Syracuse Algebra Seminar

Spring 2026 Schedule:

Next Talk

• March 27: Steven Diaz (Syracuse University), Combinatorial criterion for spectral decomposition of tensors

  • Abstract: Much work has been done on generalizing the concepts of eigenvalues and eigenvectors to tensors of higher order. Previously Diaz and Lutoborski introduced the concept of a nested spectral decomposition of a tensor which in a sense generalizes the classical result that a real symmetric matrix is orthogonally diagonalizable. They showed that symmetric tensors of order a power of 2 have such a decomposition and in fact full symmetry is not needed. In this talk we present a necessary and sufficient combinatorial criterion for such a decomposition to exist for tensors of order a power of 2.

Upcoming Talks

• April: 3: No talk

• April 10: TBA

  • Abstract: TBA

• April 17: TBA

  • Abstract: TBA

Past Talks: 

• January 23: Josh Pollitz (Syracuse University), Embedded deformations and the homotopy Lie algebra

  • Abstract: A classical question of Avramov asks whether embedded deformations of a local ring correspond exactly to central elements in the homotopy Lie algebra of the ring. In this talk, I will discuss the question and some recent advancements. This is joint work with Briggs, Grifo, and Walker.

• January 30: Zachary Nason (University of Nebraska-Lincoln), Level Inequalities for Complexes

  • Abstract: Let R be a commutative noetherian ring. In the derived category of R, the level of a bounded R-complex M with respect to a collection of objects C (often referred to as the C-level of M) is the fewest number of mapping cones involving objects in C needed to obtain M. When C is a nice collection of objects in D(R) (such as the projective modules), the C-level of a complex can give a wealth of information about that complex and the ring itself. For example, if R is local, then R is regular if and only if the projective level of all bounded complexes is finite. Recently, Christensen, Kekkou, Lyle, and Soto Levins have found optimal upper bounds for the Gorenstein projective level of bounded complexes with finitely generated homology. In my talk, I'll show how to improve their result to find optimal upper bounds for the projective, injective, flat, Gorenstein projective, Gorenstein injective, and Gorenstein flat levels of all bounded R-complexes. As an application of my results, I'll prove a version of the Bass Formula for injective levels and for Gorenstein injective levels.

• February 13: Dorian Kalir (Syracuse University), Frobenius Endomorphisms for Koszul Complexes

  • Abstract: Recent work of Ballard, Iyengar, Lank, Mukhopadhyay, and Pollitz has shown that for an F-finite locally complete intersection ring, the first Frobenius pushforward of the ring is a strong generator for the bounded derived category. A key ingredient in their proof is that locally each residue field has finite level over the localized pushforward. In this talk, we will present an extension of these results to the dg setting that also refines the key ingredient even in the affine case. Namely, we show that for any Koszul complex over an F-finite regular ring the local residue fields have level 1 over the appropriate localizations of the first pushforward of the Koszul complex.  

• February 20: Kory Pollicove (Syracuse University), Hochschild Cohomology of Quasi-Complete Intersections in Positive Characteristic

  • Abstract: Quasi-complete intersections were initially studied for their connection to a conjecture of Quillen on the vanishing of André-Quillen cohomology. This class of morphisms strictly contains the class of complete intersections, while still retaining some nice smoothness properties. Hochschild Cohomology is another derived functor that relates to smoothness, and has been used to great success in studying complete intersections. In this talk, we will discuss recent work in computing Hochschild Cohomology for local quasi-complete intersections, with a focus on the case of positive characteristic residue field.

• March 13:  No Talk (Spring Break)