Events
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Math Department Picnic
Pullen Park, Shelter #4 RaleighThe department provides hamburgers, hot dogs, veggie burgers, buns, fixings, utensils, etc. We will send out an invitation and sign up sheet for volunteering to help-out or bring drinks, desserts, side dishes, etc. in the first or second week of September.
Heekyoung Hahn, Duke University, Langlands’ beyond endoscopy proposal and related questions on algebraic groups and combinatorics
SAS 4201Langlands' beyond endoscopy proposal for establishing functoriality motivates the study of irreducible subgroups of $\mathrm{GL}_n$ that stabilize a line in a given representation of $\mathrm{GL}_n$. Such subgroups are said to be detected by the representation. In this talk we present a family of results when the subgroup is a classical group in the important special…
Sung Ha Kang, Georgia Tech, Variational image processing and computational challenges
SAS 4201Starting with an introduction to variational/PDE based image processing, this talk will focus on new developments of fast algorithms for higher order variational imaging models. For example, recent developments of fast algorithms, based on operator splitting, augmented Lagrangian, and alternating minimization, enabled us to revisit some of the variational image models, such as Euler's Elastica…
Chris Tralie, Duke University, From Musical Rhythms To Vibrating Vocal Folds: Geometric (Quasi)Periodicity Quantification in Multimedia Time Series
SAS 4201A large variety of multimedia data inference problems require analysis of repeated structures. In audio, for instance, the rhythm, or ``pulse'' of the music, occurs in a periodic pattern, and understanding this pattern is an important preprocessing step in music information retrieval. In medical video analysis, there is interest in determining heart pulse rate in…
Kristen Boyle, NC State, On derivations of Leibniz algebras
Leibniz algebras are a generalization of Lie algebras. In this talk I will discuss some results on characteristic ideals, which are analogs of known results from Lie algebra. I will use these results to prove that the radical of a Leibniz algebra is a characteristic ideal. We will also explore the derivation algebra of cyclic…
Garrett Nieddu, Montclair State University, Rare Events in Stochastic Population Models
Cox 306Noise can play a critical role in a wide array of physical and biological dynamical systems. The noise may be internal or external to the system. Internal noise is intrinsic to the system itself, and in stochastic population models, arises due to the random interactions of discrete agents in the system. On the other hand,…
Joshua Hallam, Wake Forest University, Whitney duals of graded partially ordered sets
SAS 4201To each graded poset one can associate two sequences of numbers; the Whitney numbers of the first kind and the Whitney numbers of the second kind. One sequence keeps track of the Möbius function at each rank level and other keeps track of the number of elements at each rank level. We say two posets…
Slava Krushkal, University of Virginia, Flow and Yamada polynomials, planar triangulations, and TQFT
SAS 1102In the 1960s Tutte observed that the value of the chromatic polynomial of planar triangulations at (golden ratio +1) obeys a number of remarkable properties. In this talk I will explain how TQFT gives rise to a conceptual framework for studying planar triangulations. I will discuss several extensions of Tutte's results and applications to the…
Murthy Gudatti, NC State, Efficient Forward and Inverse Algorithms for Guided Wave Inversion
SAS 4201Guided waves are widely utilized in the fields of nondestructive testing and geophysical inversion, to estimate the medium properties through inversion of the dispersion curves. In this talk, we present improved methodologies for computing both dispersion curves and their derivatives, the two main ingredients of guided wave inversion. Specifically, a novel discretization approach based on Pade Approximants, named complex-length finite element…
The Storm Next Time: Hurricanes and Climate Change
Genome Sciences Building, G100 Auditorium at UNC Chapel Hill" The recent tragedies of Hurricanes Harvey and Irma, together with earlier extreme events such as Hurricanes Katrina and Sandy, has raised the question whether the apparent increasing severity of such events can be attributed to the human influence on greenhouse gas warming. Dr. Emanuel will review the growing consensus that the incidence of the…
Sercan Yildiz, SAMSI,Polynomial Optimization with Sums-of-Squares Interpolants
Sums-of-squares certificates define a hierarchy of relaxations for polynomial optimization problems which are parametrized with the degree of the polynomials in the sums-of-squares representation. Each level of the hierarchy generates a lower bound on the true optimal value, which can be computed in polynomial time via semidefinite programming, and these lower bounds converge to the…
Ronghua Pan, Georgia Institute of Technology, Global regularity v.s. finite time blowup for compressible Euler equations
SAS 4201As one of the oldest nonlinear PDE systems, the compressible Euler equations has been studied by many outstanding mathematicians. However, some basic questions, such as the global existence of classical solution v.s. finite time blowup, are still open even in one space dimension. In this lecture, we will report our recent progress in this direction, including a complete understanding on…
Missy Gaddy, NC State, SIAM Tutorial Series: Nonlinear Optimization Basics
SAS 1218This tutorial will provide an introduction to nonlinear optimization. We will begin by presenting a general constrained nonlinear program, defining concepts like local versus global optimality, and examining the differences between convex and nonconvex problems. We will then present the Karush-Kuhn-Tucker optimality conditions. Students who have taken OR 706 (Nonlinear Programming) will find this tutorial…
Vladimir Baranovsky, UC Irvine, Chromatic graph homology for brace algebras
SAS 4201Earlier Helme Guizon and Rong have defined chromatic graph homology complex for a graded commutative algebra, and it is easy to extend the definition to graded commutative DG algebra. One of important applications, considered earlier in our joint work with Radmila Sazdanovic, is to the case of an algebra computing cohomology of a manifold, such…
Jane Coons, NC State
Algebraic geometry and combinatorics play an important role in the analysis of phylogenetic models. I will give a brief overview of toric geometry. Then I will introduce a particular phylogenetic model, called the Cavander-Farris-Neyman model with a molecular clock, and I will discuss how we can study this model from the point of view of…
Tim David, University of Canterbury, NZ, The Dynamics of Coupled Cells: From the Discrete to the Continuous
Cox 306Why do atherosclerotic plaques only occur at specific sites in the arteries? Does the surface geometry of the brain affect the way waves move through the cortex? These questions and many others in the physiological sphere contain implicitly a real difficulty for modellers. How do we contend with the multiple scale lengths. Plaques are quite large compared to cells making…
Ralph Smith and Mansoor Haider
SAS 4201H. Sebastian Heese, Poole College of Management, NC State, Effects of Assortment Breadth Announcements on Manufacturer Competition
Daniels 218Retailers typically use assortment planning to maximize store profits given product characteristics. We study the manufacturers' price-setting interactions and how these can be manipulated by the retailer's assortment strategy. We show that constraining the breadth of the assortment has two main effects on retailer profits: first, a larger assortment may intensify competitive pressure and decrease…
Casey Diekman, New Jersey Inst. Tech., Circadian regulation of gene expression and electrical activity in neurons and cardiomyocytes
Cox 306Circadian (~24-hour) rhythms offer one of the clearest examples of the interplay between different levels of nervous system organization, with dynamic changes in gene expression leading to daily rhythms in neural activity, physiology, and behavior. The main output signal of the master circadian clock in mammals has long been believed to be a simple day/night…