Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers and Littlewood-Richardson coefficients (the type A weight multiplicities and Clebsch-Gordan coefficients). ...

In this work, we study two different manipulations of electromagnetic waves governed by macroscopic Maxwell's equations. One is frequency conversion of such waves using small intrinsic material nonlinearities. We study ...

We develop a new understanding of outliers and the behavior of linear programs under perturbation. Outliers are ubiquitous in scientific theory and practice. We analyze a simple algorithm for removal of outliers from a ...

Geometry is the synthetic tool we use to unify all existing analytical cone-beam reconstruction methods. These reconstructions are based on formulae derived by Tuy [Tuy, 1983], Smith [Smith, 1985] and Grangeat [Grangeat, ...

The overall goal of this thesis is to apply the theory of Goodwillie calculus to the category Algo of algebras over a spectral operad. Its first part generalizes many of the original results of Goodwillie in [14] so that ...

We present several graph polynomials, of which the most important one is the Tutte polynomial. These various polynomials have important applications in combinatorics and statistical physics. We generalize the Tutte polynomial ...

The Mayer-Vietoris sequence in cohomology has an obvious Eckmann-Hilton dual that characterizes the homotopy of a pullback, but the Eilenberg-Moore spectral sequence has no dual that characterizes the homotopy of a pushout. ...