# NCSU Algebra and Combinatorics Seminar

This is the webpage for the NCSU Algebra and Combinatorics seminar, run by the NCSU Algebra and Combinatorics research group.

We typically meet Mondays from 3:00 pm - 4:00 pm. For the Spring 2021 semester, we will be meeting online with Zoom. If you would like to attend, please email Corey Jones at to be added to the mailing list for weekly announcements of abstracts and Zoom links.

Below is a list of currently scheduled talks for this semester (which is updated regularly!):

Spring 2021:

2/29/2021- Corey Jones, North Carolina State University:

Symmetries of affine buildings and tilting modules for SL_n.

In this talk, we will explain a (mysterious?) connection between the combinatorics of affine buildings and representation theory in positive characteristic. If a group acts simply and transitively on the vertices of an affine building in type A_n, it gives rise to a certain combinatorial structure called a triangle presentation. We will describe how triangle presentations can be used to build exotic fiber functors on the category of tilting modules for SL_n (for n odd) in positive characteristic.

3/15/2021- Cris Negron, University of North Carolina, Chapel Hill: TBA

3/29/2021- Samantha Kirk, North Carolina State University:

How to Construct Representations of Twisted Toroidal Lie Algebras via Lattice Vertex Algebras

If you take a simple finite-dimensional Lie algebra g and tensor it with the Laurent polynomials in one variable, then you will get an infinite-dimensional Lie algebra known as a loop algebra. Affine Lie algebras are the central extensions of such loop algebras and their representations have been of interest to several mathematicians. What happens if we tensor g with the Laurent polynomials in several variables (instead of just one) and create a central extension? The result is known as a toroidal Lie algebra. I am interested in representations of certain toroidal Lie algebras that have been twisted.

In this talk, I will show how representations of twisted toroidal Lie algebras can be constructed using lattice vertex algebras. The method I will use builds on what is known about the connection between lattice vertex algebras and representations of affine Lie algebras. In fact, the only difference is I will use a bigger lattice! This talk should be approachable for students who have taken MA 720 and/or MA 725.

(Joint work with Bojko Bakalov)

4/5/2021- Julia Plavnik, Indiana University: TBA

4/19/2021- GaYee Park, University of Massachusetts Amherst: TBA