Related papers: Unlikely intersections in Shimura varieties and be…
The purpose of the present note is to review and improve the convergence of the renormalized winding fields.
We strengthen and put in a broader perspective previous results of the first two authors on colliding permutations. The key to the present approach is a new non-asymptotic invariant for graphs.
A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current…
In this paper we define a flow with limited intersection of its worldlines and we construct and solve functional equations for such flow using a special kind of set embedding. For examples we use particular cases studied in the past by…
Due to the complex and dynamic character of intersection scenarios, the autonomous driving strategy at intersections has been a difficult problem and a hot point in the research of intelligent transportation systems in recent years. This…
We list combinatorial criteria of some singularities, which appear in the Minimal Model Program or in the study of (singular) Fano varieties, for spherical varieties. Most of the results of this paper are already known or are quite easy…
In this work we present a general introduction to the Signorini problem (or thin obstacle problem). It is a self-contained survey that aims to cover the main currently known results regarding the thin obstacle problem. We present the theory…
We survey recent results on a conjecture of Kudla regarding the modularity of generating series of special cycle classes in toroidal compactifications of orthogonal and unitary Shimura varieties. Along the way, we formulate several…
This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with other functional inequalities and also large…
The isometry class of the intersection form of a compact complex surface can be easily determined from complex-analytic invariants. For projective surfaces the primitive lattice is another naturally occurring lattice. The goal of this note…
In this survey, we review the many faces of the Hornich-Hlawka inequality. Several open problems that seem of utmost interest are mentioned.
Autonomous Vehicles are currently being tested in a variety of scenarios. As we move towards Autonomous Vehicles, how should intersections look? To answer that question, we break down an intersection management into the different conundrums…
The first three sections of this survey represent an updated and much expanded version of the abstract of my talk at FPSAC'2010: new results are incorporated and several concrete conjectures on the interactions between the three…
We give examples of smooth quasi-projective varieties over complex numbers, in the context of connected Shimura varieties, which are not homeomorphic to a conjugate of itself by an automorphism of the complex numbers.
In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.
The main purpose of this article is to study from the geometric point of view the problem of limit cycles bifurcation of perturbed completely integrable systems.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
This paper presents an overview of the current state of knowledge in the field of equivariant map algebras and discusses some open problems in this area.
The main purpose of the note is to show that Yoshinaga's arrangement of $18$ lines having $48$ triple and $9$ double intersection points leads to a new (short) series of non-containment examples for $I^{(3)} \subset I^{2}$, the question…
We prove the Eichler-Shimura relation on intersection cohomolgoy of minimal compactifications of Shimura Varieties of Hodge type.