Wednesday, May 8th, 2024
Physics Seminar: Vladimir Rosenhaus
Time: 1:00 PM - 2:00 PM
Location: 313
Title: Wave turbulence and quantum field theory
Abstract: Wind blows over the ocean, exciting long wavelength waves, whose energy then cascades to shorter wavelength waves. The state is statistically stationary and the measured spectrum of energy per mode is a power law, over some range of scales. At very short scales there is sea foam (whitecaps), and the spectrum is believed to again be power law, but a different power. At long scales the nonlinearity is weak (if the wind is not too strong and the waves are small) and the spectrum can be derived analytically. At short scales the nonlinearity is strong, and one loses analytic control. Wave turbulence has been studied theoretically and experimentally in a wide range of systems for half a century. To date, all theoretical results have been at leading order in the nonlinearity. We demonstrate how wave turbulence — a stochastic classical system — can be turned into a quantum field theory. The computation of the spectrum becomes a problem of computing correlation functions. This gives a scheme for computing beyond leading order in the nonlinearity. We consider wave turbulence in a large N system, allowing us to study strong wave turbulence. We develop the analog of the epsilon expansion, allowing us to go from one power law spectrum in the UV to a slightly different power law in the IR (the analog of flow between critical points).
Title: Wave turbulence and quantum field theory
Abstract: Wind blows over the ocean, exciting long wavelength waves, whose energy then cascades to shorter wavelength waves. The state is statistically stationary and the measured spectrum of energy per mode is a power law, over some range of scales. At very short scales there is sea foam (whitecaps), and the spectrum is believed to again be power law, but a different power. At long scales the nonlinearity is weak (if the wind is not too strong and the waves are small) and the spectrum can be derived analytically. At short scales the nonlinearity is strong, and one loses analytic control. Wave turbulence has been studied theoretically and experimentally in a wide range of systems for half a century. To date, all theoretical results have been at leading order in the nonlinearity. We demonstrate how wave turbulence — a stochastic classical system — can be turned into a quantum field theory. The computation of the spectrum becomes a problem of computing correlation functions. This gives a scheme for computing beyond leading order in the nonlinearity. We consider wave turbulence in a large N system, allowing us to study strong wave turbulence. We develop the analog of the epsilon expansion, allowing us to go from one power law spectrum in the UV to a slightly different power law in the IR (the analog of flow between critical points).
Simons Lectures in Mathematics: Assaf Naor
Time: 2:15 PM - 3:30 PM
Location: 103
Title: Unplanned consequences of the Ribe program, part II: Obstructions
Speaker: Assaf Naor (Princeton University)
Abstract: Almost 50 years ago, Martin Ribe proved a remarkable geometric rigidity theorem for normed spaces. This inspired an intricate web of conjectures and analogies that aims to transfer phenomena, concepts and intuitions from the structured realm of linear spaces to the seemingly uncontrollably diverse world of general metric spaces. While research on this program has led to powerful, creative and deep discoveries, numerous mysteries remain. These talks will start by introducing the audience to the aforementioned research endeavor, which is known today as the “Ribe program,” assuming no prior knowledge of it. This program naturally enhanced our understanding of the structure of normed spaces, and we will indeed present examples of this, but our main focus will quickly shift to describing some of its unplanned applications. Namely, we will demonstrate how it informs us about objects that are further afield, such as groups, curvature, algorithms and probability.
Title: Unplanned consequences of the Ribe program, part II: Obstructions
Speaker: Assaf Naor (Princeton University)
Abstract: Almost 50 years ago, Martin Ribe proved a remarkable geometric rigidity theorem for normed spaces. This inspired an intricate web of conjectures and analogies that aims to transfer phenomena, concepts and intuitions from the structured realm of linear spaces to the seemingly uncontrollably diverse world of general metric spaces. While research on this program has led to powerful, creative and deep discoveries, numerous mysteries remain. These talks will start by introducing the audience to the aforementioned research endeavor, which is known today as the “Ribe program,” assuming no prior knowledge of it. This program naturally enhanced our understanding of the structure of normed spaces, and we will indeed present examples of this, but our main focus will quickly shift to describing some of its unplanned applications. Namely, we will demonstrate how it informs us about objects that are further afield, such as groups, curvature, algorithms and probability.