Fall 2021 NC State Mathematics Graduation Ceremony
SAS 2203The Math Graduation Ceremony for will be held on Tuesday December 14 at 3:00 pm in 2203 SAS Hall.
Events
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Marissa Loving, Georgia Institute of Technology, Symmetries of Surfaces: Big and Small
ZoomWe will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the…
Alperen Ergur, University of Texas at San Antonio, Toward an Algorithmic Theory of Real Polynomials
ZoomI will present problems arising from biochemical reaction networks, optimization, computer science, and complexity theory. These problems share the following characteristics: 1) they can be modeled by multivariate polynomials, 2) they demand different theorems than the ones offered by the traditional theory of computation and state-of-the-art theory of polynomials. I will present recent results that blend…
Kyle Hayden, Columbia University, Braids and Badly Behaved Surfaces
ZoomThe topology of smooth manifolds is governed largely by geometry in low dimensions and by algebraic topology in high dimensions. The phase transition occurs in dimension four, leading to "exotic" phenomena where continuous and differential topology diverge sharply. I will begin by surveying some ways that surfaces can be used to investigate this phase transition. Then I…
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.
Caroline Moosmueller, University of California San Diego, Efficient learning algorithms through geometry, and applications in cancer research
ZoomIn 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…
Alice Nadeau, Cornell University, Mathematical Causes of Tipping Points: Bifurcations and Heteroclinic Connections in Time
ZoomQualitatively, 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…
Theresa Anderson, Purdue University, Two meetings of analysis and number theory
ZoomIn 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
Nan Chen, University of Wisconsin-Madison, Conditional Gaussian Nonlinear System: a Fast Preconditioner and a Cheap Surrogate Model For Complex Nonlinear Systems
ZoomDeveloping 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…
David Padgett, Vadum, Different aspects of how machine learning and artificial intelligence algorithms can be used in national defense
Poe 218Founded 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…
Romit Maulik, Argonne National Laboratory, Emulating complex systems from data using scientific machine learning
ZoomIn 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…
Lili Yan, University of California Irivine, Inverse boundary problems for biharmonic operators and nonlinear PDEs on Riemannian manifolds
ZoomIn 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…
Barbara Keyfitz, The Ohio State University, Hyperbolic Conservation Laws and Stability in L^2
ZoomRecently 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…
Shiliang Gao, University of Illinois at Urbana-Champaign, Newell-Littlewood numbers
ZoomJointly 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.…
Terry Rockafellar, University of Washington, Augmented Lagrangian Methods and Local Duality in Nonconvex Optimization
ZoomAugmented 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…
Rayanne Luke, Johns Hopkins University, Parameter Estimation for Tear Film Breakup
ZoomDry 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…
Ella Pavlechko, Determination of a strictly convex Riemannian manifold from partial travel time data
SAS 4201In 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…
Teemu Pennanen, King’s College London, Convex duality in nonlinear optimal transport
ZoomWe 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 Cook, NC State Alumni, Mathematics in Industry
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…