Colloquium Abstracts Fall 2026

Abstracts will be posted here for the colloquium talks when they are available.

Debaditya Raychaudhury

University of New Mexico
September 10, 2026

Geometry and Topology of Singularities via Hodge Theory

Algebraic geometry is the study of algebraic varieties that are defined as the solution sets of systems of polynomial equations. The topology of algebraic varieties plays a central role in algebraic geometry, particularly in the classification of singularities. Among the most studied singularity classes are the so-called Du Bois and rational singularities, and in recent years their higher analogues have emerged as natural extensions and have become active areas of research. In this talk, I will explain how these notions give rise to refined measures of singularities that connect algebro-geometric and topological viewpoints through Hodge-theoretic techniques. I will also discuss their applications to the study of singularities of secant varieties, a classical and important class of varieties with a history spanning more than a century and broad impact across mathematics.