The workshop will not be held on 2018 because I’ll be at ICERM.

This workshop starting meeting in the Summer of 2010, organized by Moira Chas with the help of Tony Phillips Dennis Sullivan and contributions from, among others, Chandrika Sadanand, Nissim Ranade, Cameron Crowe, Jimmy Matthews and Anibal Medina.

**When**: We held weekly meetings on Wednesdays from 10am to 4pm in the Common Room (4th Floor Math Tower). Meetings start at the end of May.

**What**: During these hours, we have (very 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 post in this site the exact date and time whenever 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.

- Basic topology of curves an surfaces.
- Notes and Mostly Surfaces by Richard Schwartz.
- The Lecture Notes On Geometry of Surfaces by Hitchins are great (although depending on your background can be a bit difficult)
- Hyperbolic Geometry by Cannon, Floyd, Kenyon and Parry. (also require mathematical maturity)

**Interesting articles**

- What is geometry? and From triangles to manifolds, by Chern.
- The geometry of Markoff numbers by Caroline Series
- Markoff theory, a geometric approach by Barbara Harzevoort.
- 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 guarantee that you will learn something). Some students ended up with a result that was presented in undergrad conferences, and even published.

**Sample of topics**

- Two dimensional hyperbolic geometry.
- Topology of curves on surfaces
- Covering spaces and deck transformations.

**Articles by workshop participants**

- A combinatorial algorithm for visualizing representatives with minimal self-intersection by Chris Arettines
- Experiments Suggesting That the Distribution of the Hyperbolic Length of Closed Geodesics Sampling by Word Length Is Gaussian, by Moira Chas, Keren Li and Bernard Maskit
- Ideals in the Goldman Lie algebra, by Minh Nguyen.

Previous participants and projects