We review both theoretical and experimental developments in the area of quantum games
since the inception of the subject circa 1999. We will also offer a narrative on the controversy …

The use of simulation for high-dimensional intractable computations has revolutionized
applied mathematics. Designing, improving and understanding the new tools leads to (and …

This is a survey of distance-regular graphs. We present an introduction to distance-regular
graphs for the reader who is unfamiliar with the subject, and then give an overview of some …

We develop a new toolbox for the analysis of the global behavior of stochastic discrete
particle systems. We introduce and study the notion of the Schur generating function of a …

We introduce and study stochastic N N-particle ensembles which are discretizations for
general-β β log-gases of random matrix theory. The examples include random tilings …

In this monograph, we present a complete and self-contained presentation of the direct and
inverse scattering theories for the matrix Schrödinger equation on the half line with the …

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In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which
exhibit the special property of perfect quantum state transfer (PQST): the transmission of …

Macdonald-positive specializations of the algebra of symmetric functions: Proof of the Kerov
conjecture Page 1 Annals of Mathematics 189 (2019), 277–316 https://doi.org/10.4007/annals.2019.189.1.5 …

In this paper, we study the relationship between polynomial integrals on the unitary group
and the conjugacy class expansion of symmetric functions in Jucys–Murphy elements. Our …