Overview

The Meeting on Applied Algebraic Geometry (MAAG) is a regional gathering that attracts participants primarily from the Southeastern United States. MAAG 2026 takes place at Clemson University on April 18-19, 2026. Previous meetings were held at Georgia Tech in 2015, 2018, 2019, and 2023; at Clemson in 2016; and at Auburn in 2025.

Organizers: Michael Burr, John Cobb, Kisun Lee, Anton Leykin, Julia Lindberg, Luke Oeding

For any inquiries regarding the meeting, please contact kisunl@clemson.edu.

Talks

• Yulia Alexandr (University of California, Los Angeles)
  Algebraic invariants in machine learning
  Abstract

  This talk explores how algebraic geometry offers powerful tools for understanding machine learning models. I will explain how the algebraic and semi-algebraic structure of modern models (ReLU, polynomial, and self-attention) gives rise to polynomial invariants and complexity measures, such as Euclidean distance degree. These tools provide theoretical guarantees for neural network verification, optimization, and robustness, supporting safety-critical applications.

• Ayah Almousa (University of Kentucky)
  Computing with positroid varieties via Gröbner bases
  Abstract

  Positroid varieties are subvarieties of the Grassmannian defined by the vanishing of selected Plücker coordinates determined by a matroid. In joint work with Daoji Huang and Shiliang Gao, we study their defining ideals from a computational perspective. We prove that these ideals admit Gröbner bases with respect to natural term orders and describe the resulting initial ideals explicitly. These Gröbner degenerations allow explicit computation of invariants such as Hilbert series and provide tractable models for further geometric study.

• Julianne Barnhart (Clemson University)
  Restricted monodromy groups and applications to sparse polynomial systems
  Abstract

  The monodromy group of a branched cover $\pi:X\to Y$ is a permutation group resulting from taking loops in the base space $Y$, as the lift of each loop induces a permutation of points in a fibre. We consider restricting $\pi$ to some generic subvariety $V$ of $Y$, with $X_V$ the preimage of $V$ under $\pi$. When $X_V \to V$ is a branched cover, we prove relationships between the monodromy group of the full branched cover and the monodromy group of the restricted branched cover. The existence of a transposition in the restricted monodromy group guarantees that the restricted monodromy group and the full monodromy group share a unique minimal block structure. As a consequence, we give conditions for the restricted monodromy group to be the full symmetric group. Additionally, we discuss applications of restricted monodromy groups in various settings in applied algebraic geometry including sparse polynomial systems and computer vision.

• Alex Dunbar (Georgia Tech)
  Applications of duality for quadratic inequalities
  Abstract

  Systems of (affine) linear inequalities have a well-known duality theory that is a fundamental tool in pure and applied mathematics. Systems of quadratic inequalities also have a duality theory, though it is less well-known. Specifically, the homology of a set defined by a system of quadratic inequalities is related to the topology of (the complement of) a real algebraic hypersurface, which serves as a dual object to the given system. In this talk, we discuss applications of this framework to problems in applied mathematics. A key example will be the description of convex hulls of sets defined by three quadratic inequalities.

• Emily King (Colorado State University)
  Group actions in frame theory, quantum information theory, and machine learning
  Abstract

  Group actions may be leveraged to create subspace configurations which are optimal in frame theory and quantum information theory, with equiangular Fourier frames and symmetric, informationally complete, positive operator-valued measures (SIC-POVMs) being two of the most well-known examples. In machine learning, highly symmetric vectors emerge when training neural networks under certain regimes (neural collapse), while orbits of group actions may be leveraged to perform classification tasks (e.g., bilipschitz invariants, group-invariant max filtering, invariant/equivariant neural networks). This talk will introduce these applications and conclude with some open problems.

• Christopher Manon (University of Kentucky)
  Khovanskii bases and Cox rings
  Abstract

  Khovanskii basis is a set of elements that generate both an algebra and one of its associated graded algebras. Khovanskii bases are instrumental in solving various problems, from computing Newton-Okounkov bodies to modeling applied systems like chemical reaction networks and coupled oscillators. I'll give an overview of the theory of Khovanskii bases and then describe a recent application to the problem of computing the Cox ring of a variety. In particular, I will focus on computing Cox rings from the class of projectivized toric vector bundles. In this setting, the Khovanskii basis algorithm interacts in interesting ways with the theory of matroids.

• Kalina Mincheva (Tulane University)
  Integral elements and normalization in tropical geometry
  Abstract

  This work is part of a broader program to develop necessary commutative algebra tools for the semirings arising from tropicalization. We will discuss different notions of integrality which while equivalent for rings are not for idempotent semirings. We will define integral closure and give different characterizations. If time permits we will give some examples of normalization in tropical geometry.

• Ezra Nance (The University of Tennessee at Martin)
  Slicing the cone of positive polynomials
  Abstract

  Parametrizing sets is often a good way to gain understanding about them. In this talk, we focus on the cone of all univariate non-negative polynomials over a closed interval. This set is connected to the theory of moment problems, which have several applications. Throughout the talk we develop a parametrization of this cone which naturally partitions it into several high-dimensional polyhedral cones, each polyhedral cone being easier to understand than the entire set itself. This is a joint work with Hoon Hong.

Poster Presentations

• Ryan Anderson (University of California, Los Angeles) - A quantifier-free description of the semi-algebraic set of value functions in partially observable Markov decision processes
• Cheng Chen (University of Wisconsin, Madison) - Algebraic characterization of reliability phase transitions in infinite-depth supply networks
• Aviva Englander (University of Wisconsin, Madison) - The Allee effect: A case study in numerical methods
• Rickey Huang (Georgia Tech) - Approximating periodic orbits with algebraic curves and related minimal problems
• Kisun Lee (Clemson University) - CertifiedHomotopyTracking.jl
• Jingyi Long (Georgia Tech) - Algorithms for rational univariate representation and geometric resolution

Macaulay2 Mini-Workshop

• Kisun Lee (Clemson University) - Complex interval arithmetic implementation in Macaulay2
• Jose Israel Rodriguez (University of Wisconsin, Madison) - TDA
• Douglas Torrance (Piedmont University) - What's new in the next Macaulay2 release

Schedule

All talks in Martin Hall M102.

Participant Information

Funding

This conference is supported all or in part by the National Science Foundation under DMS Award No. 2552457.

To be considered for travel support, please register by March 15, 2026. Students and early career mathematicians are strongly encouraged to present a poster; priority for travel funding will be given to poster presenters.