# Representation Theory, Math 562b, Spring 2007

## Presentations

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 S
_{n} (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 SL
_{q}(2)
(not in text)
- modular representation theory, i.e. representations over finite
fields (not in text)

Timeline:

- 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
your date.
- 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:

- 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)

You should use the blackboard, and you should practice the talk
at least once or twice beforehand, on a blackboard with someone
listening.