BSTRctProbability distributions on the set of trees are fundamental in evolutionary biology, as models for speciation processes. These probability models for random trees have interesting mathematical features and lead to difficult questions at the boundary of combinatorics and probability. This talk will be concerned with the question of how much two random trees have in…
We consider a long-time behavior of a stochastically forced nonlinear oscillator. In a long-time limit the force converges to fractional Brownian motion, a process that has memory. In contrast, we show that the limit of the nonlinear oscillator driven by this force converges to diffusion driven by standard (not fractional) Brownian motion, and thus retains…
We will look at the brand new MATLAB Grader functionality in Moodle, featuring examples, tips and tricks, and a few drawbacks. Participants are encouraged to activate their MathWorks account first (https://www.mathworks.com/, use your Unity credentials) and bring a laptop to experiment with. If you would like to be a student in a Moodle Project space…
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…
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.…
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…
Students will provide their job application materials in advance to the organizers, who will read and discuss them as a group with a view towards making positive improvements before submission. A good opportunity to get feedback from a range of faculty.
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…
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…
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…
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…