Current Series

[View Past Series]

Tue Jan 26

Commutative Algebra Seminar

 3:35pm - via Zoom
Commutative Algebra Seminar - Social Hour
TBD

Zoom Link: https://umn.zoom.us/j/96978192398?pwd=ajFBN3BIUFNudHpVdXMrbXF0RUFjQT09Meeting ID: 969 7819 2398Passcode: RingsHave1
Tue Feb 09

Commutative Algebra Seminar

 3:35pm - via Zoom
The BGG correspondence for toric varieties
Michael Brown , Auburn University

This is ongoing joint work with David Eisenbud, Daniel Erman, and Frank-Olaf Schreyer. The Bernstein-Gel'fand-Gel'fand (BGG) correspondence is a derived equivalence between a standard graded polynomial ring and its Koszul dual exterior algebra. One of the many important applications of the BGG correspondence is an algorithm, due to Eisenbud-Fløystad-Schreyer, for computing the cohomology of sheaves on projective space that is, in some cases, the fastest available. The goal of this talk is to discuss a generalization of the BGG correspondence from standard graded to multigraded polynomial rings and how one can use it to develop an Eisenbud-Fløystad-Schreyer-type algorithm for computing sheaf cohomology over projective toric varieties. I will also discuss how we can apply our results to give a proof of a conjecture of Berkesch-Erman-Smith concerning the length of virtual resolutions over toric varieties.Zoom Link: https://umn.zoom.us/j/96978192398?pwd=ajFBN3BIUFNudHpVdXMrbXF0RUFjQT09Meeting ID: 969 7819 2398Passcode: RingsHave1
Tue Feb 23

Commutative Algebra Seminar

 3:35pm - via Zoom
Uniform Asymptotic Growth of Symbolic Powers of Ideals
Robert Walker , University of Wisconsin

Algebraic geometry (AG) is a major generalization of linear algebra which is fairly influential in mathematics. Since the 1980's with the development of computer algebra systems like Mathematica, AG has been leveraged in areas of STEM as diverse as statistics, robotic kinematics, computer science/geometric modeling, and mirror symmetry. Part one of my talk will be a brief introduction to AG, to two notions of taking powers of ideals (regular vs symbolic) in Noetherian commutative rings, and to the ideal containment problem that I study in my thesis. Part two of my talk will focus on stating the main results of my thesis in a user-ready form, giving a "comical" example or two of how to use them. At the risk of sounding like Paul Rudd in \textit{Ant-Man}, I hope this talk will be awesome.A first course in AG would be helpful but I review what I need for my thesis problem.Zoom Link: https://umn.zoom.us/j/96978192398?pwd=ajFBN3BIUFNudHpVdXMrbXF0RUFjQT09Meeting ID: 969 7819 2398Passcode: RingsHave1
Tue Mar 09

Commutative Algebra Seminar

 3:35pm - via Zoom
Extremal Singularities in Positive Characteristic
Janet Page, University of Michigan

In this talk, I will introduce an interesting class of polynomials which define the most singular possible (reduced) hypersurfaces in positive characteristic as measured by an invariant called the F-pure threshold. These polynomials have a rich algebraic structure coming from the fact that they have a matrix factorization mirroring the theory of quadratic forms, and there are only finitely many of them in any bounded degree and number of variables (up to a linear change of coordinates). We fully classify them by associating to them directed graphs which capture their combinatorial data. Time permitting, we will apply this theory to see some interesting properties of cubic surfaces in characteristic two.Zoom Link: https://umn.zoom.us/j/96978192398?pwd=ajFBN3BIUFNudHpVdXMrbXF0RUFjQT09Meeting ID: 969 7819 2398Passcode: RingsHave1