Description
Speaker: Ezra Miller.
Time: 7pm IST (gate opens 6:45pm IST).
Google meet link: meet.google.com/rxx-wfnm-kkq.
By phone: (US) +1 402-277-8494 (PIN: 677936904).
Title: Minimal resolutions of monomial ideals.
Abstract: It has been an open problem since the 1960s to construct
closed-form, canonical, combinatorial minimal free resolutions
of arbitrary monomial ideals in polynomial rings. This
talk explains how to solve the problem, in characteristic 0
and almost all positive characteristics, using sums over
lattice paths of combinatorial data from simplicial
complexes, one simplicial complex for each lattice point.
Any minimal free resolution of any monomial ideal must --
either implicitly or explicitly -- produce homomorphisms
between various homology groups of these simplicial
complexes. Therefore an important aspect of the solution
is an explicit way to write down canonical homomorphisms
between these homology groups without choosing bases.
Joint work with Jack Eagon and Erika Ordog.