Mathematics

We study the maximal variation problem for linear systems associated with a very ample line bundle, using Hodge theory and Picard-Lefschetz theory. We provide an affirmative answer to the maximal variation problem for a broad class of…

In this paper, we study pencils of plane curves of sufficiently large degree $d$ with simple base points, and their reducible curves whose irreducible components have degree at most $k\geq 2$. Combining techniques from algebraic geometry…

Kinetic equations are used to model a wide range of phenomena important for real-world applications. Their applications span astrophysics, nuclear physics, engineering, and social sciences. Due to their high-dimensional phase space,…

In this paper we count the number of common values shared by two linear recurrence sequences, whose characteristic polynomials are a generalized Ankeny-Brauer-Chowla polynomial and its reciprocal. More precisely, we show that these…

We consider the category of finitely generated modules over an artin algebra $A$. It is known that any module $M$ has a brick chain filtration. We say that M has brick chain complexity at most $t$ provided $M$ has a brick chain filtration…

We introduce a unified framework via Stein's method for bounding the Kolmogorov distance between the generalized Dickman distributions and the distribution of randomly weighted sums of non-negative integer-valued random variables that are…

We prove that, on a regular local $p$-Dirichlet space supporting a $p$-Poincar\'e inequality, if the $p$-walk dimension is strictly greater than $p$, then every curve family has zero $p$-modulus. As a consequence, we show that no…

We study smooth polarized projective varieties $(X,H)$ whose exterior powers of the tangent bundle are Ulrich. We prove that if $\bigwedge^rT_X$ is $H$-Ulrich for some $0<r<\dim X$, then $X$ is Fano and the intersection number $(-K_X)\cdot…

Let $M^n_\kappa$ be the simply connected space form of dimension $n\ge2$ and constant sectional curvature $\kappa\in\{-1,1\}$. For every bounded connected smooth domain $\Omega\subset M^n_\kappa$, assume in the case $\kappa=1$ that $\Omega$…

We study the inhomogeneous random graph with preferential attachment kernel and degree distribution with power-law exponent $\tau\in(2,3)$ as a representative of the class of graphs of preferential attachment type with infinite variance…

We develop an operator-algebraic framework for change-of-variables formulas on Wiener space, interpreting them as arising from hidden symmetries acting on observables. We show that general transformations can be represented by time-ordered…

We prove a one-variable functional inequality which is the free probability analog of Bobkov's isoperimetry inequality. The inequality involves the $L^1$ norm of the difference quotient of a function $f$ and can be viewed as a non-local…

In this paper, we introduce a suitable notion of flat solutions for the anisotropic surface diffusion equation with elasticity in three-dimensions, based on a minimizing movement scheme inspired by that introduced by Cahn and Taylor. Using…

This paper investigates the analytic structure of the parametric harmonic zeta function \[ \zeta_{H}\left( s,a,b\right) =\sum_{n=0}^{\infty}\frac{H_{n}\left( a\right) }{\left( n+b\right) ^{s}}, \] where $H_{n}\left( a\right) $ denotes the…

A pair of proper cones $(\mathsf{C}_1,\mathsf{C}_2)$ is said to have the Lorentz factorization property (LFP) if every $(\mathsf{C}_1,\mathsf{C}_2)$-positive map factors through a direct sum of Lorentzian cones, i.e., cones over Euclidean…

For a Hausdorff topology on the set of ideals of the semilattice $M(X)$ of coarse equivalence classes of metrics on a set $X$, the space $I(M(X))$ of ideals is the closure of the set of principal ideals, thus allowing to view non-principal…

We determine all involutions in the Cayley-Dickson construction that extend the involution of the original $*$-algebra. We also find all algebra isomorphisms between the resulting Cayley doubles that extend the identity automorphism of the…

We construct higher derived Artin stacks parametrizing constructible sheaves on complex algebraic varieties and compact real analytic varieties. Furthermore, we show that every perversity function gives rise to an open substack of perverse…

We analyze the asymptotics of a block-Wishart random matrix ensemble of the type ${\boldsymbol W}_k = ({\boldsymbol X}^* \otimes {\boldsymbol I}_k){\boldsymbol T}({\boldsymbol X}\otimes{\boldsymbol I}_k)$ for ${\boldsymbol X}…

In this paper we deal with Nil geometry, in whose projective model the geodesic curves are helix-like and fit onto geodesic Nil cylinders of revolution with fibrum axes. In this paper we investigate relations for geodesic cylinders and thus…