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Concept

Geometrization conjecture

Related publications (23)

Mechanics of Physical Knots: From Filaments in Contact to Surgical Suturing

Paul Johanns

In this thesis, we study the mechanics of tight physical knots. Knots are omnipresent in surgery, climbing, and sailing, with disastrous consequences when the filament or the rope fails to perform its function. Even if the importance of mechanical analysis ...

EPFL2023

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

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

The shapes of physical trefoil knots

Pedro Miguel Nunes Pereira de Almeida Reis, John Maddocks, Paul Johanns, Tomohiko Sano, Paul Grandgeorge

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in a perfectly fle ...

2021

Study and characterization of silicon metal alloys systems for the reactive infiltration process of ceramic matrix composites

Manoj Kondibhau Naikade

Silicon infiltrated silicon carbide (SiSiC) is one of the most promising and economical non-oxide ceramic matrix composites for high-temperature structural applications. In recent years infiltration by Si-alloys instead of pure Si has become popular to avo ...

EPFL2021

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

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

Modeling of TAE mode excitation with an antenna in realistic X-point geometry

Ambrogio Fasoli, Duccio Testa

Experimentally, it is observed that Toroidal Alfven Eigenmodes (TAEs) are difficult to excite with an external antenna when the plasma is in X-point geometry. Here, the effect of the X-point geometry on the efficiency of the TAE excitation with the externa ...

AMER INST PHYSICS2020

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

Predictive control of spiral vortex breakdown

François Avellan, François Gallaire, Simon Pasche

The predictive control of the self-sustained single spiral vortex breakdown mode is addressed in the three-dimensional flow geometry of Ruith et al. (2003) for a constant swirl number S = 1.095. Based on adjoint optimization algorithms, two different contr ...

Cambridge University Press2018

Lonely Runner Polyhedra

Matthias Schymura

We study the Lonely Runner Conjecture, conceived by Jörg M. Wills in the 1960's: Given positive integers n_1, n_2, ... , n_k, there exists a positive real number t such that for all 1 \le j \le k the distance of t n_j to the nearest integer is at least 1 / ...

2019

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

Lambert cubes and the Lobell polyhedron revisited

The first example of a closed orientable hyperbolic 3-manifold was constructed by F. Lobell in 1931 from eight copies of the right-angled 14-hedron. We consider the family of hyperbolic polyhedra which generalize the Lambert cube and the Lobell polyhedron. ...

Walter De Gruyter & Co2012

Third-harmonic generation microscopy with Bessel beams: a numerical study

We study theoretically and numerically third-harmonic generation (THG) from model geometries (interfaces, slabs, periodic media) illuminated by Bessel beams produced by focusing an annular intensity profile. Bessel beams exhibit a phase and intensity distr ...

Optical Soc Amer2012

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