Unlocking the secrets of modular representations

该奖学金旨在极大地提高我们对离散结构的基本对称性的理解，如计算机科学和密码学中的对称性。这项研究将产生关于有限群表示的纯数学中的变革性新知识，这些问题已经解决了一个多世纪。该奖学金的预期成果包括远远超出当前可能的计算新算法和对当前算术困难的新理解。关键的好处将体现在一项对数学有重大影响的新兴技术的发展，以及澳大利亚科学家在复杂理论和大规模计算方面的培训。

This Fellowship aims to greatly increase our understanding of the fundamental symmetries of discrete structures, like those present in computer science and cryptography. The research will generate transformative new knowledge in pure mathematics concerning the representations of finite groups, problems that have been unsolved for over a century. Expected outcomes of this fellowship include new algorithms to compute far beyond what is currently possible and a new understanding of the arithmetic difficulties present. Key benefits will be seen in the development of an emerging technology with significant implications for mathematics, and the training of Australian scientists in sophisticated theory and large-scale computation in concert.