Related papers: An Infinite Double Bubble Theorem
We study various bubble solutions in string/M theories obtained by double Wick rotations of (non-)extremal brane configurations. Typically, the geometry interpolates de Sitter space-time times non-compact extra-dimensional space in the…
Many of the conjectures of current interest in the representation theory of finite groups in characteristic $p$ are local-to-global statements, in that they predict consequences for the representations of a finite group $G$ given data about…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
Fluids made of two-dimensional hard particles with polygonal shapes may stabilize symmetries which do not result directly from the particle shape. This is due to the formation of clusters in the fluid. Entropy alone can drive these effects,…
In this article we prove the following version of the Weak-BAB conjecture for $3$-folds in char $p>5$: Fix a DCC set $I\subset [0, 1)$ and an algebraically closed field $k$ of characteristic $p>5$. Let $\mathfrak{D}$ be a collection of klt…
We characterize the critical points of the double bubble problem in $\mathbb{R}^n$ and the triple bubble problem in $\mathbb{R}^3$, in the case the bubbles are convex.
This short document illustrates QLUSTER: a toy model for populations of binary black holes in dense astrophysical environments. QLUSTER is a simple tool to investigate the occurrence and properties of hierarchical black-hole mergers…
Let $M$ be a model set meeting two simple conditions: (1) the internal space $H$ is a product of $R^n$ and a finite group, and (2) the window $W$ is a finite union of disjoint polyhedra. Then any point pattern with finite local complexity…
We focus on the analysis of local minimizers of the Mahler volume, that is to say the local solutions to the problem $$\min\{ M(K):=|K||K^\circ|\;/\;K\subset\R^d\textrm{ open and convex}, K=-K\}, $$ where $K^\circ:=\{\xi\in\R^d ; \forall…
We present a phase-space representation of quantum state vectors for two-cluster systems. Density distributions in the Fock--Bargmann space are constructed for bound and resonance states of $^{6,7}$Li and $^{7,8}$Be, provided that all these…
We give an example of a finite-dimensional algebra with a 2-cluster tilting module and a simple module which has infinite complexity. This answers a question of Erdmann and Holm.
Every choice of an orthonormal frame in the d-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, a classical statistical state space of the system; the quantum state…
A free superstring with chiral N=2 supersymmetry in six dimensions is proposed. It couples to a two-form gauge field with a self-dual field strength. Compactification to four dimensions on a two-torus gives a strongly coupled N=4…
The interior of a vacuum bubble in de Sitter space may give an open universe with sufficient homogeneity to agree with observations. Here, previous work by Bucher, Goldhaber and Turok is extended to describe a thin bubble wall with nonzero…
Within the non-relativistic potential scattering theory, we derive a generalized version of the L\"uscher formula, which includes three-particle inelastic channels. Faddeev equations in a finite volume are discussed in detail. It is proved…
Let $X$ be a finite collection of sets (or "clusters"). We consider the problem of counting the number of ways a cluster $A \in X$ can be partitioned into two disjoint clusters $A_1, A_2 \in X$, thus $A = A_1 \uplus A_2$ is the disjoint…
As the largest gravitationally collapsed objects, and as objects with a relatively low space density, clusters of galaxies offer one of the best sets of standard candles for trying to measure basic cosmological parameters such as the…
In this paper, we study vacuum bubble collisions with various potentials including gravitation, assuming spherical, planar, and hyperbolic symmetry. We use numerical calculations from double-null formalism. Spherical symmetry can mimic the…
The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to thirty polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to…
In this paper we associate with an infinite family of real extended functions defined on a locally convex space, a sum, called robust sum, which is always well-defined. We also associate with that family of functions a dual pair of problems…