### NSF Mathematics Institutes’ Modern Math Workshop (at SACNAS in Salt Lake City, Utah)

*(October 18 - 19, 2017)*

**Description**

As part of the Mathematical Sciences Collaborative Diversity Initiatives, nine mathematics institutes are pleased to offer their annual SACNAS pre-conference event, the **2017 Modern Math Workshop (MMW)**. The Modern Math Workshop is intended to encourage minority undergraduates to pursue careers in the mathematical sciences and to assist undergraduates, graduate students and recent PhDs in building their research networks. The Modern Math Workshop is part of the SACNAS National Conference; the workshop and the conference take place in the Salt Palace Convention Center in Salt Lake City, Utah. The MMW starts at 1:00 pm on Wednesday, October 18 with registration beginning at noon. The Modern Math Workshop consists of the following sessions:

**Research Session**: The intended audience is graduate students and recent PhDs. Each participating institute will provide a speaker who will present an upcoming research program at the respective institute. All presentations will be expository in nature, intended for mathematical scientists and students not necessarily working in these areas but interested in learning about new developments and the possibility of spending some time at one of the Math Institutes. Due to the diverse portfolio of the institutes, it exposes participants to a broad range of topics in modern mathematics. This session continues the morning of Thursday, October 19.**Undergraduate Mini-courses**: Two half-day mini-courses will be offered in the afternoon of the first day, running concurrently. These mini-courses are intended for undergraduate students. More information is available on the tab labeled "Sessions."

In addition, there will be a keynote lecture by Jesus De Loera, professor of mathematics at UC Davis, whose research encompasses a large number of pure and applied projects, including his work in Convexity and Combinatorial Commutative Algebra, as well as his work in Combinatorial Optimization and Algorithms. There will also be a reception on Wednesday evening that will include an information booth by each institute which will give participants ample time to find out about activities and opportunities at all the institutes. Workshop participants (graduate students and above) will be invited to present posters of their research during the reception.

#### Organizing Committee

**Hélène Barcelo**

(Mathematical Sciences Research Institute)**Leslie McClure**

(Statistical and Applied Mathematical Sciences Institute (SAMSI))**Christian Ratsch**

(Institute for Pure and Applied Mathematics)**Ulrica Wilson**

(Institute for Computational and Experimental Research in Mathematics (ICERM))

## Wednesday, October 18, 2017 |

1:00 - 4:30 |

Undergraduate Mini-courses |

Two Concurrent Sessions |

1:00 - 4:30 |

Research Talks by Math Institutes |

Part 1 (schedule coming soon) |

4:30 - 5:30 |

Jesus De Loera (UC Davis) |

Keynote Lecture: The little theorem that could: How Sperner’s coloring lemma influenced Mathematics & Economics. |

5:30 - 7:00 |

Networking Reception and Poster Session |

## Thursday, October 19, 2017 |

9:00 - 10:45 |

Research Talks by Math Institutes |

Part 2 (schedule coming soon) |

11:00 - 12:00 |

Q&A with Institute Representatives |

Abstract |

**Undergraduate Mini-Course 1:** TBA

**Taught by:** Johnny Guzm'an (Brown University)

**Time:** 1:00PM – 4:30PM (break 2:50PM-3:15PM)

**Room:** TBA (Salt Palace Convention Center)

**Abstract:** This interactive session will highlight opportunities available at the math institutes for undergraduates, graduate students, and faculty and discuss tips for successful applications to their programs. There will also be an opportunity for the audience to ask questions to the panelists. All workshop participants are welcome to attend.

**Speaker Bio:** Johnny Guzm'an is an Associate Professor of Applied Mathematics at Brown University. He earned his Ph.D. in applied mathematics from Cornell University in 2005, and was an NSF postdoc at the University of Minnesota until 2008. He works in finite element approximations of partial differential equations. He has been attending SACNAS conferences since 2000!

**Undergraduate Mini-Course 2:** TBA

**Taught by:** Tarik Aougab

**Time:** 1:00PM – 4:30PM (break 2:50PM-3:15PM)

**Room:** TBA (Salt Palace Convention Center)

**Abstract:**
A surface is an object which looks "locally" like the 2-dimensional plane if you zoom in far enough. One way of probing a surface is to study the sorts of closed loops that can be drawn on it. How many different loops (satisfying certain additional properties which we will discuss) on a particular surface have the property that they only self-cross 5 times? How many pairs of loops can you draw which jointly partition the surface into a bunch of polygons? How large of a collection of loops can you draw on a fixed surface so that no two cross each other more than 48 times? We will see how the answers to these kinds of questions can be used to study the surface and we'll discuss how this relates to group theory. We'll also talk about how to use geometry, in particular hyperbolic geometry, to help answer such questions. The goal will be to convince the audience that there are deep connections between geometry, topology, combinatorics, and abstract algebra, and, that asking these types of questions is an efficient and fun way of exploring these connections.

**Speaker Bio:** Tarik Aougab is an assistant professor of mathematics and NSF postdoctoral fellow at Brown University. Before Brown, he received his PhD from Yale University under the supervision of Yair Minsky. His research interests include low-dimensional hyperbolic geometry, geometric group theory, and Teichmuller theory. He is especially interested in relationships between combinatorics and geometry: using combinatorial tools to probe the geometry of a space, and conversely, using geometric methods to answer purely combinatorial (or algebraic) questions.

##### Title: The little theorem that could: How Sperner’s coloring lemma influenced Mathematics & Economics

**Speaker Bio:** Jesus De Loera's work includes over 80 papers and books in
Convex Geometry, Combinatorics, Algebra, Algorithms and Optimization.
He received an Alexander von Humboldt Fellowship in 2004 and the 2010 INFORMS
computer society prize. He is a fellow of the American Mathematical
Society since 2014. For his mentoring and teaching he received the 2013
UC Davis Chancellor's award for mentoring undergraduate research and, in 2017,
the Mathematical Association of America Golden Section Award. He has
supervised eleven Ph.D students, and over 50 undergraduates research
projects. He is an associate editor for 'SIAM Journal of Discrete
Mathematics' and 'SIAM journal of Applied Algebra and Geometry'.

**Abstract:** Sperner’s lemma states that a certain way of coloring triangulations of an $n$-dimensional simplex must contains at least one cell colored with a complete set of $n$ colors.
This simple result has nevertheless great depth as it is equivalent to Brouwer’s fixed point theorem and it has strong connections to Borsuk-Ulam theorem and other classical
results in topology. Sperner’s lemma has many applications too: it has been used for computation of fixed points, in root-finding algorithms, in fair division
(cake cutting, rental agreements) algorithms and it is at the foundation of the proofs of existence of Nash equilibria in Game theory. Several fascinating
variations have been discovered and applied in recent years and there is renewed interest by theoretical computer scientists to find algorithmic versions.
In my talk I will convince a non-expert why everyone should know about this lovely easy-to-understand, yet powerful, mathematical result.

AIM (American Institute of Mathematics)

IAS/PCMI (Institute for Advanced Study)

ICERM (Institute for Computational and Experimental Research in Mathematics)

IMA (Institute for Mathematics and its Applications)

IPAM (Institute for Pure and Applied Mathematics)

MBI (Mathematical Biosciences Institute)

MSRI (Mathematical Sciences Research Institute)

NIMBioS (National Institute for Mathematics and Biological Synthesis)

SAMSI (Statistical and Applied Mathematical Sciences Institute)