Related papers: Improved bounds in Weaver and Feichtinger Conjectu…

We define new natural variants of the notions of weighted covering and separation numbers and discuss them in detail. We prove a strong duality relation between weighted covering and separation numbers and prove a few relations between the…

Marcus, Spielman, and Srivastava recently solved the Kadison-Singer problem by showing that if u_1, ..., u_m are column vectors in C^d such that \sum u_iu_i^* = I, then a set of indices S \subseteq {1, ..., m} can be chosen so that \sum_{i…

The Feichtinger conjecture for exponentials asserts that the following property holds for every fat Cantor subset B of the circle group: the set of restrictions to B of exponential functions can be covered by Riesz sets. In their seminal…

We improve Kolyvagin's upper bound on the order of the $p$-primary part of the Shafarevich-Tate group of an elliptic curve of rank one over a quadratic imaginary field. In many cases, our bound is precisely the one predicted by the Birch…

The axion Weak Gravity Conjecture implies that when parametrically increasing the axion decay constants, instanton corrections become increasingly important. We provide strong evidence for the validity of this conjecture by studying the…

Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)] claims a strong submultiplicative upper bound on the rank of a three-tensor obtained as an iterated Kronecker product of a constant-size base tensor. The conjecture, if true,…

We prove an asymptotic crystallization result in two dimensions for a class of nonlocal particle systems. To be precise, we consider the best approximation with respect to the 2-Wasserstein metric of a given absolutely continuous…

We study results related to a conjecture formulated by Strohmer and Beaver about optimal Gaussian Gabor frame set-ups. Our attention will be restricted to the case of Gabor systems with standard Gaussian window and rectangular lattices of…

This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the…

For a random variable $X$ define $Q(X) = \sup_{x \in \mathbb{R}} \mathbb{P}(X=x)$. Let $X_1, \dots, X_n$ be independent integer random variables. Suppose $Q(X_i) \le \alpha_i \in (0,1]$ for each $i \in \{1, \dots, n\}$. Ju\v{s}kevi\v{c}ius…

The Einstein-Maxwell equations on a smooth compact 4-manifold are reformulated as a purely Riemannian variational problem analogous to Calabi's variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is used to show…

We investigate the small constant case of a characterization of $A_\infty$ weights due to Fefferman, Kenig and Pipher. In their work, Fefferman, Kenig and Pipher bound the logarithm of the $A_\infty$ constant by the Carleson norm of a…

In this paper we give an asymptotically tight bound for the tolerated Tverberg Theorem when the dimension and the size of the partition are fixed. To achieve this we study certain partitions of order-type homogeneous sets and use a…

We consider the massive Klein-Gordon equation on short-range asymptotically Minkowski spacetimes. Extending our results in [GW1], we show that the Klein-Gordon operator with Feynman type boundary conditions at infinite times is invertible…

We derive robust long-time a-priori estimates for the Navier-Stokes equation in a two-dimensional infinite strip which are uniform in the Reynolds number. These estimates provide several new scale invariant upper bounds for the size of the…

In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in $C^{*}$-Algebras. We will show that every bounded Bessel sequence can be decomposed into two…

Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…

We derive the asymptotic expansion at infinity for embedded ends of uniformly elliptic Weingarten surfaces with finite total curvature in $\mathbb{R}^3$, and we establish a maximum principle at infinity. Furthermore, we solve the Dirichlet…

We propose a new approach to the Fourier restriction conjectures. It is based on a discretization of the Fourier extension operators in terms of quadratically modulated wave packets. Using this new point of view, and by combining natural…

In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian-Wachs conjecture, which links the Stanley-Stembridge conjecture in combinatorics to the geometry of Hessenberg varieties through Tymoczko's permutation group…