Noticias en español
Selection principles for the N-BBM and the Fleming-Viot particle system.
Resumen: The selection problem is to show, for a given branching particle system with selection, that the stationary distribution for a large but finite number of particles corresponds to the travelling wave of the associated PDE with minimal wave speed. This had been an open problem for any such particle system. The N-branching Brownian motion with selection (N-BBM) is a particle system consisting of N independent particles that diffuse as Brownian motions in $\mathbb{R}$, branch at rate one, and whose size is kept constant by removing the leftmost particle at each branching event. We...
Read MoreOn the reachable space for the heat equation.
RESUMEN: The goal of this talk is to explain how perturbative arguments can be applied to derive a sharp description of the reachable space for heat equations having lower order terms. The main result I will present is the following one. Let us consider an abstract system $y’ = Ay + Bu$, where $A$ is an operator generating a $C^0$ semigroup $(exp(tA))_{t\geq 0}$ on a Hilbert space $X$, and $B$ is a control operator, for instance a linear operator from an Hilbert space $U$ to $X$, and let us assume that this system is null-controllable in $X$ in any positive time. Then, setting $R$ the...
Read MoreIntegrando modelos de nicho ecológico y datos de cobertura y uso de suelos para cuantificar la disponibilidad de hábitat de especies nativas del archipiélago de Hawái
Read MoreHecke groups in geometry.
Abstract: This talk discusses two geometric aspects of the so-called Hecke groups, defined by E.Hecke in the 1920s, and which are a generalisation of the modular group SL(2,Z) of 2×2 matrices with integer coefficients and determinant 1. Hecke groups will be used here as a pretext to talk about my research field, namely hyperbolic geometry and translation surfaces (no prior knowledge on these fields are required). More precisely, we will see that these groups are examples of lattice Fuchsian triangle groups, and that they also arise as Veech groups of translations surfaces. At the end we...
Read MoreDrawing Planar Graphs Badly.
Abstract: We study how far one can deviate from optimal behavior when drawing a planar graph on a plane. For a planar graph $G$, we say that a plane subgraph $H\subseteq G$ is a \textit{plane-saturated subgraph} if adding any edge (possibly with a new vertex) to $H$ would either violate planarity or make the resulting graph no longer a subgraph of $G$. For a planar graph $G$, we define the \textit{plane-saturation ratio}, $\psr(G)$, as the minimum value of $\frac{e(H)}{e(G)}$ for a plane-saturated subgraph $H\subseteq G$ and investigate how small $\psr(G)$ can be. While there exist planar...
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