Research
Research
Research
Research
1,568+ open-access research outputs.
We show that the loop homology algebras of polyhedral products of the form $(\underline{X},\underline{*})^{\mathcal{K}}$ can be written as a colimit over the flagification of $\mathcal{K}$, and obtain…
We construct a family of velocity fields demonstrating the sharpness of the classical Zvonkin--Veretennikov--Davie strong well-posedness by noise regime. We consider stochastic differential equations …
Stochastic programming models for decision-making under uncertainty often suffer from scenario scarcity, where obtaining representative samples of uncertain parameters requires expensive simulations o…
The extent to which the geometry of an object is determined by some associated spectral data is a longstanding problem. We investigate this problem in the context of the Steklov spectrum, focusing on …
We propose a method for the prediction of stationary max--stable random fields with $\alpha$-Fr\'echet marginal distribution $H_\alpha$. The method is suitable to cope with heavy tails for $\alpha\in(…
Transit network design plays an important role in public transport. With the simplicity of spanning tree, this paper adopts the concept of spanning tree to help (re-)design a public transit network th…
We study $v_n$-periodic phenomena in $C_2$-equivariant stable homotopy through the lens of the $C_2$-equivariant Adams spectral sequence at the prime 2. In particular, we construct/detect certain clas…
We study topological rigidity of real moment-angle manifolds associated to flag simplicial complexes. Using the cubical geometry arising from the Davis construction, we identify the universal cover wi…
The long-standing hypothesis formulated by Goreinov, Tyrtyshnikov and Zamarashkin \cite{GTZ1997} has been recently solved by Sengupta and Pautov \cite{SP2026} in the case of two-column matrices. In th…
Davis, Drusvyatskiy, and Jiang showed that gradient descent with an adaptive stepsize converges locally at a nearly-linear rate for smooth functions that grow at least quartically away from their mini…
In this paper we prove that if a closed set in R^N is close to a cone over a simplicial complex at each point and at each scale, then it is locally bi-H\"older equivalent to such a cone. This generali…
We show that the Charney--Davis strict hyperbolization procedure can preserve stable tangent bundles, answering a question of Charney and Davis. The key input is the construction of many hyperbolizing…
Well-known conjectures of Charney--Davis, Gal, and Nevo--Petersen predict increasingly strong positivity phenomena for the h-vectors of flag simplicial spheres. In this paper, we formulate and prove m…
Let $\Lambda$ be a set and $\mathbb{F}$ a field, and suppose that $K,Q:\Lambda^2\to\mathbb{F}$ are two functions such that for any $n\in\mathbb{N}$ and $x_1,x_2,\ldots,x_n\in\Lambda$, the determinants…
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 …
We study the problem of embedding bipartite graphs in Ahlfors-David regular sets of large dimension using results from extremal graph theory. Our main theorem states that any graph satisfying a power-…
The Grothendieck constant $K_{G}$ is a fundamental quantity in functional analysis, with important connections to quantum information, combinatorial optimization, and the geometry of Banach spaces. De…
This work addresses arbitrary convex vector optimization problems, which constitute a general framework for multi-criteria decision-making in diverse real-world applications. Due to their complexity, …
We show that Grothendieck's real constant $K_{G}$ satisfies $K_G\geq c+10^{-26}$, improving on the lower bound of $c=1.676956674215576\ldots$ of Davie and Reeds from 1984 and 1991, respectively.…
Let $A$ be a full ranked $ n\times n$ matrix, with singular values $\sigma_1 (A) \ge \dots \ge \sigma_n (A) >0$. The condition number $\kappa(A):= \sigma_1(A)/\sigma_n(A)=\|A\|\cdot \|A\|^{-1}$ is a k…
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