Summer Geometry and Topology Workshop


This workshop starting meeting in the Summer of 2010, organized by Moira Chas with the help of Tony Phillips and Dennis Sullivan.

When: We held weekly meetings  (on Wednesdays up to now but that can change this year)  from 10am to 3 or 4pm.

What: During these hours, we have (interactive) lectures. We go to lunch around 1pm and continue the discussion afterwards. Occasionally, we have invited speakers. Often the participants talk about their own research. We usually start right after classes end at Stony Brook. I will confirm by email and post in this site the exact date and time when I have it.

Who can participate: Everyone is welcome to participate, from high school students to mature mathematicians. We do request commitment, in the sense of being fully present in the lectures, and thinking about them during the week. It is not mandatory to come to all the lectures but it is encouraged.

How: Students must “earn” the right to a problem, by working on the topics we discussed.  I have problems of many kinds. In general, to undergraduate students I assign a problem that starts with establishing a conjecture, often with the help of a computer. I have developed an extensive library of software related to curves on surfaces and I am very happy to share my programs. Student who wish can also create their own code.

Preliminary readings: Below is  of material to read before and during the workshop. Some of these notes are advanced and you are not expected to work on them until you are ready. But you can start by reading 1, 2 and 5.

  1. 1.Basic topology of curves an surfaces.

  2. 2.Notes by Richard Schwartz.

  3. 3.The Lecture Notes On Geometry of Surfaces by Hitchins are great (although depending on your background can be a bit difficult)

  4. 4.Hyperbolic Geometry by Cannon, Floyd, Kenyon and Parry. (also require mathematical maturity)

  5. 5.Non-Euclidean geometry, continued fractions, and ergodic theory, by Caroline Series, The mathematical intelligencer 1982.

The goal: The main goal is to understand something in math. Research has a certain degree of unpredictability (this is part of the fun) and so we cannot guarantee that you will have your own theorem after n weeks. (If you work hard, we can guaranteed that you will learn something). Some students ended up with a result that was presented in undergrad conferences, and even published.

What is the difference with an REU: There is two main differences, you do no have to formally apply, and we do not pay you an stipend.

Sample of topics

  1. Two dimensional hyperbolic geometry.

  2. Topology of curves on surfaces

  3. Covering spaces and deck transformations.

  1. Below you will find a description  of the workshop. If, after reading it, you are interested in participating, send me an email to moira dot chas at stonybrook dot edu