The Nonvanishing Problem for varieties with nef anticanonical bundle

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We show that elliptic Calabi-Yau threefolds form a bounded family. We also show that the same result holds for minimal terminal threefolds of Kodaira dimension 2, upon fixing the rate of growth of pluricanonical forms and the degree of a multisection of th ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Estimating the stress of reinforcing bars and its variations in service conditions can be useful to determine the reserve capacity of structures or to assess the risk of fatigue in the reinforcement. This paper investigates the use crack width measurements ...

We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...

Nowadays materials to protect equipment from unwanted multispectral electromagnetic waves are needed in a broad range of applications including electronics, medical, military and aerospace. However, the shielding materials currently in use are bulky and wo ...

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

Self-tracking technologies open new doors to previously unimaginable scenarios. The diagnosis of diseases years in advance, or supporting the health of astronauts on missions to Mars are just some of many example applications. During the COVID-19 pandemic, ...

In this work, we propose a numerical approach based on forward coupled mode modeling to simultaneously evaluate second- and third-order nonlinearities inside a dispersion-engineered waveguide towards the goal of generating broadband terahertz (THz) radiati ...

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...

This thesis is constituted of one article and three preprints that I wrote during my PhD thesis. Their common theme is the moduli theory of algebraic varieties. In the first article I study the Chow--Mumford line bundle for families of uniformly K-stable F ...

Elastic interfaces display scale-invariant geometrical fluctuations at sufficiently large lengthscales. Their asymptotic static roughness then follows a power-law behavior, whose associated exponent provides a robust signature of the universality class to ...

We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...

Lightning strikes can seriously affect the reliability and availability of electrical infrastructures. The computation of lightning-electromagnetic fields represents one of the most crucial steps in the evaluation of the induced effects; thus, having at di ...

In labscale Faraday experiments, meniscus waves respond harmonically to small-amplitude forcing without threshold, hence potentially cloaking the instability onset of parametric waves. Their suppression can be achieved by imposing a contact line pinned at ...

Many physical and chemical reactions are driven by nonadiabatic processes, which imply the breakdown of the celebrated Born-Oppenheimer approximation. To understand these processes, experimentalists employ spectroscopic techniques. However, the obtained re ...

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the g ...

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

The Nonvanishing Problem for varieties with nef anticanonical bundle

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Boundedness of Elliptic Calabi-yau Threefolds

From low-rank retractions to dynamical low-rank approximation and back

Estimation of the bar stress based on crack width measurements in reinforced concrete structures

Arithmetic and geometric deformations of threefolds

Tensor approximation of the self-diffusion matrix of tagged particle processes

Numerical Study of the Optical Response of ITO-In2O3 Core-Shell Nanocrystals for Multispectral Electromagnetic Shielding

Low-Rank Tensor Methods for High-Dimensional Problems

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Designing self-tracking experiences: A qualitative study of the perceptions of barriers and facilitators to adopting digital health technology for automatic urine analysis at home

Ultra-broadband terahertz radiation by supercontinuum generation and optical rectification in a dispersion-engineered waveguide: a numerical study

On rationally connected varieties over C1 fields of characteristic 0

On the projectivity of some moduli spaces of varieties

Microscopic interplay of temperature and disorder of a one-dimensional elastic interface

A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation

A Prony-based approach for accelerating the lightning electromagnetic fields computation above a perfectly conducting ground

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

Efficient geometric integrators for the linear and nonlinear time-dependent Schrödinger equation

Robust numerical integration on curved polyhedra based on folded decompositions

TimeEvolver: A program for time evolution with improved error bound

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method