Related papers: The architect Kha's protractor

We present a class forcing notion $\mathbb M(\eta)$, uniformly definable for ordinals $\eta$, which forces the ground model to be the $\eta$-th inner mantle of the extension, in which the sequence of inner mantles has length at least…

We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…

Here I am discussing a possible use of a Roman Dodecahedron, a bronze artifact of gallo-roman origin, for measuring distance. A dodecahedron, found at Jublains, the ancient Nouiodunum, dating from the 2nd or 3rd century AD, is used to…

This paper is motivated by the k-nearest neighbors search: given an arbitrary metric space, and its finite subsets (a reference set R and a query set Q), design a fast algorithm to find all k-nearest neighbors in R for every point q in Q.…

We show a one-to-one correspondence between arrangements of d lines in the projective plane, and lines in P^{d-2}. We apply this correspondence to classify (3,q)-nets over the complex numbers for all q<=6. When q=6, we have twelve possible…

The nature of a metal-insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions, as reported in recent experiments of Roddaro et al [1], is examined. We attribute this phenomenon to a splitting of…

We analyze proton decay via dimension six operators in certain GUT-like models derived from Type IIA orientifolds with $D6$-branes. The amplitude is parametrically enhanced by a factor of $\alpha_{GUT}^{-1/3}$ relative to the coresponding…

This set of notes is based on a lecture I gave at "50 years of Finite Geometry | A conference on the occasion of Jef Thas's 70th birthday," in November 2014. It consists essentially of three parts: in a first part, I introduce some ideas…

For a rigid object $M$ in an algebraic triangulated category $\mathcal{T}$, a functor pr$(M)\to\mathcal{H}^{[-1,0]}({\rm proj}\, A)$ is constructed, which essentially takes an object to its `presentation', where pr$(M)$ is the full…

The {\em Four-dimensional Light Orchestra} or {\em 4DLO} was an interactive sculpture at the National Museum of Mathematics (MoMath) from November 20, 2025 through January 2026, illustrating various sub-symmetries of the 24-cell with…

We investigate the transport of energy in a linear chain of two-level quantum emitters ("atoms") weakly coupled to a blackbody radiation bath. We show that, simply by displacing one or more atoms from their regular-chain positions, the…

We determine the space of commuting symmetries of the Laplace operator on pseudo-Riemannian manifolds of constant curvature, and derive its algebra structure. Our construction is based on the Riemannian tractor calculus, allowing to…

Contraction$^*$-depth is considered to be one of the analogues of graph tree-depth in the matroid setting. In this paper, we investigate structural properties of contraction$^*$-depth of matroids representable over finite fields and…

Kei Yuen Chan and Kayue Daniel Wong constructed a functor from the category of Harish-Chandra modules of $\mathrm{GL}(n, \mathbb C)$ to the category of modules over graded Hecke algebra $\mathbb H_m$ of type A. This functor has several nice…

Two books, the "De Architectura" by Vitruvius and the "Naturalis Historia" by Pliny the Elder, give us a portrait of the Materials Science, that is, the knowledge of materials, in Rome at the beginning of the Empire. Here, I am reporting…

Projected gradient descent has been proved efficient in many optimization and machine learning problems. The weighted $\ell_1$ ball has been shown effective in sparse system identification and features selection. In this paper we propose…

We investigate fracture toughness of architected interfaces and their ability to maintain structural integrity and provide stable damage propagation conditions beyond the failure load. We propose theoretical and numerical frameworks to…

We describe a new tool, KATKA, that stores a phylogenetic tree $T$ such that later, given a pattern $P [1..m]$ and an integer $k$, it can quickly return the root of the smallest subtree of $T$ containing all the genomes in which the $k$-mer…

The ceiling of the Buttery in All Souls College, Oxford, designed by the English Baroque architect Nicholas Hawksmoor, has a vaulted form on an oval base. It is coffered with an array of approximately square sunken lacunaria, whose sizes…

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…