Normal bundles of canonical curves

The extrinsic geometry of the canonical model of a nonhyperelliptic curve captures many aspects of the intrinsic geometry of the curve.  In this talk I will discuss joint work with Izzet Coskun and Eric Larson in which we show that the normal bundle of a general canonical curve of genus at least 7 is always semistable.  This makes substantial progress towards a conjecture of Aprodu–Farkas–Ortega, and answers it completely in a third of all cases.