Noticias en español
Quantum dissipative systems.
Abstract: The problem of modeling dissipative effects in quantum physics dates back to the 1970s. After reviewing the main challenges associated with developing such models, I will present a specific model introduced by Bruneau and De Bièvre in the early 2000s. This model describes the interactions between a classical particle and an abstract environment, where the environment acts on the classical particle as a linear friction force. One of the key strengths of this approach is that it can be naturally extended to the quantum setting. In the second part, I will discuss the dynamical...
Read MoreDeterministic Impartial Selection with Weights.
Abstract: In the impartial selection problem, a subset of agents up to a fixed size k among a group of n is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of being selected by changing its vote. It is \alpha-optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of \alpha of the votes received by the subset of size k with the highest number of votes. We study deterministic impartial mechanisms in a more general setting with arbitrarily weighted...
Read MoreFracture of heterogeneous materials: a phase-field approach.
ABSTRACT: In this talk, I will describe recent attempts at devising a rigorous framework for the analysis and numerical simulation of crack propagation in heterogeneous materials. I will focus on the challenge of devising a mathematically sound and mechanistically coherent concept of effective toughness and computing it. I will first explain how classical theories such as homogenization fail to provide a meaningful answer to this question. Then, I will propose a framework based on the idea of computational homogenization in trajectory space. I will how it can account for new toughening...
Read MoreRobust Admission via Two-Stage Stable Matching under Ranking Uncertainty.
Abstract: The Bachillerato Inicia UC program offers a pathway for students from Chilean technical high schools to articulate into undergraduate programs at Pontificia Universidad Católica de Chile. Upon applying, candidates rank up to three preferred programs. However, articulation is determined only after one year, based on their academic ranking within the cohort – a value unknown at the time of admission. This setting gives rise to a two-stage admission problem with downstream matching constraints and exogenous uncertainty. The challenge is to select a feasible subset of students...
Read MoreBalancedness Constants of Words Generated By Billiards in The Hypercube.
RESUMEN In this talk, I will consider words generated by coding the trajectory of a ball inside a hypercubic billiard table. Balancedness is a combinatorial notion related to the dynamical concept of discrepancy, which characterizes square billiard words. It is then natural to ask: what is the imbalance (i.e., the optimal balancedness constant) of hypercubic billiard words in higher dimensions? After reviewing the partial results obtained by Vuillon in 2003, I will present a complete characterization of the imbalances of hypercubic billiard words generated by the trajectory of a ball...
Read MoreComparison of arm exponents in planar FK-percolation.
Resumen: FK-percolation is a generalisation of Bernoulli percolation that was found to be related to a wide range of other models in statistical mechanics, including the Ising model and the six-vertex model. In this talk, we will focus on the specific case of critical planar FK-percolation in the continuous phase transition regime. In this setting, the model exhibits properties similar to those of critical planar Bernoulli percolation; in particular, the Russo-Seymour-Welsh theory applies and the model is conjectured to be conformally invariant. Conformal invariance would imply that the...
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