Related papers: The Gaussian Double-Bubble Conjecture

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…

We give a proof of the $A_2$ conjecture in geometrically doubling metric spaces (GDMS), i.e. a metric space where one can fit not more than a fixed amount of disjoint balls of radius $r$ in a ball of radius $2r$. Our proof consists of three…

In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue…

The doubling conjecture predicts that a manifold admits positive scalar curvature with mean convex boundary if and only if its double admits positive scalar curvature. We show that it holds true for manifolds where the inclusion of the…

In a SUSY GUT having an extra reverse doublet-triplet splitting near the GUT scale, where the mass of an extra doublet is greater than the mass of an extra triplet by two orders of magnitude, a low prediction of $\alpha_s$ can be achieved…

Let $n\geq 2$ and $(X_i,1\leq i\leq n)$ be a centered Gaussian random vector. The Gaussian minimum conjecture says that $E\left(\min_{1\leq i\leq n}|X_i|\right)\geq E\left(\min_{1\leq i\leq n}|Y_i|\right)$, where $Y_1,\ldots,Y_n$ are…

In Grand Unified Theories (GUTs) from orbifold and various string constructions the generic vector-like particles do not need to form complete SU(5) or SO(10) representations. To realize them concretely, we present orbifold SU(5) models,…

We construct a little Higgs model with the most minimal extension of the standard model gauge group by an extra U(1) gauge symmetry. For specific charge assignments of scalars, an approximate U(3) global symmetry appears in the…

Combining the tools of geometric analysis with properties of Jordan angles and angle space distributions, we derive a spherical and a Euclidean Bernstein theorem for minimal submanifolds of arbitrary dimension and codimension, under the…

We propose a class of models with gauge mediation of supersymmetry breaking, inspired by simple brane constructions, where R-symmetry is very weakly broken. The gauge sector has an extended N=2 supersymmetry and the two electroweak Higgses…

We study vacuum structure of N=1 supersymmetric quiver gauge theories which can be realized geometrically by D brane probes wrapping cycles of local Calabi-Yau three-folds. In particular, we show that the A_2 quiver theory with gauge group…

We present a simple scheme for constructing models that achieve successful gauge mediation of supersymmetry breaking. In addition to our previous work [1] that proposed drastically simplified models using metastable vacua of supersymmetry…

We propose a simple model of split supersymmetry from gauge mediation. This model features gauginos that are parametrically a loop factor lighter than scalars, accommodates a Higgs boson mass of 125 GeV, and incorporates a simple solution…

We prove that for a symmetric, strictly log-convex density on the real line, there are four possible types of perimeter-minimizing triple bubbles. This extends the work of Bongiovanni et al., which shows that there are two possible types of…

A five-dimensional minimal supergravity theory coupled to vector and hypermultiplets is specified by a set of trilinear couplings, given by an intersection form $C_{IJK}$, and gravitational couplings specified by an integer-valued vector…

The $k$-median and $k$-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the $k$-median (resp. $k$-means) problem is to find $k$ representative…

It is conjectured that every cusped hyperbolic 3-manifold has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation of the manifold). Under a mild homology assumption on the manifold we construct…

We seek to connect ideas in the theory of bridge trisections with other well-studied facets of classical knotted surface theory. First, we show how the normal Euler number can be computed from a tri-plane diagram, and we use this to give a…

We analyze supersymmetry breaking by anti-self-dual flux in the deformed conifold. This theory has been argued to be a dual realization of susy breaking by antibranes. As such, one might expect it to lead to a hierarchically small breaking…

Minimization of the (regularized) entropy of classification probabilities is a versatile class of discriminative clustering methods. The classification probabilities are usually defined through the use of some classical losses from…