The paper "Minimum positive entropy of complex Enriques surface automorphisms " by Keiji Oguiso and Xun Yu has recently been accepted for publication in the Duke Mathematical Journal, one of the world's leading mathematical journals.
Automorphisms of algebraic surfaces are closely related to complex dynamics and number theory, and such relations are extensively studied by many authors in the last two decades. An important problem in the area is to determine the minimum positive entropy of complex surface automorphisms in each class of the Enriques-Kodaira classification of complex surfaces. Introducing a new positivity criterion and a new notion of Enriques quadruple, the paper by Oguiso and Yu determines the minimum positive entropy of complex Enriques surface automorphisms. This together with McMullen's work [1],[2],[3] completely solves the problem mentioned above.
[1] C. T. McMullen, Dynamics on blowups of the projective plane, Publ. Math. Inst. Hautes Études Sci. 105 (2007) 49–89.
[2] C. T. McMullen, K3 surfaces, entropy and glue, J. Reine Angew. Math. 658, (2011), 1–25.
[3] C. T. McMullen, Automorphisms of projective K3 surfaces with minimum entropy, Invent. Math. 203 (2016), no. 1, 179—215.
Xun Yu received his Ph.D. from The Ohio State University in 2013, with Herb Clemens. After that, he was a postdoc at Max Planck Institute for Mathematics in Bonn and at Center for Geometry and its Applications of Pohang University of Science and Technology. Since 2016, he is an associate Professor at Tianjin University.He received the 2019 JMSJ Outstanding Paper Prize.
