POSTER SESSION – XX RED RAIDER MINI-SYMPOSIUM
GEOMETRIC ANALYSIS AND APPLICATIONS


The poster session will be part of the conference program. Time 11:30 am – 2:00 pm – 1st Floor Lounge, Math Building


Poster Presentations

Name & University Title Abstract
Miraj Samarakkody
Tougaloo College 		Formalizing the Isoperimetric Inequality in Lean 4 With the rapid development of artificial intelligence, mathematicians, particularly geometricians, must decide how to engage with these tools. Just as the introduction of calculators and mathematical software transformed practice, AI presents both opportunities and challenges. Until recently, automated systems offered little assistance with complex mathematical proofs, primarily due to the lack of rigorous reasoning and machine-verifiable precision. We address this gap using Lean 4, a proof assistant that enables formally verified proofs in mathematics, with a focus on differential geometry, an area that has gained renewed attention in the context of modern machine learning. Formalizing proofs in Lean 4 is non-trivial, as the structure of computer-verified proofs differs substantially from traditional handwritten ones. In this work, we present an introduction to Lean 4 and demonstrate its use by formalizing the classical isoperimetric inequality, which states that among all closed curves of a given length, the circle encloses the maximum area.
Michael Keeler
Texas A&M University 		Symplectification Procedure for Rank 4 Distributions with Abnormal Distributions of Rank 2 This poster studies the equivalence problem for rank 4 bracket-generating distributions. Doubrov and Zelenko (2006-2016) developed the general procedure, called symplectification, which assigns to a distribution a new distribution, called its symplectification, on a special subbundle of the projectivized cotangent bundle from which the original distribution can be uniquely recovered. The advantage of studying the equivalence problem for the original distribution through its symplectification is that the Tanaka symbols associated with the symplectification are frequently discrete and classifiable. In particular, this happens when the so-called abnormal subdistribution has rank 1, under the additional assumption of maximality of class. However, rank 4 distributions provide the first instance in which the abnormal subdistribution can have rank greater than 1. In this work, we extend the symplectification procedure to rank 4 distributions with a rank 2 abnormal subdistribution. The problem reduces to classifying certain graded representations of the Heisenberg algebra. Using techniques from the theory of matrix pencils and quiver representations, we classify the Tanaka symbols of the symplectification under the assumption of maximality of class and a generic assumption on the step-2 truncation of the original distribution's Tanaka symbol. In several cases, the classification is discrete.
Hasitha Geekiyanage
Texas Tech University 		Vector bundles, projective modules and Swan’s theorem The Serre–Swan correspondence provides a connection between algebra and geometry. It identifies vector bundles with finitely generated projective modules: in algebraic geometry, locally free sheaves of finite rank on an affine scheme correspond to finitely generated projective modules over its coordinate ring. In topology, vector bundles over a compact Hausdorff space correspond to finitely generated projective modules over C(X). In this poster, I will discuss the role of global sections in linking geometry and algebra.
Magdalena Toda and Erhan Güler
Texas Tech University 		Generalized Weierstrass–Enneper Representation Formula for Minimal Surfaces in Four-Dimensional Space We present a new formulation of the Weierstrass–Enneper representation for minimal surfaces immersed in R4. Although the classical representation in R3 is based on holomorphic data and isotropic conditions in complex space, its extension to higher dimensions requires a refined geometric framework. Our approach relies on four holomorphic functions satisfying a natural isotropy condition in C4, which generate conformal minimal immersions in four-dimensional Euclidean space. This formulation preserves the essential analytic structure of the classical theory while revealing additional geometric and algebraic features specific to codimension two. We discuss structural properties of the representation and provide explicit examples illustrating its flexibility and geometric implications. The construction offers a coherent extension of the classical Weierstrass–Enneper method and provides new tools for studying minimal surfaces in higher dimensions.