The 2020 Worskhop is cancelled.

The 2019 workshop will start on Wednesday May 29th. If you want/plan to attend please fill out this form and email me.

The workshop was not held on 2018 because I was 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.

#### Some Links

- Piazza Workshop 2019
- GROW
- Young Mathematicians Conference 2019
- Undergraduate Mathematics Symposium 2019, University of Illinois at Chicago

- Here is a link with some of the participants and projects from previous years.

**When**: We held weekly meetings on Wednesdays from 10am to 4pm in the Common Room (4th Floor Math Tower). Meetings start at a bit after classes end at Stony Brook and end a bit before classes start (The precise meaning of “a bit” is determined each year)..

**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 take breaks by working on math crafts.

The focus is the topology and geometry of surfaces, with occasional appearances of knots and three manifolds.

**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 are some possible readings. A few 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.
- Combinatorial topology of surfaces - by Robert C. James.
- Mostly Surfaces by Richard Schwartz (this Notes are also interesting)
- 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)
- The history of coloring maps problems by Moira Chas
- Graph Theory, 1736-1936 by Briggs, Lloyd and Wilson.
- Regular Polytopes, by H. S. M Coxeter
- Relations between Word Length, Hyperbolic Length and Self-Intersection Number of Curves on Surfaces by Moira Chas
- Statistics of Intersections of Curves on Surfaces by Rachel Zhang

**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.
- Papers by Alicia Boole Stott and Pieter Schoute

**Software**:

- Program to find geodesics on the pair of pants (given a hyperbolic metric) by Matt Genkin
- Program to compute the Fricke polynomial in a free group on two generators by Minh Nugyen
- Program to compute find the Goldman bracket and Turaev cobracket on surfaces with boundary Minh Nugyen based on my program.

**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