Grants and Contributions:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023)

Every time a new instrument, such as the telescope or the microscope, is invented that allows us to observe our Universe at larger or shorter distances than before, it has led to important changes in our understanding of nature. The most powerful “microscope” ever constructed is the Large Hadron Collider (LHC), located at CERN. It accelerates protons to nearly the speed of light, makes them collide and records to product of such collisions. Protons are not elementary particles, they are made out of quarks and gluons. The LHC collisions actually happen when quarks and gluons collide, allowing us to see deeper into the structure of fundamental particles than ever before. Our best theories of natures are put to the test by comparing their predictions to the LHC detections. These predictions were traditionally made using a technique known as Feynman diagrams. Thirty years ago, Parke and Taylor found that a very special class of these computations starts out as many-pages long only to be simplified to single-line expressions. In physics, this is an indication that some new principle or idea is hiding around the corner.

For more than a decade, my research has focused on new understandings of the way quantum mechanics and Einstein’s special relativity combine that extend the “Parke-Taylor miraculous phenomenon” to all kinds of interactions at the LHC. This journey has led to the discovery of connections to new areas of mathematics and to many extensions including the collision of gravitons, particles which are the force carriers of Einstein’s gravity theory. A construction discovered in 2013, now known as the Cachazo-He-Yuan (CHY) formulation, indicates that this is just the tip of an iceberg of new structures that have the potential to teach us about the inner workings of spacetime itself.

In this proposal, my team will continue the development of the CHY formulation, its connections to other mathematical constructions and to string theory techniques. String theory is a framework for the unification of gravity and quantum mechanics which has at its core Riemann surfaces, such as the surface of a ball, a donut, or even a pretzel. The CHY formulation also has Riemann surfaces at its core. What we know about the CHY formulation indicates that Feynman diagrams are scrambled inside the Riemann surfaces in ways that need to be understood. Since Feynman diagrams tell us a story of interactions in spacetime, our spacetime will also have to emerge from the Riemann surfaces. This indicates a connection to modern ideas in holography (as applied to Einstein gravity). Just as the CHY formulation was developed by my team at the time, S. He (a postdoctoral fellow at Perimeter Institute) and E. Yuan* (my graduate student at the University of Waterloo and Perimeter Institute), my current team of master’s and PhD students is well positioned to continue playing a leadership role in this active area of research.