Relationship with Columbia

Hello! I was recently admitted as an undergraduate to Columbia’s music program, as a composer. I’m wondering if Juilliard students would generally be willing to work with undergrad composers at Columbia, for making recordings or doing performances. Though I’m excited by the possibilities at Columbia, which has some of the best graduate students in the world, I’m wondering if it may not be better to attend a conservatory just for the greater potential for performance and future connections available. I’m aware of the Columbia-Juilliard Exchange - I haven’t applied for it, but I may at the end of my freshman year if I decide I can handle it.

Basically - as a composition student at Columbia, will I be able to easily collaborate with Juilliard students in recordings, performances, or just bouncing around ideas? Have any Juilliard students ever had experience working with undergraduate Columbia composers, and what was it like?