|Date: Monday, January 08, 2018
Location: 3088 East Hall (4:00 PM to 5:00 PM)
Title: The Threshold Theorem for the hyperbolic Yang-Mills equation
Abstract: In this lecture, I will present the recent proof (joint with D. Tataru) of the Threshold Theorem for the energy critical hyperbolic Yang-Mills equation in (4+1) dimensions. This theorem provides a sharp criterion for global existence and scattering in terms of the energy of the initial data. Moreover, we prove that failure of global existence/scattering is characterized by "bubbling" of a solution to the harmonic Yang-Mills equation.
Our proof lies at the intersection of many recent developments, such as null form estimates and function spaces; parametrix construction via pseudodifferential gauge renormalization; induction on energy; monotonicity formulae arising from the normalized scaling vector field etc. Also of note is the use of the associated parabolic flow, namely the Yang-Mills heat flow, to construct a high quality global gauge (called the caloric gauge), extending the idea of Tao for the harmonic map heat flow.
Speaker: Sung-Jin Oh
Institution: Korea Institute for Advanced Study (KIAS), Seoul, South Korea