Geometry and visualization of integrable systems and applications to quantum field theory and neuroscience

从几何和可积系统理论的角度研究了一类微分方程组。这种方程的解可以被模拟和可视化为具有相邻质量之间的非线性相互作用的点质量格子的运动。量子场论的一个重要例子是由Cecotti和Vafa最先研究的TT*-Toda晶格。Guest和Lin得到了关于解的存在性的理论结果，这与计算机模拟一致。其他的例子，如仓本晶格，也在研究之中。预期未来的应用，例如对同步的数学解释。

Certain differential equations are studied from the point of view of geometry and the theory of integrable systems. The solution of such an equation can be simulated, and visualized, as the motion of a lattice of point masses with nonlinear interactions between neighbouring masses. An important example from quantum field theory is the tt*-Toda lattice, first studied by Cecotti and Vafa. Guest and Lin have obtained theoretical results on the existence of solutions, consistent with computer simulations. Other examples such as the Kuramoto lattice are being studied. Future applications, e. g. to the mathematical interpretation of synchronization, are anticipated.