Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Creación de agentes basados en gráficos de conocimiento con generación de texto estructurado y modelos open-weights
Abstract: Los gráficos de conocimiento son excelentes para representar y almacenar información heterogénea e interconectada de manera estructurada, capturando de manera eficaz relaciones y atributos complejos en diferentes tipos de datos. La generación de texto estructurado permite crear gráficos de conocimiento al proporcionar resultados perfectamente estructurados, lo que lo convierte en un método ideal para extraer información estructurada. De manera similar, la generación de texto estructurado permite la creación de agentes al definir qué...
Erd\H{o}s-Ko-Rado Problems for Graphs.
Abstract: In this talk, we introduce a new line of research exploring the size and structure of the largest intersecting family of paths in a graph. A family of sets is called intersecting if every pair of its members share an element; such an intersecting family is called a star if some element is in every member of the family. Erd\H{o}s-Ko-Rado famously proved (1938, 1962) that the maximum size intersecting families of r-subsets of {1,2,…,n} (with r<=n/2) are precisely the stars. Here, we consider families of sets where the sets...
Statistical, mathematical, and computational methods for the advancement of ecology and climate change biology.
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...
Recent Progress on the Fractional Yamabe Problem.
Abstract: Let $(M^n, [\hat{g}])$ be the conformal infinity of an asymptotically hyperbolic Einstein (AHE) manifold $(X^{n+1},g^+).$ We will take the scattering operator associated to the AHE filling in as the fractional conformal Laplacian. Equipped with fractional conformal Laplacians defined via the AHE manifold, we can define a fractional Yamabe problem, looking for a conformal metric of $(M^n,[\hat{g}])$ which has constant fractional scalar curvature. We will present some new developments on the fractional Yamabe problem assuming an AHE...
Rainbow path separation systems (RPSS)
Abstract: A family of paths P in a graph G is (k,t)-rainbow separating if it can be coloured with k colours such that for every t-tuple of edges e_1, …, e_t there exist t paths P_1, …, P_t of distinct colours such that P_i contains the edge e_i and does not contain any other edge of the t-tuple. Much work has been done on (∞,2)-RPSS, also known as strong path separation systems. In this talk I will present some optimal results on (2,2)-RPSS, together with a more general treatise on (k,2)-RPSS for all values of k.
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.
Complexities of words generated by a billiard in the hypercube.
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...
Turán problem for edge-ordered graphs.
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...
On the stationary measures of two variants of the voter model.
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...
A stroll through monotone inclusion problems and their splitting algorithms.
Abstract: Many situations in convex optimization can be modeled as the problem of finding a zero of a monotone operator, which can be regarded as a generalization of the gradient of a differentiable convex function. In order to numerically address this monotone inclusion problem it is vital to be able to exploit the inherent structure of the monotone operator defining it. The algorithms in the family of the splitting methods are able to do this by iteratively solving simpler subtasks which are defined by separately using some parts of the...
