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A medial axis-based compactness measure vs. the eye test for detecting gerrymandering*

We, like many other researchers, are interested in providing a mathematical basis for determining the likelihood of whether a congressional or legislative district has been gerrymandered. A judicial precedent exists that one cannot define an exact notion of a district's degree of “compactness” but you “know it when you see it.” Our paper explores the [Read More...]

Presenter: Ellen Gasparovic, Union College
Authors: Jason D'Amico, Ellen Gasparovic, Greg Malen, and Mushan Zhong
Symposium Year: 2022
Session: Women in Computational Topology
Presentation Time: June 18, 2022; 11:30 am

A Network of Transition Pathways in a Soft-Sphere Model

Many intriguing dynamical properties of complex systems, such as metastability or resistance to applied forces, emerge from the underlying energy landscape. We probe the energy landscape of a granular material by modeling a jammed 2D packing of bidisperse disks as a collection of overlapping circles, defining an energy penalty based on the amount of [Read More...]

Presenter: Katie Newhall, University of North Carolina at Chapel Hill
Authors: Chris Moakler, Karen Daniels, Katie Newhall
Symposium Year: 2023
Session: Application of Monte Carlo Methods to Real-World Problems [Organized by Francesca Bernardi and Andrea Arnold]
Presentation Time: October 1, 2023; 10:35 am

A New Characterization of the Deligne-Du Bois Complex

Many singularities appearing in higher dimensional geometry are Du Bois. This is especially true in moduli theory, where Du Bois singularities play a key role. In this talk, we will examine known characterizations of Du Bois singularities and introduce a hyperresolution-free characterization of the entire Deligne-Du Bois [Read More...]

Presenter: Kristine Hampton, University of Washington
Symposium Year: 2022
Session: WiAG: Women in Algebraic Geometry
Presentation Time: June 18, 2022; 11:05 am

A Nonautonomous Free Boundary Model for Tumor Growth

A non-autonomous free boundary model for tumor growth will be introduced. The model consists of a nonlinear reaction diffusion equation describing the distribution of vital nutrients in the tumor and a nonlinear integro-differential equations describing the evolution of the tumor size. Global existence and uniqueness of solutions, existence and uniqueness [Read More...]

Presenter: Xiaoying (Maggie) Han, Auburn University
Authors: Wenlong Sun, Tomas Caraballo, Xiaoying Han, Peter Kloeden
Symposium Year: 2022
Session: Deterministic and Probabilistic Approaches for Nonlinear PDEs
Presentation Time: June 17, 2022; 3:55 pm

A novel tensor regularization of nuclear over Frobenius norms for low rank tensor recovery

We consider low-rank tensor recovery problems that include low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). Based on the tensor singular value decomposition (t-SVD), we propose the ratio of the tensor nuclear norm and the tensor Frobenius norm (TNF) as a novel nonconvex surrogate of tensor's tubal rank in LRTC [Read More...]

Presenter: Yifei Lou, University of Texas at Dallas
Authors: Huiwen Zheng, Guoliang Tian, and Chao Wang
Symposium Year: 2023
Session: Women in Tensor Optimization [Organized by Longxiu Huang and Jing Qin]
Presentation Time: September 30, 2023; 3:15 pm

A problem for a material surface attached to the boundary of an elastic semi-plane

A problem for a nano-sized material surface attached to the boundary of an elastic isotropic semi-plane is considered. A normal external traction is applied to a boundary of the material surface. The material surface is modeled using the Steigmann-Ogden form of surface energy. The problem is solved by using integral representations of stresses and [Read More...]

Presenter: Anna Zemlyanova, Kansas State University
Authors: Anna Zemlyanova
Symposium Year: 2023
Session: Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]
Presentation Time: October 2, 2023; 9:20 am

A quasi-Poisson structure on the multiplicative Grothendieck-Springer resolution*

The Grothendieck-Springer resolution of a semisimple complex group G carries a canonical Poisson structure whose symplectic leaves are affine bundles over the flag variety. This structure is obtained by Hamiltonian reduction of the cotangent bundle T*G with respect to the action of a Borel. We construct a multiplicative counterpart to this setting by [Read More...]

Presenter: Ana Balibanu, Harvard University
Authors: Ana Balibanu, Maxence Mayrand
Symposium Year: 2022
Session: Geometric and Categorical Aspects of Representation Theory and Related Topics
Presentation Time: June 19, 2022; 10:05 am

A Sharp Divergence Theorem with Non-Tangential Traces

The Integration by Parts Formula, which is equivalent with the Divergence Theorem, is one of the most basic tools in Analysis. Originating in the works of Gauss, Ostrogradsky, and Stokes, the search for an optimal version of this fundamental result continues through this day and these efforts have been the driving force in shaping up entire sub-branches of [Read More...]

Presenter: IRINA MITREA, Temple University
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 19, 2022; 10:05 am

A Simplified Mathematical Model For Erosion and Deposition in a Porous Medium

In this study, we investigate the dynamic processes of erosion and deposition in a porous medium that occur when the solid internal morphology of the porous medium interacts with fluids at its contact interface. These phenomena are encountered in both natural settings, such as soil erosion, and various industrial applications, like water filtration devices [Read More...]

Presenter: Priyanka Joseph, Georgia State University
Authors: Priyanka Joseph, Sai Kunnatha, Kulsum Saber, Emeka Peter Mazi, Dr, Pejman Sanaei
Symposium Year: 2023
Session: Poster Presentation
Presentation Time: September 30, 2023; 4:10 pm

A Simplified Model for Cell Proliferation in a Tissue-Engineering Scaffold

Tissue engineering is a burgeoning multidisciplinary field that aims to regenerate damaged tissues and organs by cultivating artificial tissue outside the human body. Central to tissue engineering is the design and fabrication of scaffolds, which serve as templates for tissue growth and regeneration. Environmental factors such as flow rate, shear stress, and [Read More...]

Presenter: Amy María Sims, Georgia State University
Authors: Mona James, Ashok Joseph, Paul Joseph, Sai Kunnatha, Amy María Sims, Haniyeh Fattahpour, Pejman Sanaei
Symposium Year: 2023
Session: Poster Presentation
Presentation Time: October 1, 2023; 3:45 pm

A Spectral Target Signature for Thin Surfaces with Higher Order Jump Conditions

In this talk, we consider the inverse problem of determining the structural properties of a thin anisotropic and dissipative inhomogeneity from scattering data. In the asymptotic limit, as the thickness goes to zero, the thin inhomogeneity is modeled by an open m-1 manifold(here referred to as screen), and the field inside is replaced by jump conditions on [Read More...]

Presenter: Heejin Lee, Purdue University
Authors: Fioralba Cakoni, Heejin Lee, Peter Monk and Yangwen Zhang
Symposium Year: 2023
Session: Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]
Presentation Time: September 30, 2023; 2:50 pm

A Statistical Analysis of Strategies of Machi Koro

Machi Koro is a game where players take turns rolling dice and buying different “properties”, or cards, for their “town.” Each card has a number which corresponds to a dice roll. If a player rolls that particular number, they make money. There are many different strategies that can be used but players are often forced to think about probabilities and [Read More...]

Presenter: Danya Morman, University of Wisconsin Eau-Claire
Authors: Danya Morman
Symposium Year: 2022
Session: Poster Presentation
Presentation Time: June 17, 2022; 2:45 pm

A Study of Illumination Filtering and Movement Detection in Video Streaming Processing

We study a movement detection scheme for video streaming data using time series analysis. We employ simple scalar quantities such as (i) the Frobenius norm trajectory of a forward difference matrix and (ii) the Auto-correlation function to analyze the time series and detect movements in the video sequences. To remove the background interruptions, such as [Read More...]

Presenter: Phuong Mai Nguyen, University of North Carolina at Charlotte
Authors: Phuong Mai Nguyen, Xingjie Li
Symposium Year: 2022
Session: Contributed Talk
Presentation Time: June 19, 2022; 9:15 am

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