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Colloquium: Thomas J.R. Hughes, University of Texas at Austin, The Finite Element Method and Computational Mechanics: Past, Present, and a Vision of the Future

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I will begin by probing into the past to discover the origins of the Finite Element Method (FEM), and then trace the evolution of those early developments to the present day in which the FEM is ubiquitous in science, engineering, mathematics, and medicine, and the most important discretization technology in Computational Mechanics. However, despite its…

Differential Equations and Nonlinear Analysis Seminar: Theodore D. Drivas, Stony Brook University, Remarks on the long-time dynamics of 2D Euler

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We will discuss some old and new results concerning the long-time behavior of solutions to the two-dimensional incompressible Euler equations. Specifically, we discuss whether steady states can be isolated, wandering for solutions starting nearby certain steady states, singularity formation at infinite time, and finally some results/conjectures on the infinite-time limit near and far from equilibrium.…

Symbolic Computation: Parker Edwards, University of Notre Dame, Feature Sizes and Bottlenecks for Algebraic Manifolds

SAS 4201

 In computational topology and geometry, theoretical guarantees for algorithms often take the following form: Start with a finite sample of points from a subspace of . If the sample is "dense enough" with respect to the subspace, then the algorithm outputs a quantity of interest for the subspace, for example its Betti numbers. The quantities associated…

Pure Math Graduate Student Seminar: Kylan Schatz, NC State, Abelian 3-cocycles from Quadratic Forms – Quinn’s Formula

SAS 2235

For some nice subclass of braided monoidal categories, the associator and braiding data are described by an Abelian 3-cocycle . Eilenberg and MacLane demonstrated a surprisingly simple isomorphism between the groups of Abelian 3-cocycles with coefficients in  and quadratic forms with coefficients in , the trace map  by . Like many category theoretical results, this was proven at the level of…

Numerical Analysis: Bao Wang, The University of Utah, Implicit Methods for Deep Learning

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At the heart of modern deep learning is the deep neural nets accompanied by stochastic optimization and sampling algorithms. These architectures and algorithms have an explicit flavor. In particular, traditional deep nets compose affine and simple nonlinear transformations, defining an explicit function for representation learning. The explicit deep nets lack flexibility and adaptivity for modeling…

SIAM Seminar: Make a Difference – Mathematical Sciences R&D Careers at Sandia National Laboratories

SAS 4201

ake a Difference: Mathematical Sciences R&D Careers at Sandia National Laboratories   R&D Staff from Sandia National Laboratories will be on campus recruiting top NCSU math and statistics students. With sites in NM and CA, SNL is a Department of Energy laboratory conducting wide-ranging science and engineering R&D supporting national security. Please join us for an info session and…

Geometry and Topology Seminar: Ali Feizmohammadi, University of Toronto, Lorentzian Calderón problem under curvature bounds

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We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The set of Lorentzian metrics satisfying the curvature bounds has a non-empty interior in the sense of smooth, compactly supported perturbations of the metric, whereas all…

Special Event: National Consortium for Data Science (NCDS), Analyzing Data Science Careers

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2022 NCDS Fall Career Panel: Analyzing Data Science Careers | October 19 at 12 PM ET | Virtual Early career professionals and students won’t want to miss these data science professionals provide insight into what it takes to capture the attention of top recruiters in data science and data analytics. Our panelists represent a variety of…

Differential Equations and Nonlinear Analysis Seminar: Michel De Lara, Cermics, École des Ponts ParisTech, France, Hidden Convexity in the l_0 Pseudonorm

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The so-called $l_0$ pseudonorm counts the number of nonzero components of a vector. It is standard in sparse optimization problems. However, as it is a discontinuous and nonconvex function, the l0 pseudonorm cannot be satisfactorily handled with the Fenchel conjugacy. In this talk, we review a series of recent results on a class of Capra…

SIAM Seminar: PNNL Info Session

SAS 4201

PNNL will have an info session here on Wednesday (Oct 19) at 4:30-5:30 pm in SAS 4201 and via zoom. Free food will be provided. You will learn about the types of job/research opportunities at PNNL, hear about the experiences of NCSU alumni who are currently working there, and speak with a recruiter directly! Hope to…

Special Event: Dr. Cornelia Van Cott, University of San Francisco, The Mathematics of Card Shuffling

SAS 2203

 If you're handed an unshuffled deck of cards, you'll likely attempt to do a so-called perfect shuffle. A perfect shuffle splits a deck of cards into two equal stacks and then perfectly interlaces the cards from the two stacks. Only experienced gamblers and magicians can perform perfect shuffles reliably, and yet the mathematics behind perfect…

Special Event: The Virginia Tech Regional Mathematics Contest

SAS 4201

It is time again to prepare for the VTRMC -- The Virginia Tech Regional Mathematics Contest, which  is sponsored by the Mathematics Department at Virginia Tech. The contest began in 1979 and has grown to the point where over 100 schools with over 700 contestants participate in a typical year. This year's VTRMC competition will take place on     - Saturday October 22, 2022, 9:00 AM-11:30…

Pure Math Graduate Student Seminar: Reeshad Arian, NC State, RT invariance of 3 manifolds

SAS 2235

Ed Witten's papers in 1988 drew out the connection between Jones Polynomials of Knots and Chern-Simons theory of 3-dimensional TQFT. Following his work, Reshetikhin and Turaev formulated invariants of 3-manifolds via colored framed knots leading to new TQFTs. In this talk, I will introduce Dehn Surgery on knots, framed knots colored with representations of Hopf…

Numerical Analysis Seminar: Ngoc T. Do, Missouri State University, Full Field Photoacoustic Tomography with Variable Sound Speed

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Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT, the measured data consist of time-dependent signals measured on an observation surface. In contrast, the measured data from the recently invented full-field detection technique…

Geometry and Topology Seminar: Giada Franz, MIT, Construction and properties of free boundary minimal surfaces

SAS 4201

A free boundary minimal surface (FBMS) in a given three-dimensional Riemannian manifold is a critical point of the area functional with respect to variations that constrain its boundary to the boundary of the ambient manifold. We will talk about the existence of FBMS, with particular emphasis on an equivariant min-max method and on the computation…

Algebra and Combinatorics Seminar: Sarah Mason , Wake Forest University

SAS 2225

Speaker’s webpage: https://users.wfu.edu/masonsk/ Location: Jointly in person and virtually on Zoom. SAS 2225 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.

Differential Equations and Nonlinear Analysis Seminar: Peter W. Michor, University of Vienna, Austria, Whitney manifold germs as source for manifolds of mappings

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During the preparation of a foundational chapter on manifolds of mappings for a book on geometric continuum mechanics I found out that the following object behaves surprisingly well as source of a manifold of mappings: — A Whitney manifold germ M˜ ⊃ M consists of an open manifold M˜ together with a closed subset M…