UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

September 26, 2017

939 Evans Hall

3:45PM: The belly of a minimal free resolution

Karim Adiprasito

We discuss the shape of minimal free resolutions of monomial ideals, that is, the shape of its bigraded Betti-table, and relate it to basic homotopy theory.

5:00PM: Symbolic Powers of Determinantal Ideals

Leon Zhang

We give a description of certain products of minors of a generic matrix as pairs of standard Young tableaux. Under this description, the pairs of standard Young tableaux form a free basis of the polynomial ring whose variables are generic entries of that matrix. We also characterize the nth symbolic power of a determinantal ideal in terms of these pairs of standard Young tableaux, and use this to produce the irredundant primary decomposition of powers of determinantal ideals.

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