Department of Mathematics

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IU Mathematics faculty member Julia Plavnik has been awarded a Collaboration Grant on Global Categorical Symmetries from the Simons Foundation.

The grant provides $8 million of support over four years for an international team of physicists and mathematicians to unlock the power of symmetry in its broadest, most general form. Assistant Professor Julia Plavnik was awarded $500K to support the project at IU. Her award will support activities including the funding of postdocs, travel, and summer support. The grant is directed by Constantin Teleman of the University of California, Berkeley (who was briefly an undergraduate here at IU). Said Professor Plavnik, “We did not expect the grant to be awarded upon our first submission. As our application passed more and more levels of review, we got more excited. The process of writing this grant was interesting itself as it broadened our research horizons. I haven't collaborated with any of the other PIs yet, so this is an amazing opportunity to expand my research program and network.

The following three paragraphs are from the announcement from the Simons Foundation.

Symmetry is a powerful tool for organizing physical phenomena and anchors our understanding of the laws of nature. The notion of symmetry, however, has evolved dramatically since the emergence of groups and representations as the language for describing symmetries in geometry and mechanics. Galvanized most recently by advances in mathematics and physics, much of this evolution has been driven by the quest to achieve a deeper understanding of quantum field theory—the universal language of modern theoretical physics.

From a modern point of view, quantum field theory associates to every symmetry a topological defect, which acts on local and extended observables. This connection to topology has recently led to the discovery of new higher notions of symmetry, which in turn has shed new light on some of the most mysterious and profound phenomena described by quantum field theory, including color confinement in non-abelian gauge theories, duality and other phenomena.

The deep link between symmetry and topology finds its natural expression in the mathematics of topological quantum field theory, such as the modular tensor categories that describe invariants of knots and the long-distance physics of anyons. Recent advances have centered on the rich categorical structure of various defects and how it encodes the fundamental idea of locality, as expressed by the cobordism hypothesis. The collaboration grows out of the synergy between these areas of physics and mathematics, weaving together cutting-edge developments.

The award further expands IU’s role in developing the foundations for and applications of quantum theory. The area is already deeply investigated by fellow IU mathematics faculty members Zorn postdoctoral fellow Dr. Collen Delaney, Associate Professor Noah Snyder, Professor Dylan Thurston, and Boucher Professor Vladimir Touraev. A recently approved interdisciplinary masters program in Quantum Information Science is also supported by coursework and leadership of IU mathematics faculty.

Other institutions represented include the University of California Los Angeles, Durham University, University of California San Diego, University of Texas, Johns Hopkins University, Harvard University, the Technical University of Munich, Dahlhousie University, The State University of New York at Stony Brook, the University of Edinburgh, Rutgers University, Uppsala University in Sweden, and the University of Zurich. Details are at https://math.berkeley.edu/~teleman/simons/collaboration.html .