Abstract: The Hilbert polynomial is an invariant of a graded module or a coherent sheaf on projective space that plays a central role in commutative algebra and algebraic geometry. It has two natural refinements: the Betti table of the module, and the cohomology table of the sheaf. Boij-Soederberg theory, which has grown up over the last five years, shows that these two refinements are, in a precise sense, dual to one another. The duality pairing gives substantial new information about each of the two invariants. I will explain these ideas, some of their applications, and some of the many open problems of the field.

Click here here for a reading list on Boij-Soederberg theory.

Srikanth Iyengar, *The Betti table of a Koszul algebra*.

Click here here for the notes.

Jaya Iyer, *Linear systems on hyperelliptic varieties*.

Bangere Purnaprajna, *Syzygies and geometry*.

S. Ramanan, *An introduction to syzygies*.

Kavita Sutar-Deshpande, *Orbit closures for source-sink quivers and their resolutions*.

Hema Srinivasan, *Minimal Resolutions of ideals defining monomial curves*.

Krishna Hanumanthu.
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Coherent sheaves on projective space. Cohomology tables. Line bundles and
vector bundles on projective space. Projection formula. Higher direct images
of a sheaf under proper push-forward. Ample line bundles, embeddings of
projective varieties.
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Pramathanath Sastry.
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Homological algebra, derived categories, local and global duality.
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Macaulay2
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We will use the computer algebra program
**Macaulay2
to compute examples.
Click here for the M2 examples file.
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