Related papers: Branko Gr\"unbaum in many dimensions
Models with extra dimensions have attracted much interest recently because they may provide the solution for long standing problems in physics. One interesting and very attractive idea is that our visible universe is confined to a…
The idea that the Universe is a program in a giant quantum computer is both fascinating and suffers from various problems. Nonetheless, it can provide a unified picture of physics and this can be very useful for the problem of Quantum…
We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
We survey the history and recent developments around two decades-old problems that continue to attract a great deal of interest: the slicing $\times 2$, $\times 3$ conjecture of H. Furstenberg in ergodic theory, and the distance set problem…
This texts commemorates the memory of Haim Brezis and explores some aspects of the restriction problem, particularly its connections to spectral and geometric analysis. Our choice of subject is motivated by Brezis' significant contributions…
This article briefly describes four algorithmic problems where the notion of treewidth is very useful. Even though the problems themselves have nothing to do with treewidth, it turns out that combining known results on treewidth allows us…
Large extra dimensions provide interesting extensions of our parameter space for gravitational theories. There exist now brane models which can perfectly reproduce standard four-dimensional Friedmann cosmology. These models are not…
I published an interview of Leo Breiman in Statistical Science [Olshen (2001)], and also the solution to a problem concerning almost sure convergence of binary tree-structured estimators in regression [Olshen (2007)]. The former summarized…
We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.
We comment van Douwen's problems on the Bohr topology of the abelian groups raised in his paper (The maximal totally bounded group topology on G and the biggest minimal G-space for Abelian groups G) as well as the steps in the solution of…
In this paper, we study the planar Lp-Minkowski problem for all p, which was introduced by Lutwak [23]. A detailed exploration on solvability and uniqueness will be presented.
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
By using random multilinear maps, we provide new lower bounds for the Erd\H{o}s box problem, the problem of estimating the extremal number of the complete $d$-partite $d$-uniform hypergraph with two vertices in each part, thereby improving…
This is a perspective on "k-stretchability of entanglement, and the duality of k-separability and k-producibility" by Szil\'ard Szalay, published in Quantum 3, 204 (2019).
It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…
Existence of open string field theory solutions describing configurations of multiple space-filling D-branes has been a subject of numerous speculations for quite some time. In this talk we present some new results giving further support to…
This is a survey article on Hilbert-Kunz multiplicity and the F-signature.
We give a basic account of supersymmetric open strings and D-branes using the Green-Schwarz formalism, obtaining a manifestly spacetime supersymmetric description of their spectrum. In addition we discuss a mechanism whereby some of the…
An obituary of J.R. Dorfman. The focus is on his scientific career and on his many important publications.