Representation Theory, Math 562b, Spring 2007
In the second half of the semester, each student will give a
presentation on a topic related to the course. The presentations
will be 45-50 minutes each, and
will start roughly April 3 and continue for five classes (2 per class).
Possible topics. Some of these could easily be split into
more than one presentation:
- representations of Sn (2.8 and Appendix C)
- representations of SU(2) (4.3) and/or SU(n) (chapter 5)
- 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)
- the representation ring of a group (not in text, although
Appendix C.4 contains some relevant material)
- representations of semidirect products of groups (3.8 in text,
but I believe there are slicker ways to do it)
- Haar measure, the Peter-Weyl theorem (Appendix E)
- characters and fixed point formulas for Lie groups (Appendix G)
- representations of Lie algebras (4.10) and su(2) (4.11)
- representations of quantum groups, or just SLq(2)
(not in text)
- modular representation theory, i.e. representations over finite
fields (not in text)
- Choose your date before spring break.
- Meet with me to discuss topics.
- Choose your topic ≥ 3 weeks ahead of your date.
- Give me an outline (1 to 2 pages) ≥ 2 weeks ahead of
- Give me a draft of the talk ≥ 1 week ahead of your date.
The presentation is worth about 1/3 of the final grade.
Grade based on:
You should use the blackboard, and you should practice the talk
at least once or twice beforehand, on a blackboard with someone
- knowledge of material
- organization of material (what you choose to cover and how
you choose to organize it)
- clarity of presentation (how you present it)
- blackboard use (go in order, don't erase what you just wrote,
don't stand in front of what you write, etc)
- timing (45-50 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)