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Concept

Diviseur (géométrie algébrique)

Publications associées (24)

Singularities of general fibers and the LMMP

Zsolt Patakfalvi

We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by p - 1. We deduce ...

JOHNS HOPKINS UNIV PRESS2022

On the Kodaira vanishing theorem for log del Pezzo surfaces in positive characteristic

Emelie Kerstin Arvidsson

We investigate the vanishing of H1(X,OX(−D)) for a big and nef Q-Cartier Z-divisor D on a log del Pezzo pair (X,Δ) over a perfect field of positive characteristic p. ...

2021

Vanishing theorems in positive characteristic

Emelie Kerstin Arvidsson

The topic of this thesis is vanishing theorems in positive characteristic. In particular, we use "the covering trick of Ekedahl" to investigate the vanishing of

H^1(X, \mathcal{O}_X(-D))

for a big and nef Weil divisor

D

on a normal projective variety w ...

EPFL2021

Logic Resynthesis of Majority-Based Circuits by Top-Down Decomposition

Giovanni De Micheli, Heinz Riener, Siang-Yun Lee

Logic resynthesis is the problem of finding a dependency function to re-express a given Boolean function in terms of a given set of divisor functions. In this paper, we study logic resynthesis of majority-based circuits, which is motivated by the increasin ...

IEEE2021

Convex Combination of Diffusion Strategies Over Networks

Ali H. Sayed

Combining diffusion strategies with complementary properties enables enhanced performance when they can be run simultaneously. In this article, we first propose two schemes for the convex combination of two diffusion strategies, namely, the power-normalize ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Affine Combination of Diffusion Strategies Over Networks

Ali H. Sayed

Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple diffusion strate ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Local Theory of the Insulating State

Antimo Marrazzo

An insulator differs from a metal because of a different organization of the electrons in their ground state. In recent years this feature has been probed by means of a geometrical property, the quantum metric tensor, which addresses the system as a whole, ...

AMER PHYSICAL SOC2019

Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0

Lei Zhang, Zsolt Patakfalvi

Let k be an algebraically closed field of characteristic p > 0. We give a birational characterization of ordinary abelian varieties over k: a smooth projective variety X is birational to an ordinary abelian variety if and only if kappa(S)(X) = 0 and b(1)(X ...

DUKE UNIV PRESS2019

The Bounded Cohomology of SL2 Over Local Fields and S-Integers

Nicolas Monod

It is proved that the continuous bounded cohomology of SL2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for ...

OXFORD UNIV PRESS2019

THE LMMP FOR LOG CANONICAL 3-FOLDS IN CHARACTERISTIC p > 5

We prove that one can run the log minimal model program for log canonical 3-fold pairs in characteristic p > 5. In particular, we prove the cone theorem, contraction theorem, the existence of flips and the existence of log minimal models for pairs with log ...

2018

The Shifted Convolution of Generalized Divisor Functions

Berke Topacogullari

We prove an asymptotic formula for the shifted convolution of the divisor functions d(k)(n) and d(n) with k >= 4, which is uniform in the shift parameter and which has a power saving error term, improving results obtained previously by Fouvry and Tenenbaum ...

OXFORD UNIV PRESS2018

Algebraic and topological methods in combinatorics

Adrian Claudiu Valculescu

The present thesis deals with problems arising from discrete mathematics, whose proofs make use of tools from algebraic geometry and topology. The thesis is based on four papers that I have co-authored, three of which have been published in journals, and o ...

EPFL2017

A Singular Elliptic System with Higher Order Terms of p-Laplacian Type

Linda Maria De Cave

We use variational techniques to prove existence and nonexistence results for the following singular elliptic system: {div(vertical bar del u vertical bar(p-2)del u) = theta z(q)/u(1-0), u > 0 in Omega is an element of W-0(,1p) (Omega), -div(vertical bar d ...

Walter De Gruyter Gmbh2016

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Optimal polynomial blow up range for critical wave maps

Joachim Krieger, Can Gao

We prove that the critical Wave Maps equation with target

S^2

and origin

\R^{2+1}

admits energy class blow up solutions of the form

u(t, r) = Q(\lambda(t)r) + \eps(t, r)

where

Q:\R^2\rightarrow S^2

is the ground state harmonic map and $\lambd ...

2015

Optimal polynomial blow up range for critical wave maps

Can Gao

We prove that the critical Wave Maps equation with target

S^2

and origin ℝ

^{2+1}

admits energy class blow up solutions of the form

u(t, r) = Q(\lambda(t)r) + \epsilon(t, r)

where

Q:ℝ²\rightarrow S^2

is the ground state harmonic map and $\lambda ...

EPFL2015

Graph Embedded Nonparametric Mutual Information For Supervised Dimensionality Reduction

Nikolaos Arvanitopoulos Darginis

In this paper, we propose a novel algorithm for dimensionality reduction that uses as a criterion the mutual information (MI) between the transformed data and their cor- responding class labels. The MI is a powerful criterion that can be used as a proxy to ...

Institute of Electrical and Electronics Engineers2015

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Philippe Michel

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

European Mathematical Soc2014

Orbital Magnetization as a Local Property

The modern expressions for polarization P and orbital magnetization M are k-space integrals. But a genuine bulk property should also be expressible in r space, as an unambiguous function of the ground-state density matrix, "nearsighted'' in insulators, ind ...

Amer Physical Soc2013

Generalized tensor idempotents and the telescope conjecture

Giordano Favi

We transpose Rickard's construction of idempotent representations to the general context of tensor triangulated categories. We connect our construction to the telescope conjecture and prove that the latter is of local nature. As an illustration, we extend ...

2011

Publications associées (24)

Singularities of general fibers and the LMMP

Zsolt Patakfalvi

JOHNS HOPKINS UNIV PRESS2022

On the Kodaira vanishing theorem for log del Pezzo surfaces in positive characteristic

Emelie Kerstin Arvidsson

We investigate the vanishing of H1(X,OX(−D)) for a big and nef Q-Cartier Z-divisor D on a log del Pezzo pair (X,Δ) over a perfect field of positive characteristic p. ...

2021

Vanishing theorems in positive characteristic

Emelie Kerstin Arvidsson

The topic of this thesis is vanishing theorems in positive characteristic. In particular, we use "the covering trick of Ekedahl" to investigate the vanishing of

H^1(X, \mathcal{O}_X(-D))

for a big and nef Weil divisor

D

on a normal projective variety w ...

EPFL2021

S^2

and origin

\R^{2+1}

admits energy class blow up solutions of the form

u(t, r) = Q(\lambda(t)r) + \eps(t, r)

where

Q:\R^2\rightarrow S^2

is the ground state harmonic map and $\lambd ...

2015

Optimal polynomial blow up range for critical wave maps

Can Gao

We prove that the critical Wave Maps equation with target

S^2

and origin ℝ

^{2+1}

admits energy class blow up solutions of the form

u(t, r) = Q(\lambda(t)r) + \epsilon(t, r)

where

Q:ℝ²\rightarrow S^2

is the ground state harmonic map and $\lambda ...

EPFL2015