If two people arbitrarily twist and tangle different but identical ropes of the same size and seal the ends together, even the most discerning eye might have difficulty determining if the two knots are the same or different.Īs Lauda explains it, we can try to wiggle one knot to look the same as the other, but if we don’t succeed, we can’t necessarily conclude that the two knots are different. “If I wiggle it around, as long as I don’t cut it or break it, it’s fundamentally the same,” Lauda says. No matter how the knot is positioned, it’s still the same knot. In vastly oversimplified language, topology refers to the properties of a geometric shape that don’t change no matter how much you futz with it.Ī length of rope twisted and tangled, and then joined at the ends to make a single, contiguous knot, has its own topology. The complex math that Lauda and the other researchers are exploring centers on topology.

Simons collaboration aims to solve knotty math problems The remaining $6.9 million is divided among 10 other institutions: Caltech, the Massachusetts Institute of Technology, UCLA, the University of North Carolina at Chapel Hill, and Columbia, Stanford, Princeton and Harvard universities, as well as the Centre for Quantum Mathematics at Southern Denmark University and the University of Zurich. It’s one of the largest awards ever obtained for USC Dornsife’s math department. Lauda as director, along with grant co-principal investigator Cris Negron, assistant professor of mathematics, brings nearly 14% of the total - about $1.1 million - to USC. The funding comes from the Simons Foundation. The grant is unique in that it is sufficiently large to fund a sizable team working in a similar direction and will support extended visits by team members and other experts that will enhance the research activities and community at USC, says Lauda, who directs the collaboration. Lauda led the charge to obtain the prestigious grant, which establishes the Simons Collaboration on New Structures in Low-Dimensional Topology. “In math, all we typically need is a paper and pencil, so grants tend to be much less,” says Aaron Lauda, professor of mathematics and physics and astronomy at the USC Dornsife College of Letters, Arts and Sciences. Most grants funding science go to experimental equipment, postdoctoral scholars, graduate students and other expensive resources. That’s $2 million per year, and a few more digits than are typically found on grants awarded for math research. The simple math adds up to an exceptional amount of money - $8 million, in fact - to study the other, more complex math over the next four years. This story involves two kinds of math: simple and very complex. USC-Huntington Early Modern Studies Institute Shinso Ito Center for Japanese Religions and Culture Max Kade Institute for Austrian-German-Swiss Studies

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Huntington-USC Institute on California and the West Casden Institute for the Study of the Jewish Role in American LifeĬenter for Islamic Thought, Culture and PracticeĬenter for Latinx and Latin American Studies

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