Seminários

The irregularity of surfaces fibered by trigonal genus 5 curves

Resumo: The relative irregularity of a fibration $f: S\to B$ from a smooth projective surface to a curve is $q_f(S)=h^{1,0}(S)-g(B)$. A conjecture of G. Xiao formulated in 1988 (and modified by Pirola in 1992 to avoid some simple counterexamples) predicts that the relative irregularity of f is bounded from above by $g/2+1$, where g is the genus of the generic fiber of f. The most important progress towards this conjecture is due to Barja, González-Alonso, and Juan Carlos Naranjo who proved in 2016 that the conjecture holds provided that the generic fiber of f satisfies a certain genericity assumption. In this talk I will explain a strategy to prove the Xiao conjecture when the generic fiber of f is minimally generic. I will focus my attention on the simplest open case, namely that of surfaces fibered by trigonal genus 5 curves.

Metaverse / Social Networks Novels

Resumo: In this talk we will discuss the three (r)evolutions that lead to the current state-of-the-art in new media. We will present the concepts behind these societal, scientific and cultural innovations. Furthermore, we will also show a vision of what is possible in the foreseeable future, along with its inherent mechanisms and challenges. We will close by revealing the interconnections between recent trends in this scenario.

Live on YouTube: https://www.youtube.com/live/UHMnDtNfIXA?si=WDsGxI4ria5NivS-

Conjuntos invariantes para homeomorfismos de $3$-variedades hiperbólicas com velocidade de escape positiva

Resumo: O objetivo desta palestra é apresentar o problema de entender homeomorfismos minimais de $3$-variedades. Vamos nos concentrar em $3$-variedades hiperbólicas, onde, através do uso de algumas propriedades geométricas, podemos obter alguns resultados de existência de compactos invariantes e formular algumas perguntas precisas. É um trabalho conjunto com Elena Gomes e Santiago Martinchich.

Investigations of SL(4)-structures.

Resumo: The studies of convex-cocompact $SO(3,1),SO(2,2),$ and $SO(2,1)\times{\Bbb R}^{2,1}$ structures are the Lie-theoretic analogues of the studies of de Sitter, anti de Sitter, and Minkowski spacetimes respectively. The analytic treatments of these three theories are almost identical, suggesting a unified treatment involving Anosov SL(4)-structures. The main challenge in constructing such a unification is the absence of any invariant metric. It is thus necessary to enquire what structures may take their place. The purpose of this talk is to present some preliminary investigations into the theory of SL(4) structures aimed at resolving this problem.