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Loc Nguyen, UNC Charlotte, Phaseless Coefficient Inverse problem using only one direction of incident wave
SAS 4201The phaseless coefficient inverse problem arises in imaging of nano-structures. One uses light source whose wavelength is in the range of hundreds of nanometers to illuminate those structures and collects the intensity of the complex scattering field on a plane behind such structures. Due to the smallness of the wavelength, measuring the phase of the…
Triangle Area Graduate Mathematics Conference (TAGMaC)
This fall semester, the Triangle Area Graduate Mathematics Conference (TAGMaC) will be held at North Carolina State University in Raleigh, NC on November 11, 2017. The one-day conference features short talks by graduate students and a keynote speech. Lunch and coffee/tea will also be provided. We would like to invite all graduate students to attend and give…
Tea and Cookies
SAS 4104Francisco Santos Leal, Universidad de Cantabria, Diameters of polyhedra and simplicial complexes
SAS 1102The Hirsch conjecture, posed in 1957, stated that the graph of a $d$-dimensional polytope or polyhedron with $n$ facets cannot have diameter greater than $n−d$ . The conjecture itself has been disproved by Klee-Walkup (1967) for unbounded polyhedra and by the speaker (2012) for bounded polytopes; but what we know about the underlying question is…
Kristina Czuchlewski, Sandia National Laboratories, New Horizons in Geospatial Analytics
Park Shops 210In recent years, Sandia National Laboratories has been accelerating research investments in data science and analytics. This change was motivated by a need for timely decisions about the state of the world in the context of increasingly large and diverse varieties of data. Data-centric challenges often cross discipline boundaries. To address these challenges, our group…
Laura Potter, Global Head of Computational Biology, Syngenta, Helping feed the world with innovative agricultural products: Opportunities for computational biology
Cox 306As the world’s rapidly growing population is driving ever increasing demand for food, feed and fuel, we are faced with the challenge to grow higher-yielding crops with less water and fewer inputs. Agriculture companies are focused on meeting these needs by delivering innovative products and technologies into the marketplace that improve crop performance. This requires…
Gleb Pogudin, Courant Institute of Mathematical Sciences, Algorithms for Checking Global Identifiability
SAS 4201The following situation arises in modeling: one has a system of differential equations with parameters and wants to determine the values of these parameters measuring unknown functions (assuming that perfect noise-free measurements are possible). Usually, some of the unknown functions are impossible or very hard to measure, so only a subset of them is available…
Ben Hollering, NC State, Longest increasing subsequences of ordered set partitions
The size of a maximum agreement subtree of two phylogenetic trees is a statistic that is often used to test the null hypothesis that no cospeciation occurred between two families of species of interest. The size of the maximum agreement subtree can be computed in polynomial time but the distribution of this statistic is not…
Ziva Myer, Duke, Product Structures for Legendrian Submanifolds with Generating Families
SAS 4201In contact topology, invariants of Legendrian submanifolds in 1-jet spaces have been obtained through a variety of techniques. I will discuss how I am enriching one Morse-theoretic invariant, Generating Family Cohomology, to an A-infinity algebra by constructing product maps. The construction uses moduli spaces of Morse flow trees: spaces of intersecting gradient trajectories of functions…
Denise Seabrooks and Jeff Scroggs Reception
SAS 4104Reception for the many years of service to this department and to NC State.
Serkan Gugercin, Virginia Tech, Interpolatory model reduction with applications to flow control and nonlinear inversion
SAS 4201Numerical simulation of large-scale dynamical systems plays a crucial role and may be the only possibility in studying a great variety of complex physical phenomena with applications ranging from heat transfer to fluid dynamics, to signal propagation and interference in electronic circuits, and many more. However, these large-scale dynamical systems present significant computational difficulties when…
Eylem Yildiz, Michigan State University, A note on knot concordance
I will discuss concordances of knots in 3-manifolds. In particular I will show that all the knots in the free homotopy class of $S^1\times pt$ in $S^1 \times S^2$ are concordant to each other. By Akbulut it turns out that many of these concordances are invertible.
Nancy Rodriguez-Bunn, UNC, On the global existence and qualitative behavior of solutions to a model for urban crime
SAS 4201We consider the no-flux initial-boundary value problem for the cross-diffusive evolution system which was introduced to describe the dynamics of urban crime. In bounded intervals I will first discuss the existence of global classical solutions for all reasonably regular non-negative initial data. Next I will address the issue of determining the qualitative behavior of solutions. Finally, I will conclude with some numerical simulations exploring possible effects…
Nikolas Bravo, NC State, SIAM Tutorial Series: Introduction to Feedback Control Systems and PID Controllers
SAS 1218Control systems impact our lives on a daily basis, whether it is from our thermostat controlling the temperature in our home to cruise control in our car to surfing the worldwide web. Feedback control systems is a type of dynamical system where it uses feedback from the system and an algorithm to determine an input…
Honors Students Research Presentation
Bryan Chu Title: Low Rank Randomized Standard Value Decomposition Abstract: The low rank randomized standard value decomposition is a fast, stable method of computing the dominant singular values of a real, large matrix A. For a large scale system we use a randomized matrix method, a so called, randomized SVD (rSVD). We improve the existing rSVD…
Yang Qi, University of Chicago, On approximations and decompositions of a general tensor
SAS 4201Tensors are closely related to secant varieties. In fact, the affine cone of the $r$th secant variety of the Segre variety is the set of tensors whose border rank is less than or equal to $r$. Similarly, we have a geometric interpretation of symmetric tensors. By studying the geometry of these secant varieties, we can…
Yakov Berchenko-Kogan, Washington University in St. Louis, Noether’s theorem, Maxwell’s equations, and numerical methods
SAS 4201Noether's theorem tells us that if a system is invariant under a group of symmetries, then we have quantities that are conserved. For example, if a system is invariant under translation, then momentum is conserved. If a system is invariant under rotation, then angular momentum is conserved. One of the challenges in numerical analysis is to make sure that these…