A lawsuit challenging Harvard University’s admissions practices is playing out in a federal courtroom in Boston, with the trial starting Monday. But the dispute may wind up before the Supreme Court, which, now with five conservative justices, could drastically alter the future of affirmative action in college admissions.

The lawsuit, filed by the group Students for Fair Admissions, claims that Harvard engages in “racial balancing” and discriminates against Asian-American students applying to the elite school in violation of federal civil rights law. Asian-Americans, the plaintiffs contend, are held to a higher standard for admission than students of other races.