James Montaldi's expertises span many areas on pure and applied mathematics. I will discuss here just one, his contributions to the motion of point vortices, specially the role of symmetries in the bifurcations and stability of equilibrium configurations in surfaces of constant curvature. This approach leads, for instance, to a very elegant proof of a classical result, the nonlinear stability of Thompson's regular heptagon in the plane. Here the plane appears "in passing", just as the transition between positive and negative curvatures.

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进入漩涡：关于詹姆斯·蒙塔尔迪的贡献

詹姆斯·蒙塔尔迪（James Montaldi）的专业知识涵盖纯数学和应用数学的许多领域。我将在这里仅讨论他对点涡旋运动的贡献，特别是对称性在分叉中的作用以及等曲率曲面中平衡构型的稳定性。例如，这种方法可以很好地证明经典结果，即汤普森正七边形在平面上的非线性稳定性。此处，该平面显示为“通过”，就像正曲率和负曲率之间的过渡一样。