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

*(October 18 - 19, 2017)*

**Description**

The NSF Mathematical Sciences Diversity Committee is pleased to announce the 2017 Modern Math Workshop at SACNAS. This workshop is intended to encourage undergraduates, graduate students and recent PhDs from underrepresented minority groups to pursue careers in the mathematical sciences and build research and mentoring networks. The Modern Math Workshop is a "pre-conference" part of the SACNAS National Conference. Both the Modern Math Workshop and the SACNAS conference take place in the Salt Palace Convention Center in Salt Lake City, Utah. The Modern Math Workshop check-in/registration begins at noon on Wednesday, October 18, with the scientific programming beginning at 1:00pm. The final session, a Q&A with NSF Math Institute representatives, ends at noon on Thursday, October 19.

**Research Sessions**: 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. These sessions run over the two days of the Modern Math Workshop: 1:00-4:30pm on the afternoon of Wednesday, October 18, and 9:00-10:45am the morning of Thursday, October 19.**Mini-courses**: Two half-day mini-courses will be offered on October 18, from 1:30-4:30pm, running concurrently: "Polynomial exact sequences in numerical analysis" and "Counting curves, intersections, and designs in hyperbolic geometry". These mini-courses are intended for undergraduate students.**Keynote Speaker**: At 4:30pm on Wednesday, October 18, all Modern Math Workshop participants are invited to enjoy the keynote lecture by Jesus De Loera (UC Davis), "The little theorem that could: How Sperner’s coloring lemma influenced Mathematics & Economics". Dr. De Loera's 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.**Reception**: The NSF math institutes' networking reception will immediately follow the keynote lecture at 5:30pm on Wednesday, October 18.**Q&A**: The closing session of the workshop is a Q&A with NSF Math Institute representatives, 11:00am-12:00pm on Thursday, October 19.

#### 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 |

12:00 - 1:00 |

Check-in/Registration at the Salt Palace Convention Center |

1:00 - 4:30 |

Undergraduate Mini-courses |

Two Concurrent Sessions |

1:00 - 4:30 |

Research Talks by Math Institutes, Part 1 |

(schedule below) |

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 below) |

11:00 - 12:00 |

Q&A with Institute Representatives |

**Undergraduate Mini-Course 1:** Polynomial exact sequences in numerical analysis

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

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

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

**Abstract:** We learn in the third semester in calculus that if a vector field has vanishing curl then it must be the gradient of a smooth function. This is the main idea behind the De Rham exact sequence. Exact sequences have been used in numerical analysis and the corresponding polynomial spaces have been used to approximate solutions of partial differential equations. The application areas are diverse, including fluid problems, solid mechanics and electromagnetism. In this mini-course, we will discuss basic concepts and techniques in polynomial exact sequences.

**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:** Counting curves, intersections, and designs in hyperbolic geometry

**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.

Research Talks by Math Institutes, Part I | |

October 18, 2017 | Locations TBA |

12:00 - 1:00 | Check-in/Registration |

01:00 – 1:05 | Welcome & Opening Remarks |

01:05 – 1:35 | Research talk TBA |

01:40 – 2:10 | Research talk TBA |

02:15 – 2:45 | Research talk TBA |

02:50 – 3:15 | Research talk TBA |

03:15 – 3:45 | Research talk TBA |

03:50 – 4:20 | Research talk TBA |

04:30 – 5:30 | Keynote Lecture by Jesus De Loera ("The little theorem that could: How Sperner's coloring lemma influenced Mathematics and Economics" |

05:30 – 7:00 | NSF Math Institutes' Networking Reception (Location TBA) |

Research Talks by Math Institutes, Part 2 | |

October 19, 2017 | Locations TBA |

09:00 – 09:30 | Research talk TBA |

09:35 – 10:05 | Research talk TBA |

10:10 – 10:40 | Research talk TBA |

10:45 – 11:00 | Break |

11:00 – 12:00 | Q&A with Institute Representatives |

Talk abstracts coming soon.

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

**Speaker Bio:** Jesus De Loera is a Professor of Mathematics at UC Davis. His 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.

We expect that Modern Math Workshop participants will apply for a SACNAS Travel Scholarship or support from their department to cover their travel and accommodations during the SACNAS conference, which runs October 19-21. Successful applicants to the Modern Math Workshop will be offered an additional night in a hotel, double occupancy for the pre-conference. Those who do not secure other means of support by early August will have an opportunity to request supplemental funding from ICERM, including additional nights in a hotel and/or a travel award. Applications are collected via MathPrograms.org. A complete application requires one letter of recommendation and a copy of your CV or resume. Applications are due by 9:00pm Eastern on Monday, July 31, 2017.

Modern Math Workshop will be held in the Salt Palace Convention Center located at 3100 S W Temple, Salt Lake City, UT 84101.
Workshop activities will take place in Rooms 150 and 151 on the first floor of the Convention Center (view floor layout).
Please consult the Salt Palace Convention Center webpage for directions and parking information.

Please send your questions to: info@icerm.brown.edu