相关论文: Fiber integration on the Demailly tower

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly…

The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…

To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

We construct a connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension. The construction is based on certain structures on the bundle, i.e. connections and…

It is shown that the kinematic system describing planar non-steady motions of ideal fibre-reinforced fluids may be reduced to a single two-dimensional third-order partial differential equation in which time enters parametrically. A…

We introduce an invariant, associated to a coherent sheaf over a projective morphism of schemes, which controls when sheaf cohomology can be passed through the given morphism. We then use this invariant to estimate the stability indexes of…

We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge $X \vee Y$ of spaces (using the Hilton-Milnor theorem) and on the cofibre $\mathrm{cof}(f)$ of a map $f: X \rightarrow Y$. We deduce some…

We propose a novel derived cohomological framework for the Birch and Swinnerton-Dyer (BSD) conjecture for elliptic curves. In our approach, local arithmetic data are encoded in derived sheaves which, when glued via a mapping cone…

For a finite extension $F$ of ${\mathbf Q}_p$, Drinfeld defined a tower of coverings of ${\mathbb P}^1\setminus {\mathbb P}^1(F)$ (the Drinfeld half-plane). For $F = {\mathbf Q}_p$, we describe a decomposition of the $p$-adic geometric…

Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired…

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…

The purpose of this work is the design of FIR QMF (Quadrature Mirror Filters) filters of perfect reconstruction and odd number of coefficients (even order). By design, these filters will have linear phase and integer delay. These filter…

A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…

Khimshiashvili proved a topological degree formula for the Eu-ler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizations of this result for non-isolated singularities. As…

We review recent results for heterotic moduli and the Hull--Strominger system. In particular, we discuss mathematical properties of the recently derived deformation operator $\bar D$ associated to the deformation complex of heterotic…

We compute the arithmetic ranks of the defining ideals of homogeneous coordinate rings of certain Segre products arising from elliptic curves. The cohomological dimension of these ideals varies with the characteristic of the field, though…

We study the Hodge filtration of the intersection cohomology Hodge module for toric varieties. More precisely, we study the cohomology sheaves of the graded de Rham complex of the intersection cohomology Hodge module and give a precise…

We develop a new method to study intersection theory of the main component of the Hilbert scheme of points on complex manifolds. The main result is an iterated residue formula for tautological integrals. We formulate a Chern-Segre-type…