Southeastern Undergraduate Mathematics Workshop
Aug. 5-9, 2019
Georgia Institute of Technology, Atlanta, GA
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.
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.
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.
Justin Lanier (Graduate student in math at Georgia Tech)
Sabetta Matsumoto (Assistant Professor in physics at Georgia Tech)
Sneha Subramanian (Data Scientist at SalesLoft)
Graduate School Panel:
Jennifer Hom (Georgia Tech)
Caitlin Leverson (Georgia Tech)
Tye Lidman (North Carolina State University)
Supported by NSF CAREER Grant DMS-1552285