多复变的离散化和切片化理论

统计物理中二维Ising模型和渗流的共形不变性是Smirnov获得2010年菲尔兹奖的工作，相应的高维问题至今是非常重要而且困难的公开问题。鉴于Ising模型的二维求解强烈依赖于离散单复变，多复变的离散化和切片化将为求解高维Ising模型问题提供有力的数学工具。本项目将研究多复变的离散化和切片化，其目标是求解多复变的离散化理论中重要的整体收敛问题，以及系统地建立实交错代数的正则二次锥上的切片理论。该项目是多复变在离散、非交换、非结合领域的推广，具有重要的理论和应用价值。

In 2010 Smirnov was awarded the Fields medal for his work on the mathematical foundations of statistical physics for the proof of conformal invariance of percolation and the planar Ising model. However, the higher dimensional problem remains a very important and difficult open problem. In view of the fact that the two-dimensional solution of the Ising model is strongly dependent on the discrete complex analysis, the discretization and slicing of several complex variables could provide a powerful mathematical tool for solving the high dimension Ising model problem. This project will study the discretization and slicing of several complex variables. The goal is to solve the important global convergence problem in the discrete theory of several complex variables and to systematically construct the slice theory on the regular quadratic cones of real alternative algebras. The project is an extension of several complex variables to the discrete, non-commutative and non-associative realm of mathematics, which has important theoretical and application value.