##### Organizing Committee

- Jeffrey Brock
*Brown University* - Ricardo Cortez
*Tulane University* - Ruth Crane
*Brown University* - Snehalata Huzurbazar
*Statistical and Applied Mathematical Sciences Institute (SAMSI)* - Jill Pipher
*Brown University - ICERM* - Ivelisse Rubio
*University of Puerto Rico*

##### Abstract

As part of the Mathematical Sciences Collaborative Diversity Initiatives, nine mathematics institutes (including ICERM) are pleased to host their annual pre-conference event, the 2013 Modern Math Workshop. This event precedes the SACNAS National Conference.

The Modern Math Workshop is intended to re-invigorate the focus of mathematics students and faculty at minority-serving institutions and the research careers of minority mathematicians.

#### Keynote Lecture

##### Tutte polynomials in combinatorics and geometry

*Federico Ardila - San Francisco State University*

###### Abstract

The Tutte polynomial is a combinatorial polynomial that one associates to a set of vectors V. This polynomial knows an incredible amount about the geometric, algebraic, and combinatorial properties of V. I will define this polynomial and illustrate a few of its properties. This talk will be accesible to undergraduate students, and will require no previous knowledge of the topic.

###### About the Speaker

Federico Ardila is an Associate Professor of Mathematics at San Francisco State University. He studies objects in algebra, geometry, topology and applications by understanding their underlying discrete structure. He leads the SFSU-Colombia Combinatorics Initiative, a research and learning collaboration between students and researchers in the United States and Colombia. When he is not at work, you might find him on the fĂștbol field or treasure hunting in little record stores.

#### Undergraduate Sessions

##### Mini-Course 1: "A Tour of Dynamical Systems"

*Araceli Bonifant, University of Rhode Island*

Dynamical Systems is the part of mathematics which studies the changes that occur as a system evolves over time. Some systems are easy to predict whereas others are not. Such difficult to predict systems are known as "chaotic systems" (for example, the stock market or the weather). It is a surprizing fact that very simple transformations can give rise to very complex (and beautiful !) behavior. In this mini-course we will start by describing the dynamics under iteration of a simple family of maps (real quadratic polynomials) and we will work our way through to the study of the dynamics of quadratic complex polynomials. We will tour the parameter space of complex quadratic polynomials, known as the Mandelbrot set, and will describe the Fatou and Julia sets for some parameters.

##### Mini-Course 2: "A Survey of Diophantine Equations"

*Edray H. Goins, Purdue University*

There are many beautiful identities involving positive integers. For example, Pythagoras knew `3 ^{2} + 4^{2} = 5^{2}` while Plato knew

`3`. Euler discovered

^{3}+ 4^{3}+ 5^{3}= 6^{3}`59`, and even a famous story involving G. H. Hardy and Srinivasa Ramanujan involves

^{4}+ 158^{4}= 133^{4}+ 134^{4}`1`. But how does one find such identities? Around the third century, the Greek mathematician Diophantus of Alexandria introduced a systematic study of integer solutions to polynomial equations. In this session, we'll focus on various types of so-called Diophantine Equations, discussing such topics as the Postage Stamp Problem, Pythagorean Triples, Pell's Equations, Elliptic Curves, the ABC Conjecture and Fermat's Last Theorem.

^{3}+ 12^{3}= 9^{3}+ 10^{3}#### Workshop Schedule

##### Wednesday, October 2, 2013

Time | Event | Location | Materials |
---|---|---|---|

12:00 - 1:00pm EDT | Registration & Lunch | Room 212 | |

1:00 - 2:25pm EDT | Undergraduate Mini Course 1: A Tour of Dynamical Systems - Araceli Bonifant, University of Rhode Island | Room 210A | |

1:00 - 1:25pm EDT | The mathematics of materials - IAS: Charles Radin, University of Texas Austin | Room 213 | |

1:00 - 2:25pm EDT | Undergraduate Mini Course 2: A Survey of Diophantine Equations - Edray Goins, Purdue University | Room 210B | |

1:30 - 1:55pm EDT | Conceptual Climate Models: Energy Balance, Feedback Elements, and Tipping Points - IMA: Anna Barry, IMA Postdoc, University of Minnesota | Room 213 | |

2:00 - 2:25pm EDT | Modeling the immune response of Cattle suffering from Johne's Disease - NIMBioS: Gesham Magombedze, NIMBioS Postdoc, University of Tennessee | Room 213 | |

2:30 - 2:40pm EDT | Break | Room 212 | |

2:45 - 3:40pm EDT | Undergraduate Mini Course 1: A Tour of Dynamical Systems - Araceli Bonifant, University of Rhode Island | Room 210A | |

2:45 - 3:10pm EDT | Neural mechanisms underlying limb coordination in crayfish swimming - MBI: Lucy Spardy, MBI postdoc, The Ohio State University | Room 213 | |

2:45 - 3:40pm EDT | Undergraduate Mini Course 2: A Survey of Diophantine Equations - Edray Goins, Purdue University | Room 210B | |

3:15 - 3:40pm EDT | Applications of Non-negative Matrix Factorization in Statistics - SAMSI: Kenny Lopiano, SAMSI postdoc | Room 213 | |

3:45 - 4:10pm EDT | Break | Room 212 | |

4:15 - 5:00pm EDT | Keynote Lecture: Tutte polynomials in Combinatorics and geometry - Federico Ardila | Room 213 | |

5:15 - 6:25pm EDT | Math Institutes Panel | Room 213 | |

6:30 - 8:00pm EDT | Math Institutes Reception | Room 212 |

##### Thursday, October 3, 2013

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:25am EDT | Convection, Stability, and Turbulence - IPAM: Charlie Doering, University of Michigan | Room 213 | |

9:30 - 9:55am EDT | Change-point detection for non-stationary high-dimensional timeseries with missing data - ICERM: Rebecca Willett, University of Wisconsin-Madison | Room 213 | |

10:00 - 10:25am EDT | Shimura varieties, Galois representation and Automorphic forms - MSRI: Elena Mantovan, Caltech | Room 213 | |

10:30 - 10:55am EDT | Break | Room 212 | |

11:00 - 12:00pm EDT | Information Session with Funding Agencies | Room 213 |