Marc Burger: Catalogue data in Autumn Semester 2018

Name Prof. Dr. Marc Burger
FieldMathematik
Address
Dep. Mathematik
ETH Zürich, HG G 37.1
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 49 73
Fax+41 44 632 10 85
E-mailmarc.burger@math.ethz.ch
URLhttp://www.math.ethz.ch/~burger
DepartmentMathematics
RelationshipFull Professor

NumberTitleECTSHoursLecturers
401-3200-64LProofs from THE BOOK Restricted registration - show details
Number of participants limited to 24.
4 credits2SM. Burger, further speakers
Abstract
ObjectiveZiel des Seminares ist zu lernen wie man Mathematik vortraegt. Als
Vorlage fuer dieses Seminar dient das Buch von Aigner und Ziegler "Proofs from the BOOK"
das aus allen Gebieten der Mathematik fundamentale Saetze und deren "schoensten" Beweise
praesentiert. Die Auswahl der Themen ist also gross und es gibt etwas fuer jeden Geschmack.
401-3225-00LIntroduction to Lie Groups Information 8 credits4GM. Burger
AbstractTopological 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.
ObjectiveThe 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.
LiteratureA. 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)
Prerequisites / NoticeTopology 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/2018/hs/401-3225-00L/
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, University lecturers
AbstractResearch colloquium
Objective
406-2004-AALAlgebra II
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
5 credits11RM. Burger
AbstractGalois theory and Representations of finite groups, algebras.

The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
ObjectiveIntroduction to fundamentals of Galois theory, and representation theory of finite groups and algebras
ContentFundamentals of Galois theory
Representation theory of finite groups and algebras
Lecture notesFor a summary of the content and exercises with solutions of my lecture course in FS2016 see:
https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/
LiteratureS. Lang, Algebra, Springer Verlag
B.L. van der Waerden: Algebra I und II, Springer Verlag
I.R. Shafarevich, Basic notions of algebra, Springer verlag
G. Mislin: Algebra I, vdf Hochschulverlag
U. Stammbach: Algebra, in der Polybuchhandlung erhältlich
I. Stewart: Galois Theory, Chapman Hall (2008)
G. Wüstholz, Algebra, vieweg-Verlag, 2004
J-P. Serre, Linear representations of finite groups, Springer Verlag
Prerequisites / NoticeAlgebra I
406-2005-AALAlgebra I and II
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
12 credits26RM. Burger, E. Kowalski
AbstractIntroduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras.

The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
Objective
ContentBasic notions and examples of groups;
Subgroups, Quotient groups and Homomorphisms,
Group actions and applications

Basic notions and examples of rings;
Ring Homomorphisms,
ideals, and quotient rings, rings of fractions
Euclidean domains, Principal ideal domains, Unique factorization
domains

Basic notions and examples of fields;
Field extensions, Algebraic extensions, Classical straight edge and compass constructions

Fundamentals of Galois theory
Representation theory of finite groups and algebras
Lecture notesFor a summary of the content and exercises with solutions of my lecture courses in HS2015 and FS2016 see:
https://www2.math.ethz.ch/education/bachelor/lectures/hs2015/math/algebra1/index-2.html
https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/
LiteratureS. Lang, Algebra, Springer Verlag
B.L. van der Waerden: Algebra I und II, Springer Verlag
I.R. Shafarevich, Basic notions of algebra, Springer verlag
G. Mislin: Algebra I, vdf Hochschulverlag
U. Stammbach: Algebra, in der Polybuchhandlung erhältlich
I. Stewart: Galois Theory, Chapman Hall (2008)
G. Wüstholz, Algebra, vieweg-Verlag, 2004
J-P. Serre, Linear representations of finite groups, Springer Verlag