Mathematics

Let $(\mathcal{E}, \mathbb{E}, \mathfrak{s})$ be an extriangulated category. Motivated by the theory of hereditary algebras, we introduce the notion of a hereditary-type subcategory $\mathcal{W}\subseteq \mathcal{E}$. We prove that the…

We generalize some results of Campana-P\u{a}un regarding foliations, slope stability, and positivity of log canonical bundles on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces.…

This note studies the 1D stochastic heat equation driven by a one-dimensional Brownian motion. We prove that the associated Markov process satisfies the strong Feller property under mild non-degeneracy conditions. The approach combines…

We produce refined index obstructions, generalizing recently constructed index obstructions due to de Jong and Perry, for topologically trivial Brauer classes on smooth and projective complex varieties. We show that our refined obstructions…

We study the fluctuations of the number of real roots of random polynomials with independent, nonzero-mean coefficients. Such non-centered ensembles arise naturally in signal-plus-noise models and in random perturbations of deterministic…

In this thesis we use the Beauville-Bogomolov decomposition to compute the LLV algebra of smooth projective complex varieties admitting a holomorphic symplectic form, generalizing known results from hyperk\"ahler and abelian varieties.…

Decarbonizing electricity generation, heating, and transportation simultaneously requires integrated planning tools that can coordinate multiple energy production sources and demand points while remaining reliable under uncertainty. This…

We consider polynomial maps of affine space over an algebraically closed field of characteristic zero. We prove that every irreducible component of the zero locus of the Jacobian determinant corresponds to either a contracted divisor or a…

Lezama \cite{LezamaLatorre2017} introduced the notion of semi-graded ring with the aim of generalizing $\mathbb{Z}$-graded rings and several families of noncommutative rings of polynomial type non-$\mathbb{N}$-graded such as the skew…

Policy learning in modern operations environments faces a fundamental tension between limited operational data and the large, often continuous, state and action spaces over which good decisions must be identified and deployed. We study…

Let $k$ be an $F$-finite and infinite field of characteristic $p>2$. We show, there exist infinitely many $F$-finite local domains $(R,\mathfrak{m})$ which are not $\mathbb{Q}$-Gorenstein and $\tau_{\mathrm{b}}(R;\mathfrak{m}^t)$ has all…

We develop a framework for studying how global spectral structure emerges from interacting local sectors in stratified operadic systems. The central object is the interaction residue, which measures the failure of exact spectral…

We show that, given $d \geq 4$ and two closed connected oriented PL $4$-manifolds $M$ and $N$ such that $N$ has a handle decomposition with no $1$- and $3$-handles, there exists a $d$-fold simple branched covering $p \colon M \darrow{d} N$…

We determine the $RO(C_2)$-graded Hurewicz images of the $C_2$-equivariant Eilenberg--MacLane spectra $H\underline{\mathbb F_2}$, $H\underline{\mathbb Z}$ and $H\underline{A}$, where $\underline{\mathbb F_2}$ and $\underline{\mathbb Z}$…

Most generalized fractional operators rely on prescribed memory kernels, restricting hereditary behavior to predefined forms and limiting flexibility in modeling diverse memory effects. Motivated by these limitations, this paper develops a…

Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…

We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The…

In this article, we provide the first theoretical framework guaranteeing that computers can, in principle, be used to analyze the parameter space of complex H\'{e}maps. More precisely, we obtain computability results for hyperbolic…

This paper has a threefold aim. On the one hand, we provide a complete description of Laguerre-Hahn forms of class zero. This fills a gap in the literature: more precisely, up to an affine change of variables, there are ten families,…

For every integer \(n\ge 3\), every \(1\le \ell\le n-2\), and every sufficiently large integer \(m\), we construct harmonic functions \(u_{m,\ell}\) on the unit ball \(B_1(0)\subset\mathbb{R}^n\) such that the frequency is bounded…