Mon, April 8, 2019
Public Access


Category:
Category: All

08
April 2019
Mon Tue Wed Thu Fri Sat Sun
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30          
8:00am  
9:00am  
10:00am  
11:00am  
12:00pm  
1:00pm  
2:00pm  
3:00pm  
4:00pm  
5:00pm  
6:00pm  
7:00pm [7:30pm] Luke Oeding, Auburn University, Mathematics Colloquium
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.

8:00pm