Algebraic Cycles and Representation Theory

A. Cycle groups

1. Operations on cycles
2. Equivalence relations
3. The Chow group

B. Cycle-class maps and the Hodge Conjecture

1. Cycle classes and Lefschetz (1,1)
2. Mumford-Tate groups of Hodge structures
3. The theorem of Hazama and Murty
4. Mumford-Tate domains and period mappings
5. Weil-Hodge classes and Schoen's construction
6. Algebraicity of Hodge loci
7. Absolute Hodge classes and Voisin's strategy

C. The Abel-Jacobi map and normal functions

1. Extensions of MHS and the Deligne cycle class
2. Cycles modulo algebraic equivalence
3. Infinite generation of the Griffiths group
4. Admissible normal functions and their invariants
5. Cycles on projective hypersurfaces
6. Homogeneous VHS and cycles on abelian varieties
7. Normal functions and the Hodge Conjecture

D. Higher Abel-Jacobi maps and filtrations on Chow groups

1. Mumford's theorem on zero-cycles
2. Spreads and Bloch-Beilinson filtrations
3. Higher cycle- and AJ-classes: examples

A. Bloch's construction

1. K₀ and algebraic cycles
2. Milnor K-theory and relative 0-cycles
3. Higher Chow groups and their properties
4. Moving lemmas for higher cycles
5. Abel-Jacobi maps for higher Chow cycles

B. The Borel regulator

1. K-theory of number fields
2. Sketch of Borel's theorem
3. Applications of Borel's theorem

C. The Beilinson conjectures

1. Statements and motivation
2. CM elliptic curves
3. The Eisenstein symbol