Meetings in Applied Algebraic Geometry 2025

April 19-20, 2025

Organizers: John Cobb, Luke Oeding, Michael Burr, Kisun Lee, and Anton Leykin.

Overview

The Meeting on Applied Algebraic Geometry (MAAG) is a regional gathering which attracts participants primarily from the South-East of the United States. MAAG 2025 takes place at Auburn University on April 19-20, 2025. Previous meetings took place at Georgia Tech in 2015, 2018, 2019, and 2023 and at Clemson in 2016.

For funding, please apply by March 12th.

Talks

All talks will take place in room 161 at the ACLC. There are eight 50-minute talks by:

• Thomas Kahle (OvGU Magdeburg)
  Title: The likelihood correspondence

  Abstract: We study SNC arrangements of hypersurfaces and the critical locus of Laurent monomials in the equations of the smooth hypersurfaces. This locus is an irreducible variety in the product of two projective spaces, known in algebraic statistics as the likelihood correspondence and in particle physics as the scattering correspondence. We establish an explicit determinantal representation for the bihomogeneous prime ideal of this variety. SNC arrangements are characterized by the non-vanishing of the Euler discriminant. This is joint work with Hal Schenck, Bernd Sturmfels, and Maximilian Wiesmann.
• Felice Manganiello (Clemson University)
  Title: Code-based Cryptography: The Future of Security Against Quantum Threats

  Abstract: In today's digital age, where our personal data and information are predominantly stored online, security has become a crucial concern. The cryptographic standards currently in use are vulnerable to attacks from quantum computers, which may pose a significant threat in the coming years. Post-quantum cryptography is an area of research focusing on developing cryptosystems that can withstand quantum attacks while working on classical computers. Code-based cryptosystems have proven to be the most resilient over time among the various post-quantum cryptosystems. In this seminar, as a coding theorist, I will present the fundamentals of code-based cryptography, discuss how to build secure mechanisms like authenticated key exchanges, and provide guidelines to prevent weak instances that may create vulnerabilities. This presentation aims to enhance awareness of the importance of security and demonstrate the potential of code-based cryptography in safeguarding our online information against the quantum threat.
• Julia Lindberg (University of Texas-Austin)
  Title: Gaussian Voronoi Cells

  Abstract: Gaussian discriminant analysis is a supervised learning algorithm for classification. Fundamental to understanding the performance of this algorithm is to understand the set of points closest to a given Gaussian, where "closest" is defined in terms of the maximum likelihood function. This set of points is the Gaussian Voronoi cell of the Gaussian. In this talk, I will outline new results regarding the geometry and combinatorics of Gaussian Voronoi cells and I will discuss implications for the expectation maximization (EM) algorithm, a popular method of density estimation for Gaussian mixture models. This is joint work with Joe Kileel.
• Michael Byrd (Clemson University)
  Title: Certified approximation algorithms of algebraic curves

  Abstract: A common challenge in computational algebraic geometry is to compute  certified approximations of algebraic curves. In this talk, we will look at two algorithms that solve versions of this task. The first task is to simultaneously approximate a set of curves given by bivariate polynomials. The second task is to approximate a generic projection of a regular curve to the plane. For the first task, we introduce an algorithm for approximating multiple curves in the plane. This is a nontrivial extension of the Plantinga and Vegter algorithm for approximating a single curve. We then follow this with an adaptive complexity analysis of our algorithm based on continuous amortization and condition numbers. For the second task, we use a two-step procedure to construct this approximation. The first step is construct a tubular neighborhood of a regular curve in $\mathbb{R}^n$. This is done using an extension of certified homotopy path tracking as introduced in Duff-Lee and Guillemot-Lairez. We then consider the projection of this approximation and provide conditions under which this image has the same topology as the projection of the curve.
• Parker Edwards (Florida Atlantic University)
  Title: Computing local monodromy and local irreducible decompositions

  Abstract: The standard approach to numerical algebraic geometry is global in the sense that one computes irreducible components, samples, etc. for a whole algebraic set. The theories of algebraic and analytic geometry are replete with interesting examples of local behavior, however. For instance: Given a singular point on a complex algebraic set, what is the minimum number of connected components in a stratification at the point? I will discuss work with Jon Hauenstein developing theory and an algorithm for answering some of these types of questions. The strategy writ large is to begin with a generic finite linear projection, localize a generic fiber, localize the projection's singular locus, and partition the localized fiber by tracking monodromy loops. We prove that this procedure is exhausitve in the sense that we compute a generating set of loops for the appropriate fundamental group which acts on the fiber. I will also present several examples computed with an open source implementation of the algorithm.
• Dustin Cartwright (University of Tennessee, Knoxville)
  Title: Faithful tropicalization of curves

  Abstract: Tropicalization of an algebraic curve has both an abstract version (as a dual graph) and an embedded version (as a polyhedral complex). A bridge that links the two is provided by faithful tropicalization, which depends on a suitable embedding. I will discuss work in progress on effective methods for finding embeddings for faithful tropicalizations. As a consequence, this gives computational methods for computing dual graphs.
• Greg Blekherman (Georgia Tech)
  Title: Stubborn polynomials

  Abstract: A real polynomial $F$ nonnegative on a variety $X$ is stubborn if no odd power of $F$ is a sum of squares. Stubborn polynomials on smooth curves admit an elegant characterization, which can be leveraged to understand stubbornness on higher dimensional varieties. The case of the projective plane is already quite interesting and complicated, and I will present some results on stubborn sextics.
• Irina Kogan (North Carolina State University)
  Title: Equi-affine minimal-degree moving frames for polynomial curves

  Abstract: Classical equivariant moving frames play an important role in differential geometry and invariant theory. However, these frames associated with a polynomial curve are, in general, neither polynomial nor even rational. We develop a theory and an algorithm for constructing minimal-degree polynomial moving frames for polynomial curves in an affine space. The algorithm is equivariant under volume-preserving affine transformations of the ambient space and the parameter shifts. We show that any matrix-completion algorithm can be turned into an equivariant moving frame algorithm via an equivariantization procedure that we develop. We prove that if a matrix-completion algorithm is of minimal degree, so is the resulting equivariant moving frame algorithm. We propose a novel minimal-degree matrix-completion algorithm, complementing the existing body of literature on this topic. This is a joint work with Hoon Hong, North Carolina State University.

Schedule

Participant Information

Lodging: We will be housing all participants at the The Hotel at Auburn University. If you are driving, there is parking at the hotel for the price of $ $ $25/night for valet parking or 20/night for self parking, which we can reimburse. There is also free parking on College Street on the weekends.

Airport: We recommend flying to ATL and then taking the Groome Shuttle.

Policies

We are required by the NSF Proposal & Award Policies & Procedures Guide (Chapter II.E.7), effective February 25, 2019, to provide all event participants with information on the University’s policy on sexual and other forms of harassment or sexual assault as well as directions on how to report any violations of this policy. For purposes of this requirement, “other forms of harassment” is defined as “non-gender or non-sex-based harassment of individuals protected under federal civil rights laws, as set forth in organizational policies or codes of conduct, statutes, regulations, or executive orders.”

Auburn University is committed to creating and maintaining a community dedicated to the advancement, application and transmission of knowledge and creative endeavors through academic excellence, where all individuals who participate in University programs and activities can work and learn together in an atmosphere free of harassment, exploitation, or intimidation.

The University has general policies prohibiting harassment and discrimination on the basis of protected categories, including the Auburn University Policies Related to the Workplace; AA/EEO Policies and Procedures; and Code of Student Conduct.

Any person may report incidents of sexual violence, sexual harassment, relationship violence, stalking, or other forms of prohibited behavior to the campus Title IX office. aub.ie/TitleIX has links to report an incident and additional information is available on this site.

Funding

This conference is supported all or in part by the National Science Foundation under DMS Award No. 2504328.