Walk the Walk, Chalk the Chalk
Fall 2026:
9/8/26: Ziyal Jandrasi - A Brief Introduction to Algebraic Geometry (Notes)
Abstract: This talk aims to whet the appetite of young graduate students unfamiliar with the field of algebraic geometry. We introduce some of the basic objects and operations in algebraic geometry, such as (affine) algebraic varieties, tangent spaces, blowups, and (smooth) schemes. Along the way, we will see numerous examples and compare to the study of geometry through manifolds. A background in algebra and likely also topology will be necessary to understand this talk.
9/15: Chris Boehlert - Ingredients of Mathematical Gauge Theory
Abstract: Over the past 50 years the same high powered idea has lead to advancements in both pure mathematics and theoretical physics; that of a gauge theory. Simply stated, albeit opaquely, gauge theory is the study of connections on principal bundles, generalizing the notion of curvature. We will clarify this statement by exploring the ingredients (principal bundles and connections) through a number of tangible (i.e., drawable) examples. This talk will be primarily conceptual without too many rigorous definitions. The goal is for everyone to leave with at least an inchoate conception of the mathematical structures underlying modern particle physics.
9/22: Lucus Brady - Unsharp Bases
Abstract: In this talk, we look at how we can utilize probability measures and Markov kernels to describe random bases for vector spaces.
9/29: Alex Ballow - 2 dimensional Factorization Homology
Abstract: We aim to integrate a 2-category over a (framed) surface: this is a purely combinatorial implementation of factorization homology. We will discuss intuitively what factorization homology is, focusing first on a combinatorial definition of factorization homology over the circle. This example is interesting in its own right as a generalized Hochschild homology. To extend this definition to surfaces, we define 2-dimensional quivers and consider representations of such in a 2-category. We finish with a discussion of string-nets to motivate the correspondence between factorization homology of a surface and a derived version of the TQFT Turaev-Viro.
10/6: Nicole Kamarat - Observation Point Order Effects on Scalable Spatial Stream Networks
Abstract: Protecting freshwater habitats is vital for supporting diverse fish, wildlife, and surrounding human communities. To accurately monitor these ecosystems, Spatial Stream Network (SSN) models were developed to account for the complex topology of river networks. Scalable Spatial Stream Network (S3N) models improve computational efficiency by utilizing a Nearest Neighbor Gaussian Process (NNGP) to optimize storage requirements for estimation and prediction. S3N and NNGP performance depend on observation point order, and Guinness (2018) demonstrated the choice of permutation can enhance model fit on rectangular planes. This study extends these findings to river networks by evaluating four distinct point-ordering permutations to determine their influence on S3N model goodness of fit and computational efficiency. Using simulated data, we investigate breadth-first or depth-first searches, originating from the most upstream or most downstream observation point. As this research is ongoing, preliminary findings on the impact of systematic versus random ordering will be presented.