Explore the first lecture in a series on Nikodym sets and maximal functions associated with spheres, delivered by Jongchon Kim from City University of Hong Kong. Delve into advanced topics in harmonic analysis as part of the "Modern Trends in Harmonic Analysis" program at the International Centre for Theoretical Sciences. Gain insights into cutting-edge developments in polynomial methods and discrete harmonic analysis, with a focus on Fourier restriction, Bochner-Riesz conjectures, and their applications. Engage with this comprehensive lecture, designed for mathematicians and researchers working in related fields, to enhance understanding of recent breakthroughs and potential future research directions in harmonic analysis.