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Today

Michael Redle, NC State, Well-Balanced Scheme for the Shallow Water MHD Equations with a New Divergence-Free Treatment of the Magnetic Field

Zoom

We consider the shallow water magnetohydrodynamic (SWMHD) equations, in which multiscale phenomena appear in geophysics, astrophysics, and energy production applications. However, capturing both large and small scales numerically requires an exact treatment of the physically-observed divergence-free condition of the magnetic field and typically a very fine spatial grid. An alternative to requiring a fine spatial…

Ailana Fraser, University of British Columbia, Geometries That Optimize Eigenvalues

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When we choose a metric on a manifold we determine the spectrum of the Laplace operator. Thus an eigenvalue may be considered as a functional on the space of metrics. For example the first eigenvalue would be the fundamental vibrational frequency. In some cases the normalized eigenvalues are bounded independent of the metric. In such cases…

Dave Shirokoff, New Jersey Institute of Technology, Implicit-Explicit (IMEX) Stability and Applications to the Dispersive Shallow Water Equations

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In this talk we will introduce a new stability theory for implicit-explicit (IMEX) time integration schemes—which treat some terms in a differential equation implicitly (for stability) and others explicitly (for efficiency).  Our focus will be on devising new efficient stable schemes for several fluid equations ranging from the incompressible Navier-Stokes equations, nonlinear diffusion equations, and…

Peter Olver, University of Minnesota Reconstruction and signatures of 3D bodies

Zoom

The talk will begin with the reconstruction of three-dimensional bodies from their two-dimensional projections.  Then I analyze the induced action of the Euclidean group on the body's projected outlines using moving frames, leading to a complete classification of the outline differential invariants and the associated outline signature of the body. Zoom invitation is sent to…

Sara Daneri, GSSI, Italy, On the sticky particle solutions to the pressureless Euler system in general dimension

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In this talk we consider the pressureless Euler system in dimension greater than or equal to two. Several works have been devoted to the search for solutions which satisfy the following adhesion or sticky particle principle: if two particles of the fluid do not interact, then they move freely keeping constant velocity, otherwise they join…

“What is an REU?” Presentation and Panel

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Are you an undergraduate interested in mathematical research and/or going to grad school?  Doing a Research Experience for Undergraduates (REU) is an excellent opportunity to try undergraduate research and add to your CV!  UUG is hosting the "What is an REU?" presentation and panel, with panelists including several previous REU attendees and an REU organizer to answer…

Tianyi Yu, UC San Diego, Grothendieck-to-Lascoux Expansions

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We establish the conjecture of Reiner and Yong for an explicit combinatorial formula for the expansion of a Grothendieck polynomial into the basis of Lascoux polynomials. This expansion is a subtle refinement of its symmetric function version due to Buch, Kresch, Shimozono, Tamvakis, and Yong, which gives the expansion of stable Grothendieck polynomials indexed by…

William Reese, NC State, Bayesian Level Set Approaches for Inverse Problems with Piecewise Constant Reconstructions

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There are several challenges associated with inverse problems in which the unknown parameters can be modeled as piecewise constant functions. We model the unknown parameter using multiple level sets to represent the piecewise constant function. Adopting a Bayesian approach, we impose prior distributions on both the level set functions that determine the piecewise constant regions…

Gregory Forest, UNC Chapel Hill, Modeling Insights Into SARS-CoV-2 Respiratory Tract Infections

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I and many collaborators, postdocs, and students from many disciplines have explored lung mechanics and disease pathology for over 2 decades in a pan-university effort called the UNC Virtual Lung Project. In the last decade we have explored how viruses “traffic” in mucosal barriers, including the human respiratory tract (RT), in the presence of antibodies.…

All Campus Data Science Career Expo

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Virtual Career Fair, Entrepreneurship Workshop and Industry Panel. Register for all 3 events at https://careers.dasa.ncsu.edu/data-science-career-expo/

Nishant Malik, Rochester Institute of Technology, Data-driven analysis of monsoon dynamics: ancient civilizational changes over South Asia to modern forecasting

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Monsoons are significant atmospheric phenomena that manifest over various regions in the tropics and have massive social and economic consequences. We will present hybrid methods that combine ideas from dynamical systems-based nonlinear time series analysis and machine learning and analyze the dynamics of the South Asian monsoon. Specifically, we will show two sets of results,…

Henrik Schumacher, Chemnitz University of Technology, Repulsive Curves and Surfaces

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I am going to report on recent work on the numerical optimization of tangent-point energies of curves and surfaces. After a motivation and brief introduction to the central computational tools (construction of suitable Riemannian metrics on the space of embedded manifolds, a polyhedral discretization of the energies, and fast multipole techniques), I am going to…

Erik Bates, University of Wisconsin-Madison, Making sense of disordered systems: what if Euclid, Newton, and Maxwell did probability?

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Disordered systems are mathematical models (typically of the physical world) that are governed by random variables.  These models have offered insights into a diverse array of research problems, and have also brought about a great number of powerful mathematical tools.  The through line to the subject is the essential role played by probability theory, a…

Brian Adams, Sandia National Lab, Make a Difference: Mathematical Sciences R&D Careers at Sandia National Laboratories

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 Brian Adams (NCSU PhD 2005) will conduct a mathematics and statistics-specific information session including a brief overview of SNL’s mission, R&D areas, and opportunities in mathematics, statistics, and computational science. Staff and project profiles will demonstrate the ways you can contribute to high-impact problems in the national interest through fundamental math and computational science R&D, software/hardware development,…

Cain Edie-Michell, UC San Diego, Algebras in tensor categories

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It is a classical result that the simple algebras in the category of finite dimensional vector spaces are precisely the n x n matrix algebras. The notion of algebras in more general tensor categories is easy to formulate, and we can ask for classification results in these categories. Such classification results have broad applications to conformal field…

Robin Morillo, NC State, Model Simplification Through Component Removal

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When dealing with large compartment models it can often be challenging to track how a small component of the model affects the overall system. This is an issue when trying to determine if a model is in its "simplest form" or if there are components that can be removed without significantly affecting the model's behavior.…

Jordan Almeter, NC State, P-graph Associahedra

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Graph associahedra are simple polytopes dual to tubing complexes based on graphs, where a tubing consists of compatible connected subgraphs of a graph G. Graph associahedra can be realized by repeatedly truncating faces of a simplex. We generalize graph associahedra to define P-graph associahedra, which can be realized by repeatedly truncating faces of a simple polyhedron P. When P is…