Concept

Singular point of an algebraic variety

Related publications (92)

GLOBALLY plus -REGULAR VARIETIES AND THE MINIMAL MODEL PROGRAM FOR THREEFOLDS IN MIXED CHARACTERISTIC

We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global F-regularity to mixed characteristic and identify certain stable sections of adjoint lin ...

SPRINGER HEIDELBERG2023

Algebraic twists of GL(2) automorphic forms

Vignesh Arumugam Nadarajan

In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and inc ...

EPFL2023

Small-angle scattering tensor tomography algorithm for robust reconstruction of complex textures

Marianne Liebi, Manuel Guizar Sicairos

The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural symmetries. For s ...

Chester2023

Thick points of the planar GFF are totally disconnected for all & gamma;=6 0*

Juhan Aru

We prove that the set of-y-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all-y =6 0. Our proof relies on the coupling between a GFF and the nested CLE4. In particular, we show that th ...

INST MATHEMATICAL STATISTICS-IMS2023

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Daniel Kressner, Ivana Sain Glibic

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

Oscar Salomon Kivinen

These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...

WILEY2022

On the projectivity of some moduli spaces of varieties

Quentin Arthur Frantisek Posva

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 ...

EPFL2022

Local invertibility and sensitivity of atomic structure-feature mappings

Michele Ceriotti, Sergey Pozdnyakov

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

2021

Rational-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots

Francesca Bonizzoni, Davide Pradovera

We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite el ...

2021

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

Xavier Fernandez-Real Girona

We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...

MATHEMATICAL SCIENCE PUBL2021

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