This is a joint work with Loic Grenié and Giuseppe Molteni. Given a positive integer \(d\) which is not a square, denote by \(T(d)\) the length of the period of the continued fraction expansion for \(...
The principle behind magnetic fusion is to confine high temperature plasma inside a device in such a way that the nuclei of deuterium and tritium joining together can release energy. The high temperat...
Aeppli and Bott-Chern cohomologies are useful invariants on compact complex manifolds, especially if they do not admit Kahler metrics. In this seminar we will introduce generalisations of these object...
The aim of this course is to present some recent advances in the theory of stable sheaves on higher dimensional varieties, in particular Fano and hyper-Kähler manifolds. We will start by reviewing the...
K-stability (or existence of Kähler-Einstein metrics) of explicit Fano varieties has been studied for a long time. Delta invariants (stability thresholds) detect the K-stability of Fano varieties. Mor...
Iwasawa theory studies arithmetically significant modules (e.g. class groups and Selmer groups) associated with pro-$p$-extensions $K/k$ of global fields ($p$ a prime). It usually focuses on $p$-parts...
We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actua...
This talk presents “partition theoretic” analogs of the classical work of Matiyasevich that resolved Hilbert’s Tenth Problem in the negative. The Diophantine equations we consider involve equations of...
In this talk, we deal with pointwise a priori estimates for positive solutions to m-Laplacian problems involving different types of reactions depending on the gradient. In particular, we discuss the...
Let \( G \) be a finite group. It is not hard to see that for any representation \( \rho: G \to \mathrm{GL}(V) \) for \( V \) a real vector space, there exists a \( G \)-invariant bilinear form \( \be...
