Konstantin has performed with distinguished conductors including Vladimir Spivakov, Tugan Sokhiev, Dmitry Liss, Nicholas Milton, Lawrence Foster, Alexandr Vedernikov, Jonas Alber, Kirill Karabitz, Kirill Petrenko.
Korcia performs regularly with conductors such as Semyon Bychkov, Charles Dutoit, Daniele Gatti, Valery Gergiev, Emmanuel Krivine, Kurt Masur, John Nelson (conductor), Michel Plasson, Manuel Rosenthal, Yutaka Sado, Tugan Sokhiev, Vladimir Spivakov, Yan-Pascal Tortelier, and Walter Weller.