Giovedì 23 Gennaio 2025, dalle ore 14:00 in Aula 2109 (2° Piano) - Edificio U5, Stefano Borghini (UniTn) e Giulio Bresciani (SNS Pisa) terranno i seguenti seminari
Relatore: Stefano Borghini
Titolo: On the mass of initial data with positive cosmological constant
Abstract: The concept of mass for time-symmetric initial data has been extensively explored and is now a cornerstone in the study of contemporary Mathematical General Relativity, especially in relation to spacetimes with zero or negative cosmological constants. However, the case of a positive cosmological constant presents a distinct challenge: the renowned counterexamples to the Min-Oo conjecture by Brendle, Marques, and Neves highlight that even the rigidity statement in a potential positive mass theorem has not been correctly identified yet in this context. In this presentation, I will propose a novel approach to overcome this issue, leading to insights on a new notion of mass and to a characterization of the de Sitter spacetime. This is a joint work with Virginia Agostiniani and Lorenzo Mazzieri.
Relatore: Giulio Bresciani
Titolo: Arithmetic is topology in disguise: Grothendieck's section conjecture
Abstract: After revolutionizing algebraic geometry, in his last years before retiring from mathematics, Grothendieck became very interested in arithmetic problems. As always in his career, he took a very naive approach to a subject that was relatively new to him. From his point of view, arithmetic is essentially topology, provided we take a fairly elastic definition of topology. This naive approach led him to define the étale fundamental group of an algebraic variety, which at once generalized the topological fundamental group and Galois theory, providing a bridge between the two. This new bridge inspired him to formulate a series of profound conjectures that predict how the entire geometry of certain varieties, so-called “anabelian,” is reconstructible from the étale fundamental group. Of these, the most profound is the so-called section conjecture, and it is to this day widely open. In the seminar, I will try to convince you that arithmetic is indeed topology, introduce the section conjecture, mention some results and future prospects.
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