Special Event-Distinguished, Speculative First of April Talk

Speaker: Radmila Sazdanovic (North Carolina State University)

Title:  Landscapes of knots (or: how to understand the landscape of knot invariants by visualizing points in 3000-dimensional space) 
Time: 3:45- 4:45 pm, Friday, March 31, 2023
Place: Rome 206

Abstract: Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar–valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to the Ball Mapper that enable encoding the structure, relations within and symmetries of the point cloud. New hybrid Mapper–on–Ball Mapper algorithm that extends Mapper algorithm from 1-dimensional to lens functions whose range is high dimensional is introduced. Moreover, the strengths of Mapper and Ball Mapper constructions are combined to create a tool for comparing high dimensional data descriptors of a single data set. These tools are then used to illuminate relations between polynomial and numerical knot invariants such as Jones, Alexander,  and HOMFLYPT polynomial and signature and Rasmussen s-invariant.

Short bio: Professor Radmila Sazdanovic received her Ph.D. in 2010 at George Washington University. Currently she is an Associate Professor in the Department of Mathematics at North Carolina State University. Previously, she was a Postdoctoral Fellow at the University of Pennsylvania, Philadelphia PA and Mathematical Sciences Institute (MSRI) Berkeley, CA. Her area(s) of expertise include: Low-dimensional and applied algebraic topology, categorification. Professor Sazdanovic's art-on-math explores the interplay of art, nature, culture, shape, perspective, and math in our everyday lives. Tess-celestial is her most recent exhibit that features tessellations created using the software Tess. These tessellations show symmetries of hyperbolic, negatively curved space and convey the beauty and subtlety of mathematical concepts that we encounter in our daily activities. This work is a part of her Immersive Scholar Residency at NC State University Hunt library, through the Immersive Scholar grant. For more information, kindly visit: https://sazdanovic.wordpress.ncsu.edu/

History of Distinguished Speculative First of April Talk:

Every year, the Logic and Topology group at our department in the George Washington University organizes a colloquium-style Distinguished Speculative First of April Talk. The purpose of such a talk is to allow a distinguished mathematician to present ideas that may still be only speculative, but of great interest to the broader mathematical community. 

The inaugural such talk was given by Oleg Viro on Friday, April 1, 2011. Other speculative speakers included Louis Kauffman, Seth Lloyd from MIT, Samuel Lomonaco from University of Maryland Baltimore County, Scott Aaronson from MIT, Scott Carter from University of South Alabama, Uwe Kaiser from Boise State University, Norbert A'Campo from Switzerland and last time, in 2019,  Cameron Gordon.