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1st Meeting

BICMR, PKU

Hélène Esnault (FU Berlin)

Entropy of automorphisms on surfaces in positive characteristic
We shall review the notion of entropy in this context and show the existence of automorphisms of maximal entropy, the logarithm of a degree 22 Salem number, on a supersingular K3 surface, which thus does not lift to characteristic zero. (Based on joint work with V. Srinivas, K. Oguiso and K. Oguiso-X. Yu).

Lawrence Ein (UI Chicago)

Asymptotic syzygies
We discuss joint work with Robert Lazarsfeld on asymptotic syzgies. We discuss our work on the gonality conjecture, which says that one can determine the gonality of a smooth curve X of genus g from the shape of the minimal resolution of the section ring of a line bundle L on X, when degree of L is sufficiently large. We also plan to discuss the shape of the minimal resolution of the section ring of (X, L), where X is a smooth projective variety of dimension n and L is a sufficiently positive line bundle on X.

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