Algebra Seminar DATE: Thursday, 9 September 2004 SPEAKER: Bin Wang (CU Boulder) TITLE: Clemens' conjecture ABSTRACT: We prove the Clemens' conjecture in the case the normal bundle of rational curve in generic quintic three fold is the direct sum of O(0) and O(-2), i.e., there is no one parameter family of smooth rational curve c in generic quintic threefold f such that the normal bundle of c in f is the direct sum of O(0) and O(-2).