Research
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Research
Research
736+ open-access research outputs.
We establish a half-space theorem \`a la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.…
Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$. Early work by Friedland and Stanley addressed so…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal valu…
For the fixed-size Brualdi--Hoffman--Turan problem forbidding the fish graph $H(4,3)$, Zheng and Zhang proved that every $H(4,3)$-free graph of even size $m \ge 38$ without isolated vertices satisfies…
This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties o…
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dimensional or structur…
We give a necessary and sufficient condition on a matrix for its centralizer in $\sf{GL}(n,\mathbb{Z})$ to be polycyclic, or equivalently in this case, not to contain a non-abelian free subgroup. We g…
The main result of this paper shows that almost all graphs of order $n$ have no cospectral mates with height $o(( n / \ln n)^{1/10})$, improving an earlier result on cospectral mates with fixed level …
The Bollob\'as--Nikiforov conjecture asserts that for any graph $G \neq K_n$ with $m$ edges and clique number $\omega(G)$, \[ \lambda_1^2(G) + \lambda_2^2(G) \;\leq\; 2\!\left(1 - \frac{1}{\omeg…
In this paper, we give spectral upper bounds for the independence number of even uniform hypergraphs and graphs, extend the Hoffman bound to even uniform hypergraphs, and give a simple spectral condit…
In accordance with the Cameron-Goethals-Seidel-Shult Classification Theorem, we extend the characterization of Hoffman colorability of line graphs from (Abiad, Bosma, Van Veluw, 2025) to all connected…
Let $l\ge 1$ be an integer. For any multiple index $\mathbf{s}=(s_1,s_2,\cdots,s_l)\in\mathbb{Z}_{\geq 1}^l$ with $s_l>1$, the multiple zeta value (MZV for short) is defined by \begin{align*} \zeta(s_…
We investigate whether it is typical for a sparse graph to be uniquely characterized by its adjacency spectrum up to isomorphism. Our first result shows that the giant component of an Erd\H{o}s-R\'eny…
Let $r\ge 1$ be an integer. For any multiple index $\mathbf{s}=(s_1,s_2,\cdots,s_r) \in\mathbb{Z}_{\geq 1}^r$ with $s_r>1$, the multiple zeta value (MZV for short) is defined by \begin{align*} \zeta(s…
This paper provides a systematic study of symmetry properties for cyclotomic multiple Hurwitz zeta values with multiple variables and parameters by applying the methods of contour integration and the …
For a specific rooted labeled tree topology, a labeled history is a sequence of branchings that give rise to that labeled topology as it unfolds over time. Here, for $r$-furcating trees, we use a conn…
We initiate a systematic study of spectral theory for bounded-degree Borel pmp graphs. Specifically, we study spectral properties of the associated adjacency and Laplacian operators. We start with pro…
We establish half-space type results for a class of height-dependent weighted minimal surfaces in $\mathbb{R}^3$, namely critical points of a weighted area functional whose weight depends on the heigh…
This paper establishes an upper bound on the number of generalized cospectral mates of simple graphs, where the generalized spectrum consists of the spectrum of a graph and its complement. Moving beyo…
We show that Activated Random Walk on $\mathbb{Z}$ is explosive above criticality. That is, activating a single particle in a supercritical state of sleeping particles triggers an infinite avalanche o…
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