WHEN studying music, few young conductors begin at the beginning. The Gustavo Dudamels of the world cut their teeth on a 200-year orchestral canon, starting with Mozart and ending with Shostakovich. Rarely does a conductor with an eye on a mainstream career tackle music written before Bach’s time, works typically reserved for specialists and scholars.

Not Pablo Heras-Casado. For him early music represents the core of the repertory, with contemporary music a close second. Trained as a conductor of Renaissance choral music and soon steeped in the cerebral avant-garde, Mr. Heras-Casado, who is 34 and Spanish, arrived at Beethoven and Brahms only in recent years.

And after ascending several pinnacles in Europe — he made his Berlin Philharmonic debut in October — Mr. Heras-Casado has landed in the United States. Last year he was appointed principal conductor of the Orchestra of St. Luke’s, an ensemble undergoing its own musical renaissance with the construction of an impressive rehearsal and performance space, the DiMenna Center for Classical Music, in Midtown Manhattan. On Thursday he will lead the Freiburg Baroque Orchestra at the Mostly Mozart festival at Lincoln Center in works by Schubert, Schumann and Mendelssohn, a repertory relatively new to the German period-instrument ensemble but increasingly familiar to Mr. Heras-Casado.

“We’ve clicked so well together,” Mr. Heras-Casado said of the Freiburg. He has led it in two recordings of Mendelssohn and Schubert symphonies, to be released on Harmonia Mundi in 2013. “Phrasing and harmonic sensibility and polyphonic sense — all that background we have in common. So when we have a dialogue when rehearsing, we speak the same language.”