Alina Vdovina (University of Newcastle)
Title: Buildings, Quaternions and Yang-Baxter Equations
Abstract: To be useful in theoretical physics, mathematical structure has to be sufficiently rich and cover several fields of mathematics, physics and, potentially, computer science. One of the barriers to overcome is different languages and different terminologies. We will give a brief introduction to the theory of buildings and present their geometric, algebraic and arithmetic aspects. In particular, we present explicit constructions of infinite families of quaternionic cube complexes, covered by buildings. We will use these cube complexes to describe new infinite families of Drinfeld-Manin solutions of Yang-Baxter equations.