# Past Events

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## March 2021

### Our muscles aren’t one-dimensional fibres (Prof. Nilima Nigam)

Title: Our muscles aren't one-dimensional fibres. Abstract: Skeletal muscles possess rather amazing mechanical properties. They possess an intricate structure, and behave nonlinearly in response to mechanical stresses. In the 1910s, A.V. Hill observed muscles heat when they contract, but not when they relax. Based on experiments on frogs he posited a mathematical description of skeletal muscles which approximated muscle as a 1-dimensional nonlinear and massless spring. This has been a remarkably successful model, and remains in wide use. Recently, we've…

Find out more »### Applied math. talk: Hyperbolicity-Preserving Stochastic Galerkin Method for Shallow Water Equations by Dihan Dai, Department of Mathematics, University of Utah

Abstract: The system of shallow water equations and related models are widely used in oceanography to model hazardous phenomena such as tsunamis and storm surges. Unfortunately, the inherent uncertainties in the system will inevitably damage the credibility of decision-making based on the deterministic model. The stochastic Galerkin (SG) method seeks a solution by applying the Galerkin method to the stochastic domain of the equations with uncertainty. However, the resulting system may fail to preserve the hyperbolicity of the original model.…

Find out more »### An ideal convergence: an example in noncommutative metric geometry (Prof. Konrad Aguilar)

Title: An ideal convergence: an example in noncommutative metric geometry Abstract: The ability to calculate the distance between sets (rather than just distance between points) has found applications in geometry and group theory as well as various branches of applied mathematics. The Hausdorff distance and the Gromov-Hausdorff distance are standard distances used in these applications. Moreover, a certain generalization of the Gromov-Hausdorff distance called the quantum Gromov-Hausdorff distance was built by M. A. Rieffel to answer some questions from physics…

Find out more »## April 2021

### Alexandria Volkening

Title: How do zebrafish get their stripes — or spots? Abstract: Many natural and social systems involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, voters in an election, or locusts in a swarm. Self-organization also occurs at much smaller scales in biology, though, and here I will focus on elucidating how brightly colored cells interact to form skin patterns in fish. Because they are surprisingly similar to humans genetically, we…

Find out more »### Applied math. talk: Large Eddy Simulation Reduced Order Models by Traian Iliescu, Virginia Tech

In this talk, we present reduced order models (ROMs) for turbulent flows, which are constructed by using ideas from large eddy simulation (LES) and variational multiscale (VMS) methods. First, we give a general introduction to reduced order modeling and emphasize the connection to classical Galerkin methods (e.g., the finite element method) and the central role played by data. Then, we describe the closure problem, which represents one of the main obstacles in the development of ROMs for realistic, turbulent flows. …

Find out more »### Jennifer Taback

Title: Groups, Graphs and Trees Abstract: What do we mean by the geometry of a group? Groups seem like very abstract objects when we first study them, and it's natural to ask whether we can visualize them in some way. Given a group with a finite set of generators and relators, I will describe a canonical way to construct a geometric model of that group, called a Cayley graph. We will see many examples -- both standard and unusual --…

Find out more »### Applied math. talk: Adversarially robust classification via geometric flows, by Ryan Murray, North Caroline State University

Abstract: Classification is a fundamental task in data science and machine learning, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However, recently there have been a number of works demonstrating that these improved algorithms can be "fooled" using specially constructed adversarial examples. In turn, there has been increased attention given to creating machine learning algorithms which are more robust against adversarial attacks. In this talk I will describe a recently…

Find out more »### Haydee Lindo

Title: Trace Ideals and Endomorphism Rings Abstract: In many branches of mathematics, the full set of "functions" between two objects exhibits remarkable structure; it often forms a group and in some special cases it forms a ring. In this talk, we will discuss this phenomenon in Commutative Algebra. In particular, we will talk about the endomorphism ring formed by the homomorphisms from a module to itself by first looking at commuting square matrices. I'll also introduce the trace ideal and…

Find out more »### Applied Math. Talk: Balancing Geometry and Density: Path Distances on High-Dimensional Data by Anna Little, University of Utah

Abstract: This talk discusses multiple methods for clustering high-dimensional data, and explores the delicate balance between utilizing data density and data geometry. I will first present path-based spectral clustering, a novel approach which combines a density-based metric with graph-based clustering. This density-based path metric allows for fast algorithms and strong theoretical guarantees when clusters concentrate around low-dimensional sets. However, the method suffers from a loss of geometric information, information which is preserved by simple linear dimension reduction methods such as…

Find out more »### Jennifer Franko Vasquez

Title: Puzzling Permutations Abstract: Permutations are one of the most fundamental notions in mathematics. In this talk, we will discuss a visual representation of permutations and introduce some games one can play to help "see" different properties. These puzzling games can be used to provide insight into deeper mathematical content as well. Time permitting, we will explore connections to topology and biology. This talk is based on joint work with Steven Dougherty and Michael Allocca. Dr. Vasquez is a Professor…

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