Mathematics

The aim of this paper is to estimate the irrationality of moduli spaces of hyperk\"ahler manifolds of types K3$^{[n]}$, Kum$_{n}$, OG6, and OG10. We prove that the degrees of irrationality of these moduli spaces are bounded from above by a…

This paper is the first one of two papers whose goal is to give a converse to the main result of my previous paper [6], so to prove the existence of multiple poles for the distribution |f|2$\lambda$ with an hypothesis on a Higher Bernstein…

We study slope-stable vector bundles and Bridgeland stability conditions on varieties which are a quotient of a smooth projective variety by a finite abelian group $G$ acting freely. We show there is an analytic isomorphism between…

We present a novel framework for learning cost-efficient latent representations in problems with high-dimensional state spaces through nonlinear dimension reduction. By enriching linear state approximations with low-order polynomial terms…

Multigraded linear series generalize the classical morphism to the linear series of a basepoint-free line bundle on a scheme. We investigate the collection of the natural cornering morphisms into elementary bigraded linear series obtained…

In this paper, we study certain moduli spaces of vector bundles on the blowup of the projective plane in at least 10 very general points. Moduli spaces of sheaves on general type surfaces may be nonreduced, reducible and even disconnected.…

Let $C$ and $D$ be smooth, proper and geometrically integral curves over a finite field $F$. Any morphism from $D$ to $C$ induces a morphism of their \'etale fundamental groups. The anabelian philosophy proposed by Grothendieck suggests…

The bidimensionality of a set of vertices $X$ in a graph $G$ is the maximum $k$ for which $G$ contains as a $X$-rooted minor the $(k \times k)$-grid. This notion allows for the following version of the Graph Minors Structure Theorem (GMST)…

Phasor Measurement Units (PMUs) are placed at strategic vertices in an electrical power network to monitor the flow of power. Determining the minimum number and optimal placement of PMUs is modeled by the graph theoretic process called…

We study the relationship between solutions to better-behaved GKZ hypergeometric systems near different large radius limit points, and their geometric counterparts given by the $K$-groups of the associated toric Deligne-Mumford stacks. We…

We prove a dimension-free $L^p(\mathbb{R}^d)$, $1<p<\infty$, estimate for the vector of higher order maximal Riesz transforms in terms of the corresponding Riesz transforms. This implies a dimension-free $L^p(\mathbb{R}^d)$ estimate for the…

In this paper, we consider the following nonlinear Schr\"odinger equation with derivative: \begin{align*} i\partial_tu+\partial_{xx}u+i|u|^{2}\partial_xu+b|u|^4u=0, \quad (t,x) \in \mathbb{R}\times\mathbb{R}, \quad b\geq 0. \end{align*} For…

We revisit a classic theorem of Frougny and Sakarovitch concerning automata for $\varphi$-representations, and show how to obtain it in a different and more computationally direct way. Using it, we can find simple, induction-free proofs of…

We show that for pseudoeffective projective pairs the termination of one sequence of flips implies the termination of all flips, assuming a natural conjecture on the behaviour of the Nakayama-Zariski decomposition under the operations of a…

Classical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the punctured projective line $S=\mathbb{P}^1\setminus \{0, 1, \infty\}$, which is an extension of the symmetric power of the Kummer variation by a trivial…

We work out normal forms for quasi-elliptic Enriques surfaces and give several applications. These include torsors and numerically trivial automorphisms, but our main application is the completion of the classification of Enriques surfaces…

We prove that any commutative group scheme over an arbitrary base scheme of finite type over a field with connected fibers and admitting a relatively ample line bundle is polarizable in the sense of Ng\^o. This extends the applicability of…

We analyse the aggregate Loewner evolution (ALE), introduced in 2018 by Sola, Turner and Viklund to generalise versions of diffusion limited aggregation (DLA) in the plane using complex analysis. They showed convergence of the ALE for…

The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a…

In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional It\^o formula…