Events
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Yan Zhuang, Davidson College, Counting permutations by peaks, descents, and cycle type
We present a general formula describing the joint distribution of two permutation statistics—the peak number and the descent number—over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formula involves a certain kind of plethystic substitution on quasisymmetric generating functions. We apply this result to cyclic permutations, involutions, and derangements, and…
JungHwan Park, Georgia Tech, Rational cobordisms and integral homology
We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by a unique connected sum of lens spaces whose first homology embeds in any other element in the same class. As an application, we show that the natural map from the Z/pZ homology cobordism group to the rational…
Eric Hallman, NC State, Sharp 2-norm Error Bounds for LSQR and the Conjugate Gradient Method
When running any iterative algorithm it is useful to know when to stop. Here we review LSQR and LSLQ, two iterative methods for solving \min_x \|Ax-b\|_2 based on the Golub-Kahan bidiagonalization process, as well as estimates for the 2-norm error \|x-x_*\|_2, where x_* is the minimum norm solution. We also review the closely related Craig's…
Tea and Cookies
SAS 4104Mikhail Klibanov, UNC Charlotte, Carleman Estimates for Globally Convergent Numerical Methods for Coefficient Inverse Problems
The ill-posedness and nonlinearity are two factors causing the phenomenon of multiple local minima and ravines of conventional least squares cost functionals for Coefficient Inverse Problems. Since any minimization method can stop at any point of a local minimum, then the problem of numerical solution of any Coefficient Inverse Problems becomes inherently unstable and so…
Mike Thompson, Managing Director and CEO of First Analytics, “Mathematics in Industry” Seminar
Tompkins Hall G109Mike Thompson, the Managing Director and CEO of First Analytics, will be giving a seminar on how machine learning and mathematics are used to handle large data analytics programs at First Analytics.
Mohammad Farazmand, NC State, Extreme Events in Chaos
SAS 2102Chaos refers to seemingly random and unpredictable dynamics of a system that evolves in time. Certain chaotic systems exhibit an additional level of complexity: intermittent extreme events that are noticeably distinct from the usual chaotic dynamics. These extreme events include ocean rogue waves, extreme weather patterns, and epileptic seizure. I will discuss several examples of these…
Research Statements and CVs
An afternoon workshop/discussion lead by Ilse Ipsen on preparing your research statements and CVs for the job search.
Duff Baker-Jarvis, Wake Forest University, QSym and the Shuffle Compatibility of Permutation Statistics
The fundamental basis of the Hopf algebra of quasisymmetric functions, QSym, can be thought of in terms of shuffling permutations. We can think of QSym as having a basis indexed by equivalence classes of permutations, where we identify permutations with the same descent set. This descent set, Des, is a simple example of a permutation…
Ákos Nagy, Duke University, Complex Monopoles
Self-duality equations in gauge theory can be complexified in many inequivalent ways, but there are two obvious options: One can extend Hodge duality in either a complex linear fashion, or in a conjugate linear one. In general, the two cases result in two very different equations. The first case was first studied by Haydys, while…
Shahar Kovalsky, Duke University, Planar surface embeddings and non-convex harmonic maps
Mappings between domains are among the most basic and versatile tools used in the computational analysis and manipulation of shapes. Their applications range from animation in computer graphics to analysis of anatomical variation and anomaly detection in medicine and biology. My talk will start with a brief overview of discrete computational shape mapping, surface parameterization…
Piermarco Cannarsa, University of Rome “Tor Vergata”, Bilinear control for evolution equations of parabolic type
Recently, in a series of joint papers with F. Alabau-Boussouira and C. Urbani, I have studied the response of an evolution equation on a Hilbert space to the action of a bilinear control. As is well-known, a bilinear control is a scalar function of time multiplying one of the coefficient of the equation (usually, a…
Tea and Cookies
SAS 4104Piermarco Cannarsa, University of Rome Tor Vergata, Italy, Propagation of singularities for solutions to Hamilton-Jacobi equations
SAS 1102The study of the structural properties of the set of points at which the viscosity solution of a first order Hamilton–Jacobi equation fails to be differentiable—in short, the singular set—started with the paper On the Singularities of Viscosity Solutions to Hamilton–Jacobi–Bellman Equations, Indiana Univ. Math. J. 36 (1987), 501–524 by Mete Soner and myself. These…
Arvind Krishna Saibaba, NC State, The Mathematics Behind Imaging
SAS 2102From x-ray machines to luggage scanners, our lives depend on imaging devices that let us “see” what is impossible to observe with the naked eye. I will explain some of the mathematical ideas that make image reconstructions possible. Along the way, we will solve some fun puzzles that are related to image reconstructions. This talk…
Ella Pavlechko, Visualizing Curves in the Projective Plane
The Italian Renaissance painters began to incorporate perspective into their drawings in the 1400’s, but our eyes naturally understand depth from the 2-dimensional image on the back of our eyeball. It’s this projection on the retina that allows mathematicians to represent field of view with the projective plane, and in this talk we’ll investigate what makes it so difficult to…
Jason Brown, Dalhousie University, Independence Polynomials and Their Roots
Independence polynomials are generating functions for the number of independent sets of each cardinality in a graph G. In addition to encoding useful information about the graph (such as the number of vertices, the number of edges and the independence number), the analytic and algebraic properties can say much about the shape and inter-dependence of…