**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”.**

**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.

**Mathematics Hall, Room 507**

**Monday February 12, 2018** at 12 pm