The multiple flag variety

We analytically study the Fermi-gas formulation of sphere correlation functions Coulomb branch operators for 3d \mathcal{N}=4

Grötzsch’s Theorem is one of the most famous theorems in graph colouring theory. Its original proof, given in German, in 1958, was fairly complex. In 1989, Steinberg and Younger [17] gave the first correct proof, in English, of the dual version of this theorem. This essay studies the Steinberg-Younger proof in detail, putting special emphasis on improved presentation of their arguments and clar...

This paper proposes a deterministic importance sampling algorithm for complex integrands. The idea is based on the recognition that halftoning algorithms are equivalent to importance sampling if the gray-scale image and a resulting white pixel are considered as the target importance function and the sampling position, respectively. We adopt the Floyd-Steinberg halftoning algorithm, extend it to...

In many computer graphics applications we wish to augment virtual objects with images representing a real environment (sky, city, etc.). In order to provide the illusion that the virtual objects are parts of the real scene, the illumination of the environment should be taken into account when rendering the virtual objects [Debevec 98,Kollig and Keller 03]. Since the images representing the envi...

A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...

The form π is unique up to a character twist, while ν is simply the central character of Π. The central character ω of π may be chosen to be of finite order. Moreover, we may choose π such that, for any finite place v, πv is unramified, resp. Steinberg, when Πv ⊗ νv is unramified, resp. Steinberg. Here Ad(π) denotes the Adjoint of π, a selfdual automorphic form on GL(3)/F , defined to be sym2(π...

This paper presents a comprehensive review and some new developments on canonical duality theory for nonconvex systems. Based on a tri-canonical form for quadratic minimization problems, an insightful relation between canonical dual transformations and nonlinear (or extended) Lagrange multiplier methods is presented. Connections between complementary variational principles in nonconvex mechanic...