Algebraic Geometry/Commutative Algebra Seminar, 2024–2025
To volunteer to give a talk, or for anything else regarding the seminar, contact Claudiu Raicu, Eric Riedl or Keller VandeBogert.
Abstracts can be found below.
Fall Schedule
The seminar will meet on Fridays, 3–4pm in 258 Hurley, unless otherwise noted. Related events are also listed below.
Date 
Speaker 
Title 
Friday, Sep. 6 
Xianglong Ni (Notre Dame) 
Herzog classes of grade three licci ideals 
Friday, Sep. 13 
No seminar (ND Presidential Inauguration) 

Friday, Sep. 20 
Keller VandeBogert (Notre Dame) 
TBA 
Friday, Sep. 27 


Friday, Oct. 4 


Friday, Oct. 11 
Dave Swinarski (Fordham) 
TBA 
Friday, Oct. 18 


Friday, Oct. 25 
No seminar (Fall break) 

Friday, Nov. 1 


Friday, Nov. 8 
Juan Migliore (Notre Dame) 
TBA 
Friday, Nov. 15 


Friday, Nov. 22 


Friday, Nov. 29 
No seminar (Thanksgiving) 

Friday, Dec. 6 


Abstracts
Sep. 6, 2024
 Speaker
 Xianglong Ni (Notre Dame)
 Title
 Herzog classes of grade three licci ideals
 Abstract

By work of Buchweitz and Herzog, there is a welldefined classification of licci ideals up to deformation. The equivalence classes obtained in this manner are called Herzog classes. For grade 2 perfect ideals (all of which are licci) the Herzog class of I is determined by its minimal number of generators, i.e. the vector space dimension of I/mI. Furthermore, the class of a linked ideal K:I can be inferred from the dimension of the subspace (K+mI)/mI. Assuming equicharacteristic zero, we generalize this to grade 3 licci ideals, where we can describe all Herzog classes with the assistance of representation theory. In this setting, the class of K:I depends on the incidence of (K+mI)/mI with a distinguished partial flag on I/mI. This is based on ongoing joint work with Lorenzo Guerrieri and Jerzy Weyman.