrounding it. We formulate and prove an important case of the Riemann-Hilbert correspondence.
InhaltWe study linear differential equations from an algebraic perspective, introducing differential rings, fields and differential modules (so-called Picard-Vessiot theory), and very soon the Galois group of a differential equation. We relate then the algebraic theory with the analytic theory, which leads us to the classical Riemann-Hilbert correspondence. In particular we will prove that differential equations on the complex projective line ℙ¹ with regular singularities in a finite set S correspond to representations of the fundamental group of ℙ¹∖S. If time permits, we have a look at differential equations in positive characteristic.
LiteraturM. van der Put and M. F. Singer, Galois theory of linear differential equations, Grundlehren der Math. Wiss. Vol 328, Springer 2003
401-3203-67LSmall Cancellation TheoryW4 KP2VD. Gruber
KurzbeschreibungSmall cancellation theory studies groups given by presentations in which defining relations have small common subwords. By translating group theoretic questions into geometric objects and applying concepts of negative curvature, it produces a variety of theorems on infinite groups. We will give an introduction to the theory, discuss important results, and touch on more recent developments.
LernzielFamiliarity with the fundamental methods of small cancellation theory and its main applications; ability to apply the methods to create new examples of infinite groups with prescribed properties; basic understanding of connections with Gromov hyperbolicity.
InhaltWe plan to cover a selection (depending on time) of the following topics:
- Methods of classical small cancellation theory (e.g. van Kampen diagrams, van Kampen's lemma, Greendlinger's lemma)
- Fundamental properties of small cancellation groups (e.g. Torsion Theorem, asphericity, linear/quadratic Dehn function)
- Connections with algorithmic decision problems in groups (e.g. Dehn's algorithm for solving the word problem in surface groups, solvability of word and conjugacy problems in small cancellation groups)
- Easy examples of small cancellation monsters (e.g. Pride's example, Rips construction)
- Graphical generalization of small cancellation theory and applications (e.g. groups with expander graphs embedded in their Cayley graphs)
- Connections with Gromov hyperbolicity
LiteraturV. Guirardel, Geometric small cancellation. Geometric group theory, 55-90, IAS/Park City Math. Ser. 21, Amer. Math. Soc., Providence, RI, 2014.

R. C. Lyndon, P. E. Schupp, Combinatorial group theory. Reprint of the 1977 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001. ISBN: 3-540-41158-5.

A. Yu. Olshanskii, Geometry of defining relations in groups. Translated from the 1989 Russian original by Yu. A. Bakhturin. Mathematics and its Applications (Soviet Series), 70. Kluwer Academic Publishers Group, Dordrecht, 1991. ISBN: 0-7923-1394-1.

R. Strebel, Appendix. Small cancellation groups. In: Sur les groupes hyperbolic d'après Mikhael Gromov (Bern, 1988), 227-273, Progr. Math. 83, Birkhäuser Boston, Boston, MA, 1990.
Voraussetzungen / BesonderesFamiliarity with very basic notions of group theory, definitions of free groups, group presentations, and graphs.
401-3177-67LIntroduction to Vertex Operator Algebras Information W4 KP2VC. A. Keller
KurzbeschreibungA first introduction to the theory of vertex operator algebras.
LernzielUnderstand the basic concepts of vertex operator algebras and their most important examples.
InhaltTentative plan:

1) Formal power series, local fields
2) Vertex Algebras
3) Conformal symmetry
4) Vertex Operator Algebras
5) Correlation functions
6) VOAs from lattices
7) Connection to modular forms: Zhu's Theorem
8) Connection to Monstrous Moonshine
LiteraturVictor Kac: Vertex Algebras for Beginners

James Lepowksy, Haisheng Li: Introduction to Vertex Operator Algebras and Their Representations
Voraussetzungen / BesonderesBasic algebra and linear algebra. Some background in quantum mechanics is helpful, but not necessary.
401-3059-00LKombinatorik IIW4 KP2GN. Hungerbühler
KurzbeschreibungDer Kurs Kombinatorik I und II ist eine Einfuehrung in die abzaehlende Kombinatorik.
LernzielDie Studierenden sind in der Lage, kombinatorische Probleme einzuordnen und die adaequaten Techniken zu deren Loesung anzuwenden.
InhaltInhalt der Vorlesungen Kombinatorik I und II: Kongruenztransformationen der Ebene, Symmetriegruppen von geometrischen Figuren, Eulersche Funktion, Cayley-Graphen, formale Potenzreihen, Permutationsgruppen, Zyklen, Lemma von Burnside, Zyklenzeiger, Saetze von Polya, Anwendung auf die Graphentheorie und isomere Molekuele.
Auswahl: Geometrie
NummerTitelTypECTSUmfangDozierende
401-3375-67LHomogeneous Dynamics and ApplicationsW8 KP4GM. Einsiedler, M. Akka Ginosar, Ç. Sert
KurzbeschreibungThe aim is to reach a few of the applications of homogeneous dynamics to number theory, e.g. counting results concerning quadratic forms, but also develop the theory from scratch. The first part of the course will be based on the book "Ergodic Theory with a view towards number theory" by Einsiedler and Ward, but several topics go beyond this volume.
LernzielThe aim is to reach a few of the applications of homogeneous dynamics to number theory, e.g. counting results concerning quadratic forms, but also develop the theory from scratch. The first part of the course will be based on the book "Ergodic Theory with a view towards number theory" by Einsiedler and Ward, but several topics go beyond this volume.
InhaltThe first part of the course will be based on the book "Ergodic Theory with a view towards number theory" by Einsiedler and Ward, but several topics go beyond this volume. Some of the aims of the course are:
-) Pointwise ergodic theorem for a certain class of amenable groups
-) Dynamics on hyperbolic surfaces, equidistribution of periodic horocycle orbits
-) Applications to counting
-) Some cases of Ratner theorems in Unipotent dynamics


Course website: https://metaphor.ethz.ch/x/2017/hs/401-3375-67L/
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