Spring 2022 Math Department Meeting
SAS 4201Math Department Faculty & Staff Please reserve this date/time for our Beginning of the Semester Department Meeting. Zoom link will be sent by email.
Math Department Faculty & Staff Please reserve this date/time for our Beginning of the Semester Department Meeting. Zoom link will be sent by email.
In this talk, I will discuss how incorporating geometric information into classical learning algorithms can improve their performance. The main focus will be on optimal mass transport (OMT), which has evolved as a major method to analyze distributional data. In particular, I will show how embeddings can be used to build OMT-based classifiers, both in supervised and unsupervised learning settings. The proposed framework significantly…
Qualitatively, a tipping point in a dynamical system is when a small change in system inputs causes the system to move to a drastically different state. The discussion of tipping points in climate and related fields has become increasingly urgent as scientists are concerned that different aspects of Earth’s climate could tip to a qualitatively different state without…
In many recent works, analysis and number theory go beyond working side by side and team up in an interconnected back and forth interplay to become a powerful force. Here I describe two distinct meetings of the pair, which result in sharp counts for equilateral triangles in Euclidean space and statistics for how often a random polynomial has Galois group not isomorphic to the full symmetric group. https://ncsu.zoom.us/j/91896366693?pwd=YnFuZURGc1NNenRTQ3YrbjVTK0dQZz09 Meeting ID: 918 9636 6693 Passcode: 875811
Developing suitable approximate models for analyzing and simulating complex nonlinear systems is practically important. This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian nonlinear system (CGNS), as both a cheap surrogate model and a fast preconditioner for facilitating many computationally challenging tasks. The CGNS…
Founded in 2004, Vadum delivers cutting-edge solutions to customers in the competitive field of national defense research and development. Vadum got its start developing innovative tools and techniques to protect personnel from improvised explosive devices used in Iraq and Afghanistan. Vadum has grown to tackle larger and more complex defense challenges in a range of…
In this talk, I will present recent research that builds fast and accurate data-driven surrogate models (or emulators) for various complex and high-dimensional systems. Furthermore we will use scientific machine learning techniques in lieu of black-box data-driven methods. In other words, not only will our models be informed by data, but they will also be…
In an inverse boundary problem, one seeks to determine the coefficients of a PDE inside a domain, describing internal properties, from the knowledge of boundary values of solutions of the PDE, encoding boundary measurements. Applications of such problems range from medical imaging to non-destructive testing. In this talk, starting with the fundamental Calderon inverse conductivity…
Recently there has been considerable research into the stability of shocks in systems of conservation laws, with stability understood in some square-integrable sense. In this talk I will give some background on systems of nonlinear hyperbolic partial differential equations (known as conservation laws), and on the issues concerning well-posedness. There are reasons that the still-unsolved…
Jointly in person and virtually on Zoom. SAS 4201 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at cmjones6@ncsu.edu to be added. Abstract: The Newell-Littlewood numbers are defined in terms of the Littlewood-Richardson coefficients. Both arise as tensor product multiplicities for a classical Lie group. A.…
Augmented Lagrangians were first employed in an algorithm for solving nonlinear programming problems with equality constraints. However, the approach was soon extended to inequality constraints and shown in the case of convex programming to correspond to applying the proximal point algorithm to solve a dual problem. Recent developments make it possible now to articulate that…
Dry eye disease is caused by a breakdown of a uniform tear film, which occurs when the layer of tears experiences breakup. To better understand this ocular condition, the dynamics of the tear film can be studied using fluorescence imaging. Many parameters affect tear film thickness and fluorescent intensity distributions over time; exact values or…
In this talk I will introduce a geometric inverse problem that is motivated by geophysical imaging and seismology. Specifically, I will reconstruct a compact Riemannian manifold with strictly convex boundary from wave-based data on the boundary. The given data assumes the knowledge of an open measurement region on the boundary, and that for every point…
We study problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of alarge class of related problems in probability theory and allows for generalizations of the classical problem formulations. General results on convex duality yield dual problems and optimality conditions for these problems.…
Jared finished his Ph.D. in Applied Math at NC State two years ago and since then has been working at Teledyne Technologies in their Intelligent Systems Lab. During that time he primarily worked on DARPA contracts, but also worked on internal research and development projects. He will be discussing his work on a power lines detection…
In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either only one vertex or only one hyperedge. When a player chooses to remove one vertex, all of the hyperedges that contain the chosen vertex are also removed.…
The capability of using imperfect statistical reduced-order models to capture crucial statistics in complex turbulent systems is investigated. Much simpler and more tractable block-diagonal models are proposed to approximate the complex and high-dimensional turbulent dynamical equations using both parameterization and machine learning strategies. A systematic framework of correcting model errors with empirical information theory is…
Waists and widths measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds, as well as applications to quantitative symplectic camels. Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact Peter McGrath…