Giovanni Felder: Catalogue data in Autumn Semester 2018

Award: The Golden Owl
Name Prof. em. Dr. Giovanni Felder
FieldMathematics
Address
Professur für Mathematik
ETH Zürich, HG G 46
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 34 09
E-mailgiovanni.felder@math.ethz.ch
URLhttp://www.math.ethz.ch/~felder
DepartmentMathematics
RelationshipProfessor emeritus

NumberTitleECTSHoursLecturers
401-3160-68LRepresentation Theory: Groups, Algebras and Quivers Restricted registration - show details
Number of participants limited to 14.
4 credits2SG. Felder, further speakers
AbstractRepresentation theory of groups, algebras, quivers, based on examples and solving problems.
ObjectiveThe students will learn basic notions and techniques of representation theory and to apply these techniques in concrete situations and examples.
ContentIntroduction to representation theory with many examples. Lie algebras and universal enveloping algebra. Schur lemma, representations of a matrix algebra. Jordan-Holder theorem, extensions. Category O for sl(2). Representations of finite groups. Burnside theorem, Frobenius reciprocity. Representations of symmetric groups. Representations of GL_2(F_q). Quivers. McKay correspondence.
LiteratureThe main reference is:

[E] P.Etingof, O. Goldberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, E. Yudovina, Introduction to representation theory, with historical interludes by S. Gerovitch, AMS 2010.
Much of the material (but not the historical interludes) can be found at http://math.mit.edu/~etingof/replect.pdf

Additional literature that might be helpful:
[F] W.Fulton, Representation theory, A first course.
[L] S. Lang, Algebra.
[S] J-P. Serre, Lie Algebras and Lie Groups
[BGP] I N Bernstein, I M Gel'fand and V A Ponomarev "COXETER FUNCTORS AND GABRIEL'S THEOREM"
Russ. Math. Surv. 28
[D] Igor Dolgachev
McKay's correspondence for cocompact discrete subgroups of SU(1,1)
available at http://arxiv.org/pdf/0710.2253
Prerequisites / NoticeLinear algebra and basic notions of algebra. Please refresh (or learn) basic notions of multilinear algebra to be able to solve the first problems on tensor products of vector spaces in [E].

Each participant gives a presentation and is assigned a set of exercises, whose solution is published on the wiki of the seminar.
401-5330-00LTalks in Mathematical Physics Information 0 credits1KA. Cattaneo, G. Felder, M. Gaberdiel, G. M. Graf, T. H. Willwacher, University lecturers
AbstractResearch colloquium
Objective