The theory of integral closure of ideals, originating in the early twentieth century with work of Krull, Zariski, Rees, and others, remains a vibrant area of research in algebraic geometry, commutative algebra, and singularity theory. This theory’s significance partly stems from its connections with numerical invariants such as multiplicities. During the 1950s, significant advances by Samuel, Serre, and Rees brought multiplicities into the spotlight, spurring extensive development in various directions. During the 1970s, significant advances by Teissier, Briançon, and Skoda brought multiplicities and integral closure into the forefront of singularity theory. This talk will review the history and key results in these areas, while also highlighting some open problems.

Speaker’s website: https://ycid.github.io/