Seminars

Statistical, mathematical, and computational methods for the advancement of ecology and climate change biology.

Event Date: Dec 02, 2024 in Seminars, SIPo (Seminario de Investigadores Postdoctorales)

Abstract: I will delve into three key topics of my research in quantitative ecology and how the outcomes contribute to understanding and preventing biodiversity loss. In each case, I will describe the ecological context, the data at hand, and the primary modeling tools used to address the problems of interest. First, I will talk about optimal survey design, which involves techniques to efficiently estimate population density by balancing sample size, spatial distribution, and survey effort. Next, I will explain how statistical calibration techniques are applied for error correction and data...

Event Date: Nov 27, 2024 in Seminario de Probabilidades de Chile, Seminars

Resumen:   We present a few results to get compound poisson distributions for random dynamical systems and for a class of stochastic differential equations. The main tool will be the use of spectral techniques.  

Metric properties of locally connected graphs.

Event Date: Nov 15, 2024 in Seminario de Grafos, Seminars

Abstract: A set of n points in the plane which are not all collinear defines at least n distinct lines. In 2008, Chen and Chvátal conjectured that this property holds for all finite metric spaces. This conjecture is still open, even for metric spaces induced by graphs. In this talk, we show that locally connected graphs satisfy this property and an even stronger one.

Complexities of words generated by a billiard in the hypercube.

Event Date: Nov 25, 2024 in Dynamical Systems, Seminars

RESUMEN: Sturmian words form a class of binary infinite words which sheds light, through its equivalent definitions, on remarkable interactions between combinatorics, dynamical systems, and number theory. They give rise to several generalizations over the d-letter alphabet, for d ≥ 3. A large program, initiated in the 80s, is to determine which characteristic properties of Sturmian words each of these generalizations still satisfy. My talk will focus on one dynamical representations of Sturmian words: as words generated by a billiard on a square table, which generalizes itself to a billiard...

Turán problem for edge-ordered graphs.

Event Date: Nov 22, 2024 in Seminario de Grafos, Seminars

Abstract: The Turán-type extremal problem asks how many edges an n-vertex simple graph can have if it does not contain a subgraph isomorphic to a forbidden graph. The systematic study of Turán-type extremal problems for edge-ordered graphs was initiated by Gerbner, Methuku, Nagy, Pálvölgyi, Tardos, and Vizer in 2020. A simple graph is called edge-ordered if its edges are linearly ordered. Gerbner et al. defined a parameter called order chromatic number for edge-ordered graphs and proved an Erdős-Stone-Simonovits-type theorem for edge ordered graphs that determines the Turán number of an...

On the stationary measures of two variants of the voter model.

Event Date: Nov 20, 2024 in Seminario de Probabilidades de Chile, Seminars

Resumen: The voter model is an interacting particle system describing the collective behaviour of voters who constantly update their political opinions on a given graph. This Markov process is dual to a system of coalescing random walks on the graph. This duality relationship makes the model more tractable by analysing the dynamics of the collision of random walks. This presentation is divided into two parts. First, we introduce two variants of the voter model: the voter model on dynamical percolation (in a random environment) and the voter model with stirring (where a stirring parameter...