Representation Theory, Math 9140b, Winter 2010
In the second half of the semester, each student will give a
presentation on a topic related to the course. The presentations
will be 45-55 minutes each. The dates will be
Monday, March 29, Wednesday, March 31, Monday, April 5 and
Wednesday, April 7.
All students must attend all of the presentations.
Possible topics. Some of these refer to sections of
Sternberg's book Group Theory and Physics. Additional topics
may be added later depending on where we get to in the course.
You may also suggest completely different topics. You should
choose a topic that is not something you already know about.
- the Murnaghan-Nakayama rule, giving a formula for the
irreducible characters of Sn (see Fulton, Young
Tableaux, or James-Kerber, The representation theory of the symmetric
- the Littlewood-Richardson rule describing the multiplicity
of an irrep of Sn in a tensor product of such irreps
(see James-Kerber, The representation theory of the symmetric
- the Robinson-Schensted-Knuth correspondence (see Fulton, Young
Tableaux, chapter 4)
- representations of semidirect products of groups (3.8 in Sternberg,
but I believe there are slicker ways to do it; ask me for references)
- representations of Lie algebras (4.10) and su(2) (4.11)
- representations of quantum groups, or just SLq(2)
(ask me for references)
- modular representation theory, i.e. representations over finite
fields; maybe also the stable module category of a group (ask me for
- applications to particle physics (3.9, 3.10, 3.12, 5.9 to 5.12, ...)
- applications to crystalography (1.5, 1.8, 1.9, 1.10)
- other applications (4.5 to 4.9)
- Choose your date by Feb 25
- Meet with me to discuss topics.
- Choose your topic ≥ 4 weeks ahead of your date.
- Give me an outline (~1 page) ≥ 3 weeks ahead of
- Give me a draft of the talk ≥ 2 weeks ahead of your date.
The presentation is worth 30% of the final grade.
Grade based on:
Note that knowledge of the material is only a small part of the grade.
- knowledge of the material
- organization of material (what you choose to cover and how
you choose to organize it)
- clarity of presentation (how you present it: choice of notation,
speak clearly, face the audience, etc)
- blackboard use (use boards in order, don't erase what you just wrote,
don't stand in front of what you write, etc)
- timing (45-55 min gets full marks, too short or too long
gets reduced marks; you might consider building in some flexibility
at the end of the talk)
You should use the blackboard, and you should practice the talk
at least once or twice beforehand, on a blackboard with someone
listening. And you should time the practice talks.