Title: Set-theoretic Yang-Baxter Equation, Twists & Quandle Hopf Algebras
Speaker: Anastasia Doikou
Institution: Heriot-Watt University
Date & Time: November 21, 2024, 20:30–22:30
Location: Zoom ID: 904 645 6677, Password: 2024
The theory of the set-theoretic Yang-Baxter equation is developed from a purely algebraic perspective. We review the derivation of solutions to the braid equation via self-distributive structures known as racks and quandles. Generic, non-involutive set-theoretic solutions to the braid equation are then constructed from rack solutions using a suitable Drinfeld twist, while all involutive solutions are obtained from the flip map via twisting. We also study the universal algebras associated with both rack and generic set-theoretic solutions and derive the corresponding universal R-matrices.
Anastasia Doikou is a Professor of Mathematics at Heriot-Watt University in Edinburgh. She completed her undergraduate studies in physics at the National & Kapodistrian University of Athens and earned her PhD in theoretical and mathematical physics from the University of Miami in 1999. From 1999 to 2007, she held postdoctoral positions at Durham University, the University of York (as an EPSRC Fellow), LAPTH-Annecy, and the University of Bologna. Before joining Heriot-Watt University in 2013, she served as an assistant professor at the University of Patras in Greece. Her research focuses on algebraic structures in mathematical physics, including solutions to the Yang-Baxter equation, quantum groups, and non-involutive braided systems.
