Araceli Guzmán Tristán
Centro de Investigación en Matemáticas (CIMAT), Mexico
Abstract: In Knot Theory, a seemingly simple question—how do you distinguish between two knots?—quickly leads to profound problems in topology. One way to approach them is to examine the information contained in the space remaining after removing the knot from the three-dimensional sphere.
In this talk, we will explore how the complement of a knot allows us to transform a problem concerning curves in space into a problem concerning three-dimensional manifolds. We will also review some techniques, such as knot surgery, that allow us to construct and recognize different three-dimensional spaces.
Semblance: Dr. Araceli Guzmán Tristán obtained her doctorate from the Institute of Mathematics at UNAM in Mexico City, under the direction of Dr. Mario Eudave Muñoz in 2017.
Since 2018, and to date, she has worked as a postdoctoral researcher at the Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, where she has collaborated with various researchers in the area of Topology and Topological Data Analysis.
Her work focuses primarily on the field of Knot Theory and 3-manifolds, addressing problems from topological, algebraic and geometric points of view.