Research
Research
Research
Research
3,114+ open-access research outputs.
We develop a calculus for counting pseudoholomorphic disks with boundary in tropical Lagrangians contained in almost toric manifolds, using our previous work with Venugopalan. The results are mostly i…
In this paper, we prove several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either $3\leq n\leq 5$, $1\leq m\leq n-1$, or $6\leq n\le…
Alternating sign matrices (ASMs) arise as the Dedekind-MacNeille completion of the Bruhat order on the symmetric group. They enjoy fruitful combinatorial and geometric properties, with a particularly …
We prove that the unit group of a non-discrete irreducible, continuous ring, in the sense of John von Neumann, does not admit any non-trivial unitary representation continuous with respect to the stro…
We analyze a three-dimensional discontinuous piecewise linear system \(Z=(X,Y)\) whose switching manifold \(\Sigma\) contains visible-visible two-fold intersection lines. Assuming that the matrices \(…
We introduce a linear map on symmetric functions that 'divides' a partition by a positive integer $k$, sending a Schur function indexed by a partition of $kn$ to a symmetric function indexed by partit…
This paper presents a brief overview of ravine functions using the example of the Minkowski-Cohn moduli surface from the point of view of optimization on it. Elements of representation and solution of…
In 2016, Viazovska famously solved the sphere packing problem in dimension $8$, using modular forms to construct a 'magic' function satisfying optimality conditions determined by Cohn and Elkies in 20…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues…
For $0<\delta,\tau<1$ and $1\le s\le \frac{n}{n-\delta}$, we prove that for a given $s$-John domain $\Omega\subset \mathbb{R}^n$, the following Boxing inequality holds for every Lebesgue measurable …
We investigate the geometric behavior of $\tau(E)$ for bounded finite-perimeter sets $E \subset \mathbb R^n$, where $\tau(E)$ is the trace constant introduced by Figalli--Maggi--Pratelli [Invent. Math…
The Evans function is an analytic function that encodes information about the intersection of certain subspaces in ODE boundary value problems. As such it is a useful tool for computing the spectrum o…
A number of optimization algorithms have been inspired by the physics of Newtonian motion. Here, we ask the question: do algorithms themselves obey some ``natural laws of motion,'' and can they be der…
We show that the Markov fractions introduced recently by Springborn coincide with the index of the Cohn matrices defined by Aigner. This provides a simple concatenation rule for the corresponding cont…
The generalized Tur\'an number $\text{ex}(n, H, F)$ denotes the maximum number of copies of $H$ in an $n$-vertex $F$-free graph. Let $kK_{r+1}$ be the disjoint union of $k$ copies of the complete grap…
In this paper, we investigate the relationships between the volumes of four convex bodies: the cut polytope, metric polytope, rooted metric polytope, and elliptope, defined on graphs with $n$ vertices…
Refining the sharp upper bounds $\mu_{k,d}^* $ obtained by Kr\"oger (1999) for the $k$-th Neumann eigenvalue of a convex domain $\Omega \subset \mathbb{R}^d$, we prove the following inequalities: for …
We develop refined Karush-Kuhn-Tucker (KKT) and Fritz-John (FJ)-type optimality conditions for nonsmooth, nonconvex mathematical pro\-gra\-mming problems. We pay special attention in the case that the…
The Cohn-Elkies linear programming (LP) bound for sphere packing is known to be sharp in dimensions 8 and 24 but in no other dimension above 2. We investigate why by examining three independent necess…
The main purpose of this work is to explore the existence of constant scalar curvature Sasaki metrics in the Sasaki cone of the join of two regular Sasaki manifolds, $M_1$ and $M_2$. Furthermore, we c…
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