Australia-China-Japan-Singapore-U.S. Index Theory Conference

The Australia-China-Japan-Singapore-U.S. Index Theory Conference brings together world experts on index theory and related areas. Index theory is a highly active area of mathematical research founded by Atiyah and Singer around 60 years ago.

Their foundational result provided a crucial link between the seemingly disparate fields of analysis and topology, and its subsequent generalisations founded a whole new field intertwining many areas of mathematics, from geometric analysis and topology to K-theory of operator algebras and noncommutative geometry. Moreover, index theory turned out to be of far- reaching importance in physics.

The conference is dedicated to exploring this distinctive quality of index theory—its ability to forge potent connections between disparate fields. Renowned experts in index theory will grace the conference alongside esteemed speakers with expertise in related areas, fostering an environment ripe for cross-disciplinary collaboration and the cultivation of novel research frontiers. Hosted at the University of Adelaide, a hub of expertise in index theory and its associated domains, the workshop provides an ideal setting for this endeavour. Attendees, including students, will have the opportunity to engage with cutting edge research and interact with distinguished speakers.

The conference will spotlight prominent areas such as K-theory, the natural habitat for indices of Fredholm operators; operator algebras and noncommutative geometry, laying the groundwork for index theory of generalised spaces; and mathematical physics, where index theory finds application in diverse realms from string theory to topological insulator phenomena in condensed matter physics.

Through presentations of current research, formulation of new problems, and exploration of connections between fields, the conference aims to inspire new directions of inquiry in index theory and beyond, bolstering the landscape of mathematical research in Australia and beyond.