# Representation Theory, Math 9140b, Winter 2010

## 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 45-55 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 S
_{n} (see Fulton, *Young
Tableaux*, or James-Kerber, *The representation theory of the symmetric
group*)
- the Littlewood-Richardson rule describing the multiplicity
of an irrep of S
_{n} in a tensor product of such irreps
(see James-Kerber, *The representation theory of the symmetric
group*)
- 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 SL
_{q}(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
references)
- 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)

Timeline:

- 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
your date.
- 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:

- 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)

Note that knowledge of the material is only a small part of the grade.
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.