Workshop for young scientists with research interests focused on physics at FAIR

In this talk I will review recent advances in the computation of transport coefficients of strongly-interacting theories using field-theory methods. In particular, I will make special emphasis on the computation of the shear and bulk viscosities, and aspects such as possible bounds in these coefficients, relationship with anomalies, sum rules, etcetera. The behavior of transport coefficients close to phase transitions will also be discussed. The latter is of important relevance in connection with the future heavy-ion program at the FAIR facility, since it may help to obtain a better understanding of the structure of the QCD phase diagram at finite density.