On representations of the braid group in 4 strands
Isabel Goodwin
Undergraduate Researcher
Mathematics Major (College of Arts and Sciences)
Julia Plavnik
Faculty Mentor
Julia Plavnik (College of Arts & Sciences)
Project Description
Emil Artin was the first to study braids in 1926 and introduced the braid group B_n arising from his geometric construction. There is also an algebraic definition instead and we will use that to study their representations. Representations can be thought of as a way to understand the group by looking at certain matrices. The braid group and its representations have applications in many fields, such as knot theory, mathematical physics (for example, looking at the Yang–Baxter equation), algebraic geometry, quantum computing, and quantum information, among others. In this project, we will focus on the case of 4 strands and the goal is to classify (which means to give a list) some representations of this group arising from the ones for 3 strands.
Technology or Computational Component
Coding would be very helpful because it will allow us to test small examples and in that way give us clues to understand the general situation.