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…
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…
The story of noncrossing partitions starts with a Coxeter group W anda Coxeter element c. (If you're not familiar with Coxeter things, think: W is the symmetric group S_n and c is an n-cycle.) The noncrossing partitions in W are the elements of the interval _T in a certain partial order on W (the absolute…
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…
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…
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…
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…
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…
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…
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…
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.
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…
This session's talks: - Ian Bunner: TeX-hacking for creating instructional materials - Ashley Tharp: Scaffolding - Stepan Paul: Double integrals without volume - Nathan Reading: How WebAssign lies to students Once per semester, the Teaching and Learning Seminar will host 10-minute "lightning talks" in which 4 graduate students and/or faculty members will talk about some…
In this talk, we begin by introducing the audience to some fundamentals of differential geometry of surfaces in ℝ3, focusing on curvature and the adequately named first and second fundamental forms. We will discuss what special parameterizations and properties give rise to isothermic surfaces. Equipped with these tools, we will look at the fundamental theorem for surfaces,…
Zombies are popularly presented in media as resulting from an infectious outbreak. Various modeling assumptions for zombification as an infectious disease are discussed. Populations during the outbreak are then modeled with infectious disease compartment models accounting for various effects such as latent infectious populations, quarantining, etc. Equilibrium and stability conditions for these dynamics are determined,…
Advisor Medhin, contact for Zoom access.
A major challenge in the study of dynamical systems is that of model discovery: turning data into reduced order models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their…
Categorification is a method that has many emanations hence eludes a precise definition. Therefore, we will discuss categorification through several examples of categorifying polynomials arising from different fields of mathematics, including knots, graphs, and orthogonal polynomials. Speaker’s webpage: https://sazdanovic.wordpress.ncsu.edu/ Location: Jointly in person and virtually on Zoom. SAS 2225 for in-person participation. The Zoom link is sent out…
In this talk, I will first present a very simple quantitative form of the Young-Fenchel inequality. I will then discuss some applications: a short proof of the Brøndsted-Rockafellar in Hilbert spaces and a primal-dual attainment for perturbed convex minimization problems. I will finally explain how this inequality (or some generalizations) can be used for quantitative…