• 09/22/2026: Shaan Prajapat (Maple Software)

Title: What's New in Maple 2026: AI-Assisted Mathematics for Research and Teaching

Abstract: Maple 2026 introduces a new AI Assistant that helps users generate expressions, explanations, and Maple code from natural-language descriptions, along with a document import feature that converts PDFs, printed notes, and even handwritten scans into live, executable Maple worksheets. This talk will walk through these new AI-assisted capabilities alongside updates to Maple's core symbolic and numeric engines, with an eye toward how they can support both research workflows and teaching. We'll leave time for Q&A and for hearing how NC State faculty are currently using Maple.

• 09/29/2026: Frank Sottile (Texas A&M University)

Title: Reciprocal Discriminants

Abstract: Motivated by applications and the classical theory of A-discriminants of Gel’fand, Kapranov, and Zelevinsky, we develop the basic theory of discriminants of multivariate reciprocal polynomials. These reciprocal discriminants parameterize reciprocal polynomials that define a singular hypersurface. We show that a reciprocal discriminant has a rich combinatorial structure. It is a reducible hypersurface whose components are dual varieties to Chebyshev subvarieties which correspond to certain layers in a toric arrangement associated to the exponents of the reciprocal polynomials. The layers which contribute correspond to certain matroidal decompositions of the exponents. This is joint work with Trevor Karn and Simon Telen.

• 10/06/2026: Manfred Minimair (Seton Hall University)

Title: Solving Homogeneous Polynomial-Like Iterative Functional Equations for Permutations on Finite Fields 

Abstract: An algorithm for computing all permutation solutions of homogeneous   polynomial-like iterative functional equations over finite fields is   presented. The homogeneous equations are polynomial-like iterative,   consisting of linear combinations of iterated compositions of the functional   variable with coefficients from a finite field. Solutions are sought among the permutations defined on the finite field, and the solutions among all   functions on the finite field are then described in terms of the permutation solutions. Polynomial-like iterative functional equations are widely studied for analytic solutions but have only partially been addressed over finite   domains by computing iterated roots of elements of finite permutation groups   and semigroups. The proposed algorithm employs the new concept of compositional minimal polynomial relating the cycle structure of the solutions of the polynomial-like iterative equation to the order of the minimal polynomial. The presentation concludes by discussing AI-supported formalization and verification of the work.

• 10/13/2026: George Andrews (North Carolina State University)

Title: A generalization of signature quiver construction

Abstract: Deciding whether or not two curves are congruent under a group of transformations is one of the fundamental problems in mathematics. Equality of differential signatures, introduced by Calabi et al. (1998), provides a necessary condition for such congruence, which is also sufficient for analytic curves. In the case of smooth curves, Geiger and Kogan (2021) showed that for planar curves under Euclidean action, equality of simple signatures is also sufficient to establish congruence. When signatures are not simple, an additional construction, called a signature quiver, can be used to establish congruence. In this talk, I present the progress and challenges of generalizing the signature quiver construction to the affine action on the plane.

• 10/20/2026: Ritvik Ramkumar (University of Notre Dame) 

Title: Varieties of minimal degree in weighted projective spaces

Abstract: Classically, the degree of a non degenerately embedded variety in projective space is bounded below by one more than its codimension, and varieties attaining this bound are completely classified. We show that an analogous degree bound holds in weighted projective spaces, under mild constraints on the weights. We will also discuss weighted analogues of rational normal scrolls and study their degrees, regularity, and other syzygetic properties.

• 11/03/2026: Daoji Huang (University of Massachusetts Amherst)

Title: Gorenstein Positroid Varieties

Abstract: Positroid varieties are an important class of subvarieties of the Grassmannian which carry rich combinatorial structures from both Schubert geometry and matroid theory. Knutson--Lam--Speyer showed that they are normal, Cohen--Macaulay, and have rational singularities, and Billey--Weaver gave combinatorial criteria for smoothness. In this talk, we discuss their divisors and related geometric properties. We describe the Picard groups of positroid varieties and their generators, and give an explicit graph-theoretic criterion for when a positroid variety is Gorenstein. We show that being Gorenstein, $\mathbb{Q}$-Gorenstein, and Fano are equivalent for positroid varieties. We further characterize when a Gorenstein positroid variety is arithmetically Gorenstein in the Pl\"ucker embedding. Joint with Ayah Almousa and Anders Buch.

• 11/10/2026: Avery Schweitzer (North Carolina State University)