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.

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.

Description

Ramanujan Hall, Department of Mathematics

Date

Mon, April 8, 2019

Start Time

7:30pm-8:30pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Fri, April 5, 2019 12:13pm IST