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报告题目：Minimal Model Program for semi-stable fourfolds in positive and mixed characteristic
Qingyuan Xue is a Ph.D candidate in the Department of Mathematics, the University of Utah, under the supervision of Prof. Christopher Hacon. He obtained his M.S. in mathematics from Peking University under the supervision of Prof. Chenyang Xu. His main area of interest lies in algebraic geometry, especially in birational geometry.
One of the fundamental goals of algebraic geometry is to classify all algebraic varieties (up to birational equivalence), which, conjectually, can beachieved by the Minimal Model Program (MMP). In characteristic 0, the theory of MMP has been developed for decades, and many important results have been proven. Recently there has also been much progress in developing the MMP in positive and mixed characteristics, especially for threefolds. In dimension 4 the situation becomes much more difficult, but in several special cases the validity of the MMP are known, which is established by Hacon and Witaszek and generalized by Xie and I. In this talk I will introduce the MMP for fourfolds in positive and mixed characteristic, focusing on the MMP for semi-stable fourfolds. Based on a joint work with Lingyao Xie.