Matej Bresar: Jordan homomorphisms

Let R and S be rings. An additive map $\varphi:R\to S$ is called a Jordan homomorphism if $\varphi(x^2)=\varphi(x)^2$  for every $x\in$ R.
The obvious examples are homomorphisms and antihomomorphisms.

The first part of the talk will present the development of the theory of Jordan homomorphisms. In the second part,  new results will be discussed.