Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Équation de Fermat généralisée

Publications associées (21)

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

Zsolt Patakfalvi

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

On rationally connected varieties over C1 fields of characteristic 0

Marta Pieropan

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 ...

MATHEMATICAL SCIENCE PUBL2022

The Lang-Trotter conjecture for products of non-CM elliptic curves

Vlad Serban

Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over Q and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous que ...

SPRINGER2022

A simple proof for a forbidden subposet problem

Abhishek Methuku

The poset Y-k,Y-2 consists of k + 2 distinct elements x(1), x(2), ..., x(k), y(1), y(2), such that x(1)

ELECTRONIC JOURNAL OF COMBINATORICS2020

Packing the Boolean lattice with copies of a poset

Istvan Tomon

The Boolean lattice (2[n],subset of) is the family of all subsets of [n]={1,MIDLINE HORIZONTAL ELLIPSIS,n}, ordered by inclusion. Let P be a partially ordered set. We prove that if n is sufficiently large, then there exists a packing P of copies of P in (2 ...

WILEY2020

New dense superball packings in three dimensions

Maria Margarethe Dostert

We construct a new family of lattice packings for superballs in three dimensions (unit balls for the l(3)(p) norm) with p epsilon (1, 1.58]. We conjecture that the family also exists for p epsilon (1.58, log(2) 3 = 1.5849625 ...]. Like in the densest latti ...

WALTER DE GRUYTER GMBH2020

A Crossing Lemma for Multigraphs

János Pach

Let G be a drawing of a graph with n vertices and e > 4n edges, in which no two adjacent edges cross and any pair of independent edges cross at most once. According to the celebrated Crossing Lemma of Ajtai, Chvatal, Newborn, Szemeredi and Leighton, the nu ...

SPRINGER2020

Nested Convex Bodies are Chaseable

Marek Elias

In the Convex Body Chasing problem, we are given an initial point v0. Rd and an online sequence of n convex bodies F1,..., Fn. When we receive Ft, we are required to move inside Ft. Our goal is to minimize the total distance traveled. This fundamental onli ...

SPRINGER2020

The role of atomistic simulations in probing hydrogen effects on plasticity and embrittlement in metals

William Curtin, Ali Tehranchi

Atomistic simulations are a powerful complement to experimental probes for understanding the nanoscale processes associated with the effects of hydrogen (H) on plasticity and fracture that are the underlying causes of hydrogen embrittlement (HE). Current e ...

PERGAMON-ELSEVIER SCIENCE LTD2019

On the Number of Containments in P-free Families

Abhishek Methuku

A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p

Springer2019

Almost tiling of the Boolean lattice with copies of a poset

Istvan Tomon

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...

ELECTRONIC JOURNAL OF COMBINATORICS2018

Cross-Intersecting Families of Vectors

János Pach

Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...

Springer Japan Kk2015

Remarks on Schur's conjecture

János Pach, Filip Moric

Let P be a set of n > d points in for d >= 2. It was conjectured by Zvi Schur that the maximum number of (d-1)-dimensional regular simplices of edge length diam(P), whose every vertex belongs to P, is n. We prove this statement under the condition that any ...

Elsevier Science Bv2015

Linear Growth for Certain Elliptic Fibrations

Pierre Francis André Le Boudec

We prove that the number of rational points of bounded height on certain del Pezzo surfaces of degree 1 defined over Q grows linearly, as predicted by Manin's conjecture. ...

Oxford University Press2015

Affine congruences and rational points on a certain cubic surface

Pierre Francis André Le Boudec

We establish estimates for the number of solutions of certain affine congruences. These estimates are then used to prove Manin's conjecture for a cubic surface split over Q whose singularity type is D-4. This improves on a result of Browning and answers a ...

Mathematical Science Publ2014

Proof of a conjecture by Gazeau et al. using the Gould-Hopper polynomials

Olivier Lévêque

We provide here some probabilistic interpretations of the generalized binomial distributions proposed by Gazeau et al. ["Generating functions for generalized binomial distributions," J. Math. Phys. 53, 103304 (2012)]. In the second part, we prove the "stro ...

Amer Inst Physics2013

Tight Bounds on the Redundancy of Huffman Codes

In this paper, we study the redundancy of Huffman codes. In particular, we consider sources for which the probability of one of the source symbols is known. We prove a conjecture of Ye and Yeung regarding the upper bound on the redundancy of such Huffman c ...

Ieee-Inst Electrical Electronics Engineers Inc2012

Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a ...

2011

Bin Packing via Discrepancy of Permutations

Friedrich Eisenbrand, Thomas Rothvoss, Doemoetoer Palvoelgyi

A well studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a suitable LP relaxati ...

Siam, 3600 Univ City Science Center, Philadelphia, Pa 19104-2688 Usa2011

Inferring transcript phylogenies

Bernard Moret, Yann Christinat

Alternative splicing, an unknown mechanism 20 years ago, is now recognized as a major mechanism for proteome and transcriptome diversity, particularly in mammals-some researchers conjecture that up to 90% of human genes are alternatively spliced. Despite m ...

IEEE Press2011