Vinnie Ng
Inequalities in Geometry and Analysis
Inequalities play a central role in analysis and geometry, so understanding the established inequalities and their connections is essential. In 2002, Gardner wrote an extensive survey exploring how the Brunn-Minkowski inequality
connects various inequalities in geometry and analysis and some applications of these inequalities. Since then, optimal transport has emerged as an efficient and unified tool to prove inequalities, which has opened new avenues
for discovering deep connections between inequalities in analysis and geometry.
This project aims to survey the relationships and equivalences between the isoperimetric, Brunn-Minkowski, Sobolev, and Prékopa-Leindler inequalities and to explore their applications in log-concave probability distributions and convex geometry, including their discrete counterparts. Additionally, the project will also explore whether recent advances in optimal transport can be used to establish new connections between inequalities, provide alternative proofs, or sharpen classical results.
Vinnie Ng
The University of Sydney
Vinnie is a third-year student at the Australian National University studying a Bachelor of Mathematical Sciences. While initially gravitating towards physics, Vinnie has developed a deep appreciation of the rigour and generality of mathematics, with particular interests in analysis, geometry, probability, and their intersection. Outside academics, Vinnie serves as Industry Officer of the ANU Mathematics Society and has worked as a tutor for both physics and computer science. Vinnie plans to pursue postgraduate studies overseas and hopes to contribute to interdisciplinary research at the boundary between pure and applied mathematics.
