On May 28, Chair Professor Joshua Zahl from Chern Institute of Mathematics at Nankai University was invited to the College of Science (SUSTech) to deliver a guest lecture at the 243rd session of the Science Lecture Series. His special lecture was titled “ The Besicovitch compression phenomenon and the Kakeya set conjecture”. In attendance were Chair Prof. Qing Xiang, the Head of the Department of Mathematics at SUSTech, and over 100 faculty members and students. It was hosted by Associate Professor Tongou Yang of the Department of Mathematics.

In the lecture, Prof. Joshua Zahl first introduced the rigorous statement of the Kakeya set conjecture and its discretised version using thin tubes. He then introduced Fefferman's ball multiplier theorem, which first connected the Kakeya problems from geometric measure theory to the boundedness of the Fourier multipliers from harmonic analysis. In short, the Kakeya problem is about the measure of the union of thin tubes pointing in different directions, and by the uncertainty principle, each tube can be thought of as a wave packet propagating with frequency in that tube.

Prof. Joshua Zahl then introduced more topics such as the Bochner-Riesz multiplier problem, the Fourier restriction conjecture, and the L^p boundedness of the solution of free Schrödinger equations, which are all intimatedly connected to the Kakeya problem. 

During the Q&A session, the audience asked interesting questions. Prof. Joshua Zahl answered questions concerning different formulations of the Kakeya set conjecture as well as its relations with other problems in harmonic analysis, partial differential equations, and additive combinatorics.

After the lecture, Prof. Xiang handed an honorary certificate to Prof. Joshua Zahl.