01/23/2025
By Joris Roos
The Department of Mathematics & Statistics invites you to attend a colloquium lecture by University of Connecticut Assistant Research Professor Blake Jackson on Wednesday, Jan. 29.
Title: An intersection-dimension formula for non-rigid modules of type affine Dn
Time: 11 a.m. to noon
Room: Southwick 350W
Everyone is welcome!
Abstract: We give a geometric model for the non-rigid modules over acyclic path algebras of type affine Dn. Similar models have been provided for module categories over path algebras of types An, Dn, and affine An as well as the rigid modules of type affine Dn. A major draw of these geometric models is the "intersection-dimension formulas" they often come with. These formulas give an equality between the intersection number of the curves representing the modules in the geometric model and the dimension of the extension spaces between the two modules. Essentially, these formulas allow us to calculate the homological data between two modules combinatorially. Previous work has failed to cover the case of non-rigid modules since they are not tilting objects; thus, the tilting theory tools cannot touch them. Another confounding issue is that while rigid modules have no self-extensions, non-rigid modules can have arbitrarily many distinct (up to isomorphism) self-extensions. Therefore, the curves representing these modules can have an arbitrarily high number of self-intersections.
Check the Mathematics Department website for future events in this colloquium series.