Student Commutative Algebra Meeting

Fall 2019

Thursdays 12:20 -- 1:10 @ Tate B55

(Feel free to bring your lunch!)

Fall 2019 themes: Boij-Söderberg theory, D-Modules and Spectral Sequences

For the adult Commutative Algebra Seminar see Jay's or Patricia's webpage.

When?	Who?	What?
9/19/19	Mahrud Sayrafi	Introduction to Syzygies, Free Resolutions, and Macaulay2 $I will set the stage for the next few talks leading to Boij-Söderberg theory by answering the following question: let X be a set of 7 points in linearly general position in \mathbb P^3; when is there a curve of degree 3 passing through X? After defining all the words in the title, we will see why each 6 points in \mathbb P^3 lie on a unique twisted cubic curve and the answer to the problem is yes if and only if the 7th point lies on that curve. Finally, we'll see how a syzygetic point of view makes algebraic geometry accessible to experimentation and try a few examples in the commutative algebra and algebraic geometry software Macaulay2.$
9/26/19	McCleary Philbin	Positive Cones of Betti Diagrams and the Boij-Söderberg conjectures (I) $Abstract: The Boij-Söderberg conjectures (now theorems) give a description of the graded Betti diagrams of graded modules over a polynomial ring. Instead of asking, are these (\beta_{i,j}) graded Betti numbers of a module, we ask, are m(\beta_{i,j}) the graded Betti numbers of a module for some large integer m. That is, we study the cone B formed by the positive rays t(\beta_{i,j}). The Boij-Söderberg conjectures focus on this cone of diagrams from modules of codimension c and shortest possible resolution length, i.e. Cohen-Macaulay modules. The goal of this talk is to understand the set up of these conjectures.$
10/3/19	McCleary Philbin	Positive Cones of Betti Diagrams and the Boij-Söderberg conjectures (II) $Abstract: The Boij-Söderberg conjectures (now theorems) give a description of the graded Betti diagrams of graded modules over a polynomial ring. Instead of asking, are these (\beta_{i,j}) graded Betti numbers of a module, we ask, are m(\beta_{i,j}) the graded Betti numbers of a module for some large integer m. That is, we study the cone B formed by the positive rays t(\beta_{i,j}). The Boij-Söderberg conjectures focus on this cone of diagrams from modules of codimension c and shortest possible resolution length, i.e. Cohen-Macaulay modules. The goal of this talk is to understand the set up of these conjectures.$
10/10/19	N/A	No seminar today.
10/17/19	N/A	No seminar today.
10/18/19	Mike Loper	The Boij--Söderberg Cone: A Crossover Event between STAGS and SCAM (I)
10/24/19	N/A	No seminar today.
10/31/19	Mike Loper	The Boij--Söderberg Cone (II)
11/7/19	Mike Loper	The Boij--Söderberg Cone (III)
11/14/19	Mike Loper	The Boij--Söderberg Cone (IV)
11/21/19	Mahrud Sayrafi	Cohomology of Vector Bundles from Free Resolutions over the Exterior Algebra
12/05/19	McCleary Philbin	TBD </tr> </tbody> </table> Interested in joining our mailing list or giving a talk? Contact McCleary Philbin <philb036@umn.edu>. The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota. </body> </html>