Description
IITB Mathematics Colloquium via videoconference.
Speaker: Luke Oeding.
Affiliation: Auburn University.
Date and Time: Monday 08 April, 7:30 pm - 8:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Tensors and Syzygies.
Abstract: Tensors are higher dimensional analogues of matrices. But unlike
matrices, there is still so much we don't know about their fundamental
algebraic properties. For example, for rank-r matrices we know that the
determinants of all (r+1)-minors of the matrix furnish a generating set
for the ideal of all relations among the entries of such matrices, but for
general rank-r tensors we have almost no idea what polynomials generate
their ideals. Moreover the entire minimal free resolution of the ideal in
the matrix case is know in terms of representation theory (Lascoux,
Eagon-Northocott, Weyman, and others), but relatively little is known in
the tensor case, (not even the length of the resolution).
I'll present evidence toward a conjecture on arithmetic
Cohen-Macaulay-ness that would generalize the Eagon-Hochster result in the
matrix case. I'll also highlight recent work with Raicu and Sam where we
compute precise vanishing and non-vanishing of the syzygies of rank-1
tensors.