Lecture Content：

This lecture will focus on combinatorial geometry theorems concerning finite point sets. It will center on proving the existence of small subsets such that, when enclosed by a convex shape (e.g., a ball), a significant proportion of the entire point set is also guaranteed to be captured within that shape.

Speaker Introduction:

mre Bárány is an Academician of the Hungarian Academy of Sciences. His research expertise encompasses discrete geometry, convexity theory, combinatorics, random polytopes, lattice polytopes, and algebraic topology, with additional focus on their applications in computer science, programming, operations research, and game theory. He has made seminal contributions across these domains and is globally esteemed as one of the preeminent scholars advancing the integration of theoretical research in discrete geometry with real-world applications.

Prof. Bárány has been invited to deliver plenary addresses at numerous prestigious international conferences, notably including a 45-minute invited lecture at the 2002 International Congress of Mathematicians (ICM). His scholarly achievements have been recognized with distinguished honors such as the Rényi Prize (1988), the Prize of the Hungarian Academy of Sciences (1994), the Award of the Hungarian Academy of Sciences (1998), and the Széchényi Prize (2016). He has also led a European Advanced Research Project and published over 180 papers in leading international mathematics journals, including Advances in Mathematics, Mathematische Annalen, and Proceedings of the London Mathematical Society.