Title: Horofunction Boundaries of Horospherical Products of Spaces

Abstract: Diestel-Leader graphs were introduced in connection with a question of Woess about vertex-transitive graphs not quasi-isometric to any Cayley graph, a phenomenon later confirmed by Eskin, Fisher, and Whyte. In this talk, I will discuss geometric and topological properties of horospherical products of trees and some ongoing joint work on their horofunction compactification with the goal of understanding how convergence in the individual coordinates relates to convergence in the horofunction compactification.

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Title: Measuring a Century of Film Style: Statistical Evidence for the Formation and Erosion of a Classical-Era Relationship

Abstract: Shot pacing and shot framing are among the most important formal elements of film style in filmmaking practice and film scholarship. I present a pipeline that measures both using a fine-tuned shot-boundary network (TransNetV2), a figure detector distilled from a zero-shot model (Grounding DINO to YOLO), and a zero-shot image-text model (SigLIP 2), validated against human judgments under a stratified design with known inclusion probabilities. Because a film archive is not a sample from any population, I then develop an inferential framework for closed corpora. An ANOVA-style decomposition carries design-based measurement uncertainty into the historical estimates, and Fisherian randomization inference over era labels, permuting films rather than shots, replaces confidence intervals on the historical claims. Applied to over 2,000 films across three corpora built on different selection logics (box-office hits, Academy Award nominees, critics' polls), the framework reveals a consistent arc. The tendency to hold wider, more populated shots longer, measured as the within-film association between shot scale and shot duration, is a historical formation rather than a constant of the medium: weak in silent film, peaking in the early sound era, and eroding thereafter, with the slope shrinking by roughly a factor of four. Recent films lie closer to the silents than to the 1930s. I close by showing how this extends existing accounts of post-1960s style, and by outlining the measurement-error questions (differential misclassification, SIMEX-style extrapolation) that my current research takes up.

Taylor Arnold is Professor of Data Science and Statistics at the University of Richmond, where he co-directs the Distant Viewing Lab. His work on multimodal computational methods for visual culture has been supported by the NEH, the Mellon Foundation, and Schmidt Sciences. He is the co-author of Distant Viewing (MIT Press, 2023), A Computational Approach to Statistical Learning (CRC Press, 2019), and Humanities Data in R, 2nd ed. (Springer, 2024). Prior to joining Richmond, Arnold held research positions in statistics and machine learning at AT&T Labs, Travelers R&D, and IBM.

* Refreshments start at 3:45

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Title: A Characterization of Size 2 Orbits of Plane Partitions Under Rowmotion

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Affiliation: Colorado State

Title: Weak Galerkin Finite Element Solvers for Linear and Nonlinear Poroelasticity
Abstract: This talk presents a family of any order finite element solvers for both linear and nonlinear poroelasticity problems. The backward differentiation formulas (BDFs) are used for temporal discretizations, whereas the weak Galerkin (WG) finite elements on quadrilaterals are utilized for spatial discretizations. For the latter, the discrete weak gradients of finite element shape functions are established in the vector- or matrix-version local Arbogast-Correa spaces. Such combinations of BDF and WG discretizations produce numerical solutions that have well-balanced spatial and temporal errors in all six quantities, namely, displacement, dilation (divergence of displacement), stress, pressure, velocity, and normal flux. For nonlinear poroelasticity problems in which permeability depends on solid dilation or the mean stress, Picard iterations are employed to solve the resulting nonlinear algebraic systems. Rigorous analysis together with numerical experiments demonstrates that these new solvers have optimal-order convergence and are free of locking.

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Title: TBA

Abstract: TBA

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Affiliation: Baylor University

Title: TBA

Abstract: TBA

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Title: Permutation Sorting and the Basis of Foot-sortable Sock Orderings

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Title: Well Posedness and Finite Element Convergence for a Stationary Magnetic Induction Heating Problem
Abstract: We study a coupled elliptic system which models a stationary magnetic induction heating problem in two dimensions. The model couples a complex-valued magnetic field with a real-valued temperature through temperature-dependent material coefficients and a nonlinear Joule heating source. We also attach a nonlinear radiation boundary condition to the thermal equation. Assuming continuous, uniformly bounded, and strictly positive material coefficients, we establish existence of a weak solution on bounded Lipschitz domains. Higher integrability estimates for the solutions to the magnetic and thermal equations provide the regularity and compactness needed for a Schauder fixed-point argument. We also consider a conforming piecewise linear finite element approximation on a polygonal domain. We then prove existence of discrete solutions, derive a priori bounds independent of the mesh size, and establish convergence along a subsequence to a weak solution of the coupled system. In particular, the magnetic field converges strongly in $H^1(\Omega; \mathbb{C})$, and a discrete commutator argument identifies the weak limit of the nonlinear Joule heating term.

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Affiliation: Texas A&M University

Title: TBA

Abstract: TBA

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Speaker: Prof. Gabriela Jaramillo

www.math.uh.edu/~gabriela/

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Title: TBA

Abstract: TBA

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Speaker: Prof. Atanas Stefanov

https://www.uab.edu/cas/mathematics/people/faculty-directory/atanas-stefanov

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Title: TBA

Abstract: TBA

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Affiliation: Texas A&M University

Title: Pointwise error estimates for optimal recovery of solutions to Poisson's Equation

Abstract: We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown but belongs to a model class. A finite number of measurements of the solution to recover are provided to alleviate the lack of information. This presentation focuses on the case where measurements consist of point evaluations on the interior of the computational domain. A key ingredient in the algorithm for numerically computing an optimal recovery is the finite element approximation of the Riesz representers associated with the point evaluation at the measurement locations. Our main result is a pointwise error estimate for the Riesz representers, and we apply this result to obtain sharper estimates measuring the performance of the recovery algorithm in H^1, L-infinity, and for quantities of interest. Numerical results confirm the theoretical error rates in the mesh parameter. Finally, related problems and the discussion of this project within a broader research program will be discussed.

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Title: TBA

Abstract: TBA

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Title: TBD

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