The classical problem of solving an nth degree polynomial equation has substantially
influenced the development of mathematics throughout the centuries and still has several …

Our goal is to provide an introduction to the study of minimal energy problems, particularly
from the perspective of generating point configurations that provide useful discretizations of …

This textbook covers both direct and iterative methods for the solution of linear systems, least
squares problems, eigenproblems, and the singular value decomposition. Earlier versions …

A timely and comprehensive treatment of random field theory with applications across
diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses …

George Collins' discovery of Cylindrical Algebraic Decomposition (CAD) as a method for
Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major …

We provide an elementary geometric derivation of the Kac integral formula for the expected
number of real zeros of a random polynomial with independent standard normally …

This book gathers threads that have evolved across different mathematical disciplines into
seamless narrative. It deals with condition as a main aspect in the understanding of the …

We investigate the energy of arrangements of $ N $ points on the surface of a sphere in
${\bold R}^ 3$, interacting through a power law potential $ V= r^\alpha $, $-2<\alpha< 2 …

To study a geometric model of the human spine we are led to finding a constrained minimum
of a real valued function defined on a product of special orthogonal groups. To take …

These expository notes are centered around the circular law theorem, which states that the
empirical spectral distribution of an× n random matrix with iid entries of variance 1/n tends to …