Valentin Ovsienko
Valentin Ovsienko is a Russian mathematician working in France. He received the Ph.D. degree from the Moscow University and he is currently a researcher at the University of Lyon. His research interests include many domains of algebra, differential geometry, and mathematical physics. Valentin believes that some day mathematics will be unified again, as it was in the good old days. |
"From complex numbers to quaternions and beyond": Algebra? Geometry? Number theory? Let us call this subject simply: mathematics. The main goal of these lectures is to explain why do mathematicians invent "complicated" algebraic structures. Our main character will be the algebra of quaternions. Invented by Sir William Hamilton in 1843, quaternions extend complex numbers. But, unlike usual numbers, the algebra of quaternions is non-commutative that makes it more complicated. Non-commutative? Are we sure? We will see that the algebra of quaternions is, in fact, commutative if we understand what the commutativity really means.