Convex analysis and monotone operators: forward and backward

The first connections between the research areas of convex analysis and monotone operators were noticed early in their development by authors like Kachurovskii and Rockafellar. Various other contributions in this direction followed and the rediscovery of Fitzpatrick's function in the early 2000's opened the gate towards new achievements regarding monotone operators by means of convex analysis and viceversa. In this talk we present some of the most important results obtained in one of these areas by employing tools specific to the other one, mentioning our own the contributions, too, and discuss the current tendencies and some open problems.