Hodge Theoretic Invariants of Algebraic Cycles

The geometry of a smooth algebraic variety is reflected in the  configurations of its subvarieties. Considering these subvarieties  modulo rational equivalence leads to the fundamental Chow groups. A longstanding question has been to describe these groups by Hodge theory. In this talk I will discuss joint work with Mark Green that,  assuming two of the standard conjectures in algebraic geometry, gives  a complete set of Hodge-theoretic invariants of the rational equivalence class of algebraic cycle.