Department of

February 2006 March 2006 April 2006 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 2 3 4 1 5 6 7 8 9 10 11 5 6 7 8 9 10 11 2 3 4 5 6 7 8 12 13 14 15 16 17 18 12 13 14 15 16 17 18 9 10 11 12 13 14 15 19 20 21 22 23 24 25 19 20 21 22 23 24 25 16 17 18 19 20 21 22 26 27 28 26 27 28 29 30 31 23 24 25 26 27 28 29 30

Tuesday, March 28, 2006

**Abstract:** I will review what we know about the birational geometry of moduli spaces of stable curves, beginning with the origins of the subject in the 19th century (dimension, irreducibility, ...) and ending with current work and open problems (ample and effective cones, structure of the canonical ring, ...) and, if time permits, a few applications. The talk will be expository and assume only a basic familiarity with moduli spaces or birational geometry.