Organizing Committee
 Lars Christensen
Texas Tech University  Claudia Miller
Syracuse University  Steven Sam
University of California, San Diego  Jerzy Weyman
University of Connecticut and Jagiellonian University, Cracow, Poland
Abstract
The structure of free resolutions plays an important role in analyzing singularities of varieties of low codimension. Codimension 2 CohenMacaulay varieties (resp. codimension 3 Gorenstein varieties) come from rank conditions on an n x (n+1) matrix (resp. a skewsymmetric (2n+1) x (2n+1) matrix).
This workshop seeks to push such results to CohenMacaulay varieties of codimension 3 and Gorenstein varieties of codimension 4.
This problem turns out to be related to the classification of semisimple Lie algebras. These new methods allow one to create a ‘map’ of free resolutions of a given format. The calculations that arise are very demanding and require new computational methods involving both commutative algebra and representation theory.
The organizers have shared two sets of notes for attendees to review before the workshop. These are downloadable here:
Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Ayah Almousa
Cornell University

Luchezar Avramov
UNIVERSITY of NEBRASKA–LINCOLN

Taylor Ball
University of Notre Dame

Ela Celikbas
West Virginia University

ChiaYu Chang
Texas A&M University

Lars Christensen
Texas Tech University

Brett Collins
Bucknell University

Kevin Corlette
University of Chicago

Alessandra Costantini
University of California Riverside

Corrado De Concini
University of Rome "La Sapienza"

David Eisenbud
Mathematical Sciences Research Institute and University of California, Berkeley

Özgür Esentepe
University of Connecticut

Luigi Ferraro
Wake Forest University

Sara Angela Filippini
Jagiellonian University

Louiza Fouli
New Mexico State University

Federico Galetto
Cleveland State University

Francesca Gandini
Kalamazoo College

Özhan Genç
Jagiellonian University

Mohsen Gheibi
University of Texas at Arlington

Elisa Gorla
University of Neuchatel

Joshua Grochow
University of Colorado Boulder

Lorenzo Guerrieri
Jagiellonian University of Krakow

Sema Güntürkün
Amherst College

Kevin Harris
University of Texas at Arlington

Jürgen Herzog
UNIVERSITY DUISBURGESSEN

Amy Huang
Texas A&M University

Craig Huneke
University of Virginia

Anthony Iarrobino
Northeastern University

Joachim Jelisiejew
University of Warsaw

Saeja Kim
University of Massachusetts Dartmouth

Joseph Landsberg
Mr.

Jai Laxmi
University of Connecticut

KyuHwan Lee
University of Connecticut

KueiNuan Lin
Penn State University, Greater Allegheny

Haydee Lindo
Williams College

András Lőrincz
HumboldtUniversität zu Berlin

Mahdi MajidiZolbanin
Laguardia Community College, CUNY

Pedro Marques
University of Évora

Jason McCullough
Iowa State University

Claudia Miller
Syracuse University

Jonathan Montaño
New Mexico State University

Frank Moore
Wake Forest University

Van Nguyen
U.S. Naval Academy

Arpan Pal
Texas A&M University

Michael Perlman
Queen's University

Claudia Polini
University of Notre Dame

Claudiu Raicu
University of Notre Dame

Steven Sam
University of California, San Diego

Keri SatherWagstaff
Clemson University

Mahrud Sayrafi
University of Minnesota

Alexandra Seceleanu
University of NebraskaLincoln

Liana Sega
University of Missouri  Kansas City

Aleksandra Sobieska
Texas A&M University

Eric Sommers
University of Massachusetts

Yevgeniya Tarasova
Purdue University

Jacinta Torres
Institute of Mathematics of the Polish Academy of Sciences

Bernd Ulrich
Purdue University

Keller VandeBogert
University of South Carolina

Oana Veliche
Northeastern University

Adela Vraciu
University of South Carolina

Weiqiang Wang
University of Virginia

Jerzy Weyman
University of Connecticut and Jagiellonian University, Cracow, Poland

Xian Wu
Jagiellonian University

Beihui Yuan
Cornell University
Workshop Schedule
Monday, August 3, 2020
Tuesday, August 4, 2020
Wednesday, August 5, 2020
Thursday, August 6, 2020
Friday, August 7, 2020
Lecture Videos
Cellular resolutions of powers of monomial ideals of projective dimension one
The geometry of nilpotent orbits via subbundles of the cotangent bundle
On the structure of short, gradefour, Artinian Goresntein algebras
Spinor structures on free resolutions of codimension four Gorenstein ideals
Syzygies of Determinantal Thickenings via gl(mn) Representations
On growth of the Hilbert function of a quadratic ideal
The syzygies of some thickenings of determinantal varieties
Some branching formulas for KacMoody Lie algebras
Introduction to gradings of Lie algebras and Schubert varieties II
Minimal free resolutions of orbit closures of quivers
Linkage and Tor algebra classes of codepth three perfect ideals
An example of calculating a resolution using Hilbert functions
Introduction to Schubert varieties I
The Family of Perfect Ideals of Codimension 3, of Type 2 with 5 Generator
Working Groups
Groups will focus on specific open problems related to each topic. There will be discussion to fill in the background of these problems, and we expect the groups to begin work on small subproblems throughout the week.
Resolutions of length 3: licci conjecture, genericity of Schubert examples (lead: Jerzy Weyman)
A connection between free resolutions of length 3 of socalled Dynkin formats and Schubert varieties is investigated in https://arxiv.org/abs/2005.01253. An open problem is to understand whether or not the examples coming from Schubert varieties are generic examples of such resolutions. A related problem is to understand whether every perfect ideal of codimension 3 with a resolution of Dynkin format is licci.
Resolutions of Gorenstein ideals of codimension 4 (lead: Ela Celikbas)
The group will discuss the existence of spinor coordinates on resolutions of Gorenstein ideals of codimension 4 (see https://arxiv.org/abs/1912.07510) and it implications for classifying such ideals, including the expectation that such classification should be easier for 6,7,8 generators. Also description of spinor coordinates in specific examples will be discussed.
Multiplicative structures on resolutions of perfect ideals of codimension 3 (lead: Oana Veliche)
The group will discuss the classification of multiplicative structures and their feasibility for resolutions of different formats. This is related to the material covered in arXiv:1812.11552.
Macaulay 2 software packages (lead: Lars Christensen)
The group will compute the multiplication tables of free resolutions of length 3 and 4 and related higher structure maps. Taking off from several existing pieces of code the group will develop robust and documented code that will be published as M2 packages.
Schubert examples (leads: Jacinta Torres and Sara Angela Filippini)
Continuing from https://arxiv.org/abs/2005.01253, there are open problems regarding how to extend the Schubert examples in Dynkin cases to nonDynkin settings. Furthermore, the larger examples in the E_8 case are conjectural and some of the E_7 examples rely on computer calculation and a conceptual understanding is desired.
Equivariant ideals and superalgebras (lead: Claudiu Raicu)
This group will investigate the connection between classical Lie superalgebras and families of equivariant ideals in polynomial rings. The primary example is the gl_n x gl_m equivariant ideals in the ring of polynomials on the space of n x m matrices whose linear strands are representations of gl(mn), see https://arxiv.org/abs/1411.0151.