Publications related to Few distinct distances implies no heavy lines or circles

Conjugate heat transfer in isolated granular clusters with interstitial fluid using lattice Boltzmann method

The conjugate heat transfer in mixtures of a fluid and single granular clusters is studied in this paper using a novel lattice Boltzmann method (LBM) programmed for parallel computation on the graphics processing unit (GPU). The LBM is validated for heat c ...

PERGAMON-ELSEVIER SCIENCE LTD2022

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

Many touchings force many crossings

János Pach

Given n continuous open curves in the plane, we say that a pair is touching if they have finitely many interior points in common and at these points the first curve does not get from one side of the second curve to its other side. Otherwise, if the two cur ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

On Sets Defining Few Ordinary Circles

Frank de Zeeuw

An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...

Springer2018

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

Pattern formation in thin liquid films: from coating-flow instabilities to microfluidic droplets

Gioele Mariano Nicolò Balestra

Nature and technical applications abound with thin viscous flows, ranging from the lava flow on volcanoes to the lubricating layer around confined bubbles in the microchannels of Lab-on-a-Chip devices. Countless are the examples where coating flows arise i ...

EPFL2018

Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity

Martin Vetterli, Thierry Blu, Hanjie Pan

Estimating Diracs in continuous two or higher dimensions is a fundamental problem in imaging. Previous approaches extended one dimensional methods, like the ones based on finite rate of innovation (FRI) sampling, in a separable manner, e.g., along the hori ...

2018

Distinct distances between points and lines

Frank de Zeeuw, Adrian Claudiu Valculescu, Shakhar Smorodinsky

We show that for m points and n lines in R-2, the number of distinct distances between the points and the lines is Omega(m(1/5)n(3/5)), as long as m(1/2)

Elsevier Science Bv2018

Distinct Distances on Algebraic Curves in the Plane

János Pach, Frank de Zeeuw

Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...

Cambridge Univ Press2017

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

Few distinct distances implies no heavy lines or circles

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Conjugate heat transfer in isolated granular clusters with interstitial fluid using lattice Boltzmann method

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

Many touchings force many crossings

On Sets Defining Few Ordinary Circles

Arithmetic and geometric structures in cryptography

Pattern formation in thin liquid films: from coating-flow instabilities to microfluidic droplets

Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity

Distinct distances between points and lines

Distinct Distances on Algebraic Curves in the Plane

On some algebraic and extremal problems in discrete geometry

Distinct Distances on Algebraic Curves in the Plane

Conjugate heat transfer in isolated granular clusters with interstitial fluid using lattice Boltzmann method

Arithmetic and geometric structures in cryptography

Many touchings force many crossings

Pattern formation in thin liquid films: from coating-flow instabilities to microfluidic droplets

On Sets Defining Few Ordinary Circles

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

Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity

Distinct distances between points and lines

On some algebraic and extremal problems in discrete geometry