Date Event Type Event Name Abstract
03/01/2021 Geometry-Topology Seminar Summaries and Distances for Topological Data Analysis Topological data analysis starts with encoding data as a diagram of topological spaces. To this diagram we apply standard topological, algebraic, and combinatorial tools to produce a summary of our data. Next, we would like to be able perform a quantitative analysis. I will show how a distance,...
02/26/2021 M.Sc. Presentation Consolidation with Hysteresis in Sedimentary Basins The necessitation for modeling various mechanical processes in porous media, such as consolidation and compaction, arises in several applied sciences. Within the context of sedimentary basins, we develop a model for consolidation with a permanent effect, a phenomena commonly observed in basin...
02/26/2021 Applied Mathematics and Computation Seminar Sampling of bandlimited functions with faster convergence A family of sampling theorems for the reconstruction of bandlimited functions from their samples is presented. Taking one or more additional samples is shown to yield more rapidly convergent series with lower truncation errors, as well as to facilitate the reconstruction of functions of polynomial...
02/25/2021 Ph.D.Defense Virtual Element Methods for Magnetohydrodynamics in Polygonal and Polyhedral Meshes The aim of this presentation is to construct a virtual element methods (VEM) for models in magneto-hydrodynamics (MHD), an area that studies the behavior and properties of electrically conducting fluids such as a plasma. MHD models are a coupling of the Maxwell's equations for electromagnetics and...
02/23/2021 Number Theory Seminar An Introduction to Symbolic Dynamics: Fun with Markov Partitions and Shift Spaces A casual, introductory talk defining shift spaces, a useful type of dynamical system, and Markov Partitions, a type of topological partition that can be used to represent a more general dynamical system using a shift space.
02/22/2021 Geometry-Topology Seminar Perfect generalized Fibonacci groups H(r,n,s) Cyclically presented groups are a class of finitely presented groups with a balanced presentation that is equipped with cyclic symmetry. An example of such groups is the generalized Fibonacci group H(r,n,s). A conjecture of Williams states that "if H(r,n,s) is perfect then either r or s is...
02/19/2021 Applied Mathematics and Computation Seminar Multiscale Modeling of Microbial Community Metabolism with Flux Balance Analysis The environment and the microbial community structure and function are often intimately connected. Most environments outside of the lab are physically and chemically heterogeneous, shaping and complicating the metabolisms of their resident microbial communities. On one hand, spatial variations...
02/12/2021 Applied Mathematics and Computation Seminar Flow simulations with mass conservation and viscous stresses In the first part of this talk my goal is to convey the importance of mass conservation in fluid flow simulations in an accessible manner. Mass conservation will be seen as one of two important structure preservation properties that are desirable for Stokes flow approximations. It is related to the...
02/09/2021 Number Theory Seminar The specification property of dynamical systems on the Sierpinski carpet We first construct a dynamical system induced from a hyperbolic toral map on the square torus. Then we proceed on to investigate one dynamical property called the (Bowen) specification property. In particular, we are interested if this property which holds on torus still holds on the induced system...
02/08/2021 Geometry-Topology Seminar Non-negative curvature and torus actions The classification of Riemannian manifolds with positive and non-negative sectional curvature is a long-standing problem in Riemannian geometry. In this talk I will give an overview of known results and summarize joint work with Catherine Searle on the classification of closed, simply-connected,...
02/05/2021 Applied Mathematics and Computation Seminar Modeling of geoelectric fields in the U.S. for hazard analysis and situational awareness Estimation of ground-level geoelectric fields has been identified by the electrical power industry as a key capability in assessment and mitigation of the impacts of space weather on electrical power infrastructure. In response to this societal need, an operational system to produce locally...
02/01/2021 Department Colloquium Homological Tools for Data The past two decades has witnessed a dramatic burst of applications of topological thinking and theorems in the applied sciences, ranging from statistics to sensor networks, neuroscience, and more, to be surveyed here. Several challenges remain, including: (1) how to compute topological quantities...
02/01/2021 Geometry-Topology Seminar No seminar this week. Please attend the colloquium at 4 pm.
01/29/2021 Applied Mathematics and Computation Seminar Classification of 3D point cloud LiDAR data Abstract LiDAR point clouds contain measurements of complicated natural scenes and can be used to update digital elevation models, glacial monitoring, detecting faults and measuring uplift detecting, forest inventory, detect shoreline and beach volume changes, landslide risk analysis, habitat...
01/26/2021 Number Theory Seminar Fuchsian groups from finite data
01/25/2021 Department Colloquium Kinetic models of particle systems Kinetic models are used to simulate the collective behavior of particle systems. They provide a mesoscopic description that forms a link between continuum fluid models, which are not valid in non-equilibrium settings, and molecular dynamics models, which are often too expensive for practical...
01/25/2021 Geometry-Topology Seminar The Diagram Quest A semiregular symmetry in a graph is a symmetry which moves all the vertices in cycles of the same length. The ‘diagram' of such a symmetry has one ’node’ for each cycle and links joining nodes, one for each orbit of edges joining vertices of those cycles. We will see wht we can learn about the...
01/22/2021 Applied Mathematics and Computation Seminar Numerical Approximation of Parabolic SPDE's Convergence theory for numerical schemes to approximate solutions of stochastic parabolic equations of the form $$du + A(u) \, dt = f \, dt + g \, dW, \qquad u(0)=u^0,$$ will be reviewed. Here $u$ is a random variable taking values in a function space $U$, $A:U \rightarrow U'$ is partial...
01/15/2021 Applied Mathematics and Computation Seminar Detecting anomalies in the 2020 election Election systems are critical infrastructure, protecting elections is part of national security. The right to vote, and to know that the winners are legitimate, is fundamental to American democracy. This talk will present the election data ecosystem and practical challenges to consolidating data...
01/11/2021 Department Colloquium Horofunctions, Fixed Points, and Illuminating the Unit Ball A central problem in metric fixed point theory is to understand when a nonexpansive (i.e. Lipschitz with constant 1) self-map of a metric space has a fixed point. Even in the case where the metric space is a finite dimensional normed space, this is a subtle problem, as the map need not be a...