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Mini-course in analysis by Soonsik Kwon

MIGSAA is delighted to support a mini course in analysis led by Soonsik Kwon (KAIST, Korea Advanced Institute of Science and Technology) and organised by Tadahiro Oh.  The three day course in Multilinear L^2 convolution estimates of Schrödinger waves will be held in James Clerk Maxwell Building.

Time: 2-4 pm on June 6th (Mon), 7th (Tue), and 8th (Wed)

Room: (Note a different room for the 3rd lecture)

    JCMB Lecture Theatre C on 6th and 7th,

    JCMB Lecture Theatre A on 8th

Abstract: Fourier restriction norm method, more precisely X^{s,b} spaces introduced by Bourgain, was an efficient tool for low regularity problems of nonlinear dispersive equations. In the well-posedness problems, we are often interested in proving multilinear estimates in X^{s,b} spaces. These estimates are reduced to weighted convolution estimates of L^2 functions. In [Ta], Tao systematically studies this type of weighted L^2 convolution estimates.

In the lectures, I will follow [Ta]. After introducing preliminary reduction and tools, I will cover some selected topics toward the orthogonal interaction of Schrödinger waves. Although this is motivated by a well-posedness problem in PDEs, I will mostly focus on desired bilinear estimates of harmonic analytic nature.

[Ta]  T. Tao, Multilinear weighted convolution of L^2 functions and applications to nonlinear dispersive equations, Amer. J. Math.

123(2001), 839-908.