The graph of a curve is a familiar construction in the real plane; the analogous construction for complex valued functions of a complex variable is a “curve” that is a 2-dimensional set in a 4-dimensional space. Such curves, aside from a few singularities, locally look just like pieces of the complex plane, so it is possible to carry out complex analysis on such “curves”, just as for the complex plane; but the global geometry introduces a rich and fascinating structure on these sets, called Riemann surfaces (following the work of B. Riemann).
In 1899 Frank Morley noticed that the points of intersection of the adjacent angle trisectors form an equilateral triangle. Since then, proofs of various levels of complexity have been given, and in this colloquium Professor Conway will present a surprisingly simple proof discovered by himself. In addition, Professor Conway will introduce a new theorem of himself on equilateral triangles and the subtle mathematics behind it.
I will explain the geometry of a contact form in dimension three. The basic problem is to find the isoperimetric profile in the Heisenberg group. This variational problem is approached via a mean curvature equation. However this equation is not an elliptc equation in this low dimension, hence the problem remains largely open due to regularity issues.
(email from Andy)
Celebrate the beginning of the semester and E DAY (2/7) with the new officers at BOARD GAME NIGHT!
When: 9:00 PM Friday, February 7
Where: Fine Hall Common Room
There will be tons of great food (eclairs!), great fun, and great people. We’ll even be having an e recitation contest – be prepared to recite the digits of e! See you then!!
Please take a look at the Math Department’s information on summer 2014 research. The file covers two things:
1. The summer 2014 research program in mathematics at Princeton.
2. Financial support for summer research programs elsewhere.
(Email from Zhaonan)
For those of you who are interested in participating in an REU this summer, there will be some students who have done REUs before at the math departments’ afternoon tea time to share their experiences. The time and location are:
Wednesday Jan.22nd 3:30 pm
Fine Hall 3rd floor Common Room
Come talk to former REU students and ask any questions you might have! There will be cookies as well.
I’ve also copied Alan’s earlier email for your information.
Here is a long list of REUs: http://www.nsf.gov/crssprgm/reu/list_result.jsp?unitid=5044
Deadlines range from early February to early March, so you should do some research of your own before our info session. Also, please note that most will ask for 1 or 2 recommendation letters.