Current Series

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Thu Sep 26

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Global Sections of Toric Vector Bundles
Jorin Schug

This talk will continue to follow the "Parliament of Polytopes" paper by Di Rocco, Jabbusch, and Smith. I'll discuss the result that the T-equivariant generators for the global sections of a toric vector bundle E correspond to the lattice points in the parliament of polytopes for E and look to understand this result for some examples, including direct sums of line bundles.

Thu Oct 03

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Linkage, and the licci conjecture on grade 3 perfect ideals
Mahrud Sayrafi, University of Minnesota

Let Q be a regular local ring. An ideal I in Q is said to be licci if it is in the linkage class of a complete intersection. Christensen, Veliche and Weyman conjectured that a perfect ideal of grade 3 in Q is licci if and only if its free resolution corresponds to Dynkin diagrams.

After introducing the theory of linkage, I will talk about the conjecture, how Dynkin diagrams are involved, and their approach in showing one direction of the conjecture in arXiv:1712.04016.

Thu Oct 10

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Mike Loper, University of Minnesota
Thu Oct 17

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Rebecca R.G., George Mason University
Thu Oct 24

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Spectral Sequences
Gennady Lyubeznik, University of Minnesota

This is the first of a series of three talks on the spectral sequence of a filtered complex.
This material is by now classical and is an important part of homological algebra.
The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner.

Thu Oct 31

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Spectral sequences
Gennady Lyubeznik, University of Minnesota

This is the first of a series of three talks on the spectral sequence of a filtered complex.
This material is by now classical and is an important part of homological algebra.
The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner.

Thu Nov 07

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
The spectral sequence of a filtered complex
Gennady Lyubeznik, University of Minnesota

This is the third of a series of three talks on the spectral sequence of a filtered complex. This material is by now classical and is an important part of homological algebra. The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner.

Thu Nov 14

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Gennady Lyubeznik, University of Minnesota
Thu Nov 21

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Erika Ordog, Duke University
Thu Nov 28

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
TBA
Thu Dec 05

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
McCleary Philbin, University of Minnesota
Thu Dec 12

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
TBA
Thu Dec 19

Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
TBA
Fri Feb 07

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
On a question of Dutta, joint with Linquan Ma and Anurag Singh
Uli Walther, Purdue

For a local ring (A,m) of dimension n,we study the natural map from the n-th Koszul cohomology on a minimal set of generators of m to the top local cohomology of A supported at m. We construct complete normal domains for which this map is zero, thus answering a question of Dutta in the negative. If time permits, we present precise information on the kernel of this map for a large class of Stanley-Reisner rings.

Fri Feb 14

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Tate Resolutions and Horrocks Splitting Criterion
 Mahrud Sayrafi  ,  

I will talk about the two papers Eisenbud-Fl√łystad-Schreyer-2003 and Eisenbud-Erman-Schreyer-2015 in which they introduce Tate resolutions for projective spaces and products of projective spaces. As an application, I will talk about Horrocks' criterion for vector bundles in those settings.

Fri Feb 21

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Fri Feb 28

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
$\tau$-Factorization and $\tau$-Elasticity
Bethany Kubik, University of Minnesota, Duluth

A more generalized form of factorization, called $\tau$-factorization, was introduced in 2011 by D.D. Anderson and J. Reinkoester. In $\tau$-factorization, all factors of a factorization must belong to the same equivalence class modulo a fixed ideal. We discuss $\tau$-factorization in small settings and $\tau$-elasticity in a more general setting.

Fri Mar 06

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
No Seminar
Fri Mar 13

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
No Seminar
Fri Mar 27

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Fri Apr 03

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Fri Apr 10

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Fri Apr 17

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Fri Apr 24

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA
Fri May 01

Commutative Algebra Seminar

12:20pm - Vincent Hall 213
Commutative Algebra Seminar
TBA