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“The Threshold Theorem for the Hyperbolic Yang-Mills Equation”

Special Seminar

Come join us Monday February 12, 2018 at 12 pm in RM 507, Professor Sung-Jin Oh (KIAS) will be giving a special lecture about “The Threshold Theorem for the Hyperbolic Yang-Mills Equation”.


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.

Mathematics Hall, Room 507

Monday February 12, 2018 at 12 pm

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