Southeastern Undergraduate Mathematics Workshop

This is a week-long workshop for undergraduate math majors featuring two mini-courses, problem sessions, seminar talks, as well as graduate school and career panels. Participants will also have the opportunity to give a short talk on their research and / or a poster presentation. Funding is available to help cover travel and local accommodations.

All activities will take place on the ground floor of Skiles Classroom Building in room 005 and the adjacent atrium.

Workshop Poster

Mini-courses:

An Application of Topology to Biology (Candice Price, University of San Diego and TA Kaitlin Tademy)

One typically views double-stranded deoxyribonucleic acid (DNA) either as base pairs or as a double helix. Yet looking at the shape of DNA in space can lead to interesting applications of topology, particularly those using knot theory. The first few days of this course, we will discuss some of the many mathematical tools used to model the topological shape of DNA starting with knot and link invariants and include tangle arithmetic. This course will conclude with a discussion/review of a mathematical model for the actions of proteins that change the topological shape of DNA.

Slides: Day 1

Introduction to Topological Data Analysis (Matthew Wright, St. Olaf College and TA Xiaojun Zheng)

In recent years, the mathematical area of topology has been applied to the analysis of complex data. Topological tools can discern multi-scale structure in data that is too large or high-dimensional to be easily visualized. These tools have been applied to areas such as computer graphics, neuroscience, signal processing, biology, and much more.

This mini-course will provide an introduction to topological data analysis, focusing on two topological tools: persistent homology and Euler characteristic. Participants will learn how to build topological spaces from data, how to apply persistent homology and Euler characteristic to these spaces, and how to interpret the results. No background in topology is required; ideas will be built on a simple foundation from geometry and linear algebra. The course will also highlight connections to computation and statistics, as well as modern software for computing persistent homology. Participants will be equipped to apply topological data analysis to their own problems, and to further investigate this fascinating, rapidly-developing area at the forefront of applied mathematics.

Slides: Day 1 Day 2 Day 3 Day 4

Euler characteristic exercises with solutions

Seminar Talks:

Speaker: Justin Lanier (Graduate student in math at Georgia Tech)

Title: Surfaces and their symmetries

Abstract: Surfaces are some of the most basic examples of manifolds in topology. Although surfaces have been studied for a long time, they continue to fascinate mathematicians. We'll discuss the classification of surfaces as well as mapping class groups, which are collections of symmetries of surfaces. We'll also see some connections between surfaces, 3-manifolds, braids, and knots.

Slides

Speaker: Sabetta Matsumoto (Assistant Professor in physics at Georgia Tech)

Title: Non-euclidean virtual reality

Joint work with Vi Hart, Andrea Hawksley, and Henry Segerman

Abstract: The properties of euclidean space seem natural and obvious to us, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions, revealing just how strongly our native experience of the world blinded us from consistent alternatives, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic, but with direct immersive experiences we can get a better intuitive feel for them. The latest wave of virtual reality hardware, in particular the HTC Vive, tracks both the orientation and the position of the headset within a room-sized volume, allowing for such an experience. We use this nacent technology to explore the three-dimensional geometries of the Thurston/Perelman geometrization theorem. This talk focuses on our simulations of H³ and H²×E.

Sneha Subramanian (Data Scientist at SalesLoft)

Title: Markov processes and Emails

Abstract: For the first part of this talk, we'll focus on understanding Markov fields and Conditional Random Fields. After that, we'll visit a cute application and see how these concepts can be used to segment emails.

Career Panel:

Cvetelina Hill (former high school teacher, current graduate student at Georgia Tech)

Dan Margalit (Professor at Georgia Tech)

Candice Price (Professor at University of San Diego)

Sneha Subramanian (Data Scientist at SalesLoft)

Matthew Wright (Professor at St. Olaf College)

Graduate School Panel:

John Etnyre (Professor at Georgia Tech, former graduate chair)

Justin Lanier (Graduate student at Georgia Tech)

Jung Park (Postdoc at Georgia Tech, former graduate student at Rice University)

Kaitlin Tademy (Graduate student at University of Nebraska)

Libby Taylor (Graduate student at Stanford University)

Organizers:

Jennifer Hom (Georgia Tech)

Caitlin Leverson (Georgia Tech)

Tye Lidman (North Carolina State University)

Supported by NSF CAREER Grant DMS-1552285