Topology and Geometry Seminar at Auburn

The Topology and Geometry Seminar at Auburn University covers various topics in topology, geometry, and their applications, including but not limited to:

• Differential Geometry and Geometric Analysis

• Set-theoretic and Algebraic Topology

• Topological Data Analysis

• Applications of Topology and/or Geometry in Statistics, Physics, Biology, etc

Date: August 20 

Speaker: Hal Schenck (Auburn)

Title: Algebraic statistics and particle physics meet hypersurface arrangements

Abstract: An arrangement of hypersurfaces in projective space is simple normal crossing (rough idea: hypersurfaces are generic so meet transversally) if and only if its Euler discriminant is nonzero. We study the critical loci of all Laurent monomials in the equations of the smooth hypersurfaces. These loci form 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.

(joint with T. Kahle, B. Sturmfels, M. Wiesmann; Foundations of Computational Math, to appear)

Date: August 27

Speaker: Minjae Park (Auburn)

Title: The quantum zipper beyond the known regime

Abstract: The quantum zipper is a remarkable gluing principle in two-dimensional random geometry. Roughly speaking, it says that two independent random surfaces, called Liouville quantum gravity (LQG) surfaces, can be conformally welded along their boundaries, and that the resulting interface is described by a Schramm–Loewner evolution (SLE) curve. Conversely, cutting an LQG surface along an appropriate SLE curve produces two independent LQG surfaces.

I will mostly give a friendly introduction to this correspondence, focusing on the underlying geometric ideas rather than technical details. I will then briefly discuss ongoing work aimed at extending the quantum zipper beyond the regime that is currently understood. I will conclude with some speculative questions about possible higher-dimensional analogues, particularly in dimension four, where genuinely new topological input appears to be necessary.

Date: September 10

Speaker: Emmanuel Hartman (University of Houston)

Title: Parameterization Invariant Representations of Geometric Data for Learning Applications

Abstract: Despite rapid advances in geometric deep learning, performing statistical analysis on geometric data—where observations consist of curves, surfaces, or shape graphs—remains fundamentally challenging. This difficulty stems from the non-Euclidean structure of shape spaces, which are defined as equivalence classes under invariance groups, most notably the infinite-dimensional group of reparameterizations. We will discuss addressing these challenges with tools from geometric measure theory. By embedding shapes into measure spaces, we may obtain a robust representation for deep learning tasks which are inherently invariant to reparameterization.

Date: September 17 (joint with Colloquium)

Speaker: Guo-Wei Wei (University of Georgia)

Title: Transforming Artificial Intelligence Through Modern Mathematics 

Abstract: Despite the tremendous success of artificial intelligence (AI) in science, engineering, and technology in the past decade, its explainability, generalizability, and reliability have been a major concern. The solution to these challenges holds the future of AI.  Topological deep learning (TDL), a new paradigm in rational learning introduced by us in 2017, offers interpretable and generalized AI approaches. TDL utilizes topological data analysis (TDA), which is originally rooted in persistent homology, an algebraic topology technique. However, persistent homology has many limitations, including the lack of localization, being restricted to point cloud data, and the inability to represent non-topological information. To address these challenges, we generalized TDA to combinatorial spectral theory (e.g. Topological Laplacian and Dirac), differential topology (e.g. de Rham-Hodge theory), and geometric topology (e.g. Khovanov homology) to handle data on graphs, differentiable manifolds, and curves embedded in 3-space, respectively (see Artif Intell Rev 59, 58, (2026) for a review). To further advance AI through modern mathematical theories, we introduced commutative algebra as a new frontier in data science and machine learning.

Date: September 24

Speaker: Nathan Burns (UTK)

Title:

Abstract:

Date: October 1

Speaker: Carlos Soto (UMass)

Title:

Abstract:

Date: October 15

Speaker: Pengyu Liu (University of Rhode Island) 

Title:

Abstract:

Date: October 22

Speaker: Joshua Jordan (Vanderbilt)

Title:

Abstract:

Date: October 29 (joint with Colloquium)

Speaker: Jiaping Wang (U Minnesota)

Title:

Abstract:

Date: November 5 (online)

Speaker: Jiahui Chen (University of Arkansas)

Title:

Abstract:

Date: November 12

Speaker: Shuli Chen (U Chicago)

Title:

Abstract:

Date: November 19

Speaker: Matteo Raffaelli (Georgia Tech)

Title:

Abstract:

Date: December 3

Speaker: Martin Bauer (FSU)

Title:

Abstract: