New approaches to index theory

自然规律通常用微分方程来表示，其中包括它们的变化率。如果是椭圆的，它们有一个指标，就是解的个数减去约束的个数。Atiyah-Singer指数定理给出了这个“指数”的惊人计算。分数指数理论是分数指数理论的一个扩展，它解决了一个基本的开放性问题，受到了国际上的关注。一个中心目标是进一步研究这个问题。我将通过研讨会、春季学校和监督来帮助初学者导航到研究的前沿。好处包括提高澳大利亚在国际研究前沿的地位。

The laws of nature are often expressed by differential equations, involving their rates of change. If 'elliptic,' they have an 'index,' which is the number of solutions minus the number of constraints imposed. The Atiyah-Singer index theorem gives a striking calculation of this "index'. An extension is Fractional Index Theory, which has received international attention, having solved a fundamental open problem. A central aim is to investigate this further. I will assist beginners to navigate to the cutting edge of research through workshops, spring-schools and supervision. Benefits include the enhancement of Australia's position in the forefront of international research.