Noticias en español
Generative Social Choice
The mathematical study of voting, social choice theory, has traditionally only been applicable to choices among a few predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We introduce generative social choice, a design methodology for open-ended democratic processes that combines the rigor of social choice theory with the capability of large language models to generate text and extrapolate preferences. Our framework divides the design of AI-augmented democratic processes into two components: first, proving that the process satisfies...
Read MoreTruthful Budget Aggregation: Beyond Moving-Phantom Mechanisms.
Abstract: We study a budget-aggregation setting in which a number of voters report their ideal distribution of a budget over a set of alternatives, and a mechanism aggregates these reports into an allocation. Ideally, such mechanisms are truthful, i.e., voters should not be incentivized to misreport their preferences. For the case of two alternatives, the set of mechanisms that are truthful and additionally meet a range of basic desiderata (anonymity, neutrality, and continuity) exactly coincides with the so-called moving-phantom mechanisms, but whether this space is richer for more...
Read MoreShortest Odd path on undirected graphs with conservative weights.
Abstract: We consider the Shortest Odd Path (SOP) problem, where given an undirected graph $G$, a weight function on its edges, and two vertices $s$ and $t$ in $G$, the aim is to find an $(s,t)$-path with odd length and, among all such paths, of minimum weight. For the case when the weight function is conservative, i.e., when every cycle has non-negative total weight, the complexity of the SOP problem had been open for 20 years, and was recently shown to be NP-hard. I’ll present a polynomial-time algorithm for the special case when the weight function is conservative and the set of...
Read MoreEl Grupo de Automorfismos de un Subshift.
RESUMEN: El grupo de automorfismos de un subshift es una invariante algebraica que ha sido muy estudiada desde los años 60s. Daré una introducción al tema pasando por los teoremas clásicos y terminaré presentando un resultado reciente que relaciona estos grupos con aspectos de la geometría del grupo subyacente al subshift. Trabajo en conjunto con Nicanor Carrasco Vargas y Paola Rivera Burgos.
Read MoreA (dis)continuous percolation phase transition on the hierarchical lattice.
Abstract: For long-range percolation on $\mathbb{Z}$ with translation-invariant edge kernel $J$, it is a classical theorem of Aizenman and Newman (1986) that the phase transition is discontinuous when $J(x-y)$ is of order $|x-y|^{-2}$ and that there is no phase transition at all when $J(x-y)=o(|x-y|^{-2})$. We prove analogous theorems for the hierarchical lattice, where the relevant threshold is at $|x-y|^{-2d} \log \log |x-y|$ rather than $|x-y|^{-2}$: There is a continuous phase transition for kernels of larger order, a discontinuous phase transition for kernels of exactly this order,...
Read MoreThe role of Korteweg-de Vries symmetries in the partition function of extremal Black Holes.
Abstract: Abstract: In this talk, we will explore the role of generalized symmetries—symmetry groups that classify families of partial differential equations—in identifying fundamental symmetries in physics. We will also examine how this framework is crucial for defining conservation laws, building on Noether’s theorems and the contribution of Sophus Lie to the understanding of continuous symmetries. We focus on gravity, particularly within the Hamiltonian formalism, and highlight the importance of surface integrals to define conserved quantities, as shown in the pioneering work of...
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