On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...

The current leading 6D object pose estimation methods rely heavily on annotated real data, which is highly costly to acquire. To overcome this, many works have proposed to introduce computer-generated synthetic data. However, bridging the gap between the s ...

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 ...

We consider the following class of fractional Schrodinger equations: (-Delta)(alpha)u + V(x)u = K(x)f(u) in R-N, where alpha is an element of (0, 1), N > 2 alpha, (-Delta)(alpha) is the fractional Laplacian, V and K are positive continuous functions which ...

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 ...

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 ...

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/ ...

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 ...

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 ...

We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...

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 ...

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT ...

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

We show that the transcendence degree of a real function field over an arbitrary real base field is a strict lower bound for its Pythagoras number and a weak lower bound for all its higher Pythagoras numbers. ...

In this paper we study a nonlinear elliptic boundary value problem with a general singular lower order term, whose model is {-Delta u = H(u)mu, in Omega, u = 0 on partial derivative Omega, u > 0 on Omega, where Omega is an open bounded subset of R-N, mu is ...

A simple topological graph is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any two of them meet at most once. Let be a complete simple topological graph on vertices. The three edges induced by any t ...

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

In this paper, we present a distributed control strategy, enabling agents to converge onto and travel along a consensually selected curve among a class of closed planar curves. Individual agents identify the number of neighbors within a finite circular sen ...

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

Chat with Graph Search

Global Frobenius liftability I

SD-Pose: Semantic Decomposition for Cross-Domain 6D Object Pose Estimation

Many touchings force many crossings

Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrodinger Equations

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

Arithmetic and geometric structures in cryptography

Distinct Distances on Algebraic Curves in the Plane

Algebraic and topological methods in combinatorics

On some algebraic and extremal problems in discrete geometry

Few distinct distances implies no heavy lines or circles

Computational Aspects of Jacobians of Hyperelliptic Curves

An Inner-Product Calculus for Periodic Functions and Curves

Medial axis transformation as a solid modeling representation method for computer aided design software

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Similarity-Based Shape Priors for 2D Spline Snakes

Lower bounds for Pythagoras numbers of function fields

Elliptic equations with general singular lower order term and measure data

Empty Triangles in Complete Topological Graphs

Constructing reparameterization invariant metrics on spaces of plane curves

Decentralized Self-Selection of Swarm Trajectories: From Dynamical Systems to Robotic Implementation