Nigel Higson - 2010

20-Minute Presentations

The Notices of the American Mathematical Society runs a series of short pieces whose titles all begin with What Is …?  They're meant to quickly introduce topics of current interest in mathematics. You should check them out.

I'd like you to prepare two 20-minute presentations during the semester that are roughly like the What Is articles but aimed a bit lower, at beginning graduate students like yourselves. Your presentations could center on definitions, theorems, particular mathematical objects, or they could range a little more broadly over a subject area (but not too broadly since you only have 20 minutes).  We talked about suitable topics in class and I've added to our list at the bottom of this page.  But you're welcome to suggest your own topics.

I'm going to give several sample presentations in the seminar that I hope will show you what is expected. But you needn't copy my style!  If your audience learns something of interest and value then you will have succeeded, no matter how you did it.

Here's what you need to do:

  1. 1.Select a topic for your first presentation and submit it to me for approval before Friday January 20.  At the same time select a date for your presentation between Monday January 30 and Friday March 2 (see the class calendar; give me a list of two or three dates and I'll choose the first one on your list that is available).

  2. 2.Prepare your presentation and discuss it with me at least two days before the event (for example, if you will speak on Wednesday, talk to me on Monday at the latest).

  3. 3.Submit a written version of your presentation at most seven days after the event.

Your second presentation will be handled in the same way.  The deadline for topic and date selection will be Friday February 24. Presentations will be given between Monday March 12 and Friday April 27.

Finally, here is the topics list:

What is ...

    a Lie algebra?

    quadratic reciprocity?


    a Coxeter group?

    a Penrose tiling?

    the Schrodinger equation?

    a partition?

    Bezout’s theorem?

    the Gibbs phenomeon?

    a random graph?

    a Sobolev space?

    Ramsey theory?

    Gaussian curvature?

    the word problem?

    a building?

    an elliptic partial differential operator?

    a Markov process?

    the continuum hypothesis?

    a sheaf?

    the Fredholm index?

    a Poisson bracket?

    the Euler-Lagrange equation?

    a C*-algebra?

    the Riemann zeta function?

    the Runge-Kutta method?

    a p-adic number?

    a manifold?

    the hyperbolic plane?

    Minkowski space?

    an octonion?

    the Hopf fibration?