Fractional analytic index theory

阿蒂亚-辛格指数理论，M.F.阿蒂亚和I.M.辛格因此获得了2004年阿贝尔奖，刺激了数学家和数学物理学家之间的大量互动。这个理论的延伸是分数指数理论，由R.B.梅尔罗斯、I.M.辛格和我共同发明，得到了国际关注，解决了一个基本的开放性问题。我的研究项目的中心目标是将我们的理论扩展到椭圆边值问题。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。

Atiyah-Singer index theory, for which M.F. Atiyah and I.M. Singer received the 2004 Abel Prize, has stimulated considerable interaction between mathematicians and mathematical physicists. An extension of this theory is Fractional Index Theory, co-invented by R.B. Melrose, I.M. Singer and myself, which has received international attention, having solved a fundamental open problem. A central aim in my research project is to extend our theory to elliptic boundary value problems. 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.