[1] Márquez started his guitar studies at the age of 10 and gave his first performance three years later with an orchestra in Salta, north-western Argentina, where he grew up and received his first training.

As a musician, Márquez studied conducting with Eric Sobzyck, Rodolfo Fischer and Peter Eötvös, and followed the teaching of pianist György Sebők.

[2] He collaborated with Anja Lechner, Anne Gastinel, Patricia Kopatchinskaja, the Rosamunde Quartett of Munich, Dino Saluzzi and María Cristina Kiehr.

He performs regularly as a soloist with orchestras and ensembles, including Bayerischer Rundfunk of Munich, Orchestre Philharmonique de Radio France, Philharmonie Baden-Baden, and Nouvel Ensemble Moderne de Montreal, under the baton of Josep Pons, Susanna Mälkki, Lorraine Vaillancourt, Fabián Panisello and others.

Márquez received the Konex Prize for lifetime achievement for being a great musician ,[4] and in 2006 was announced as an Honorary Citizen of Salta, Argentina.