In group theory, various properties of the abelianization of a cyclically presented group can be deduced by the Smith normal form of an integer circulant matrix. Motivated by this fact, we present a number of results on the Smith form of matrices that are polynomials in the companion matrix of a polynomial with coefficients in a generic elementary divisor domain. Our tools are of purely matrix theoretical nature and I will present them from the point of view of a matrix theorist. However, they enable significant advances in pure algebra.
Sala Seminari (Dip. Matematica)
The inviscid surface quasigeostrophic equation (SQG) describes (roughly speaking) the temperature in a rapidly rotating stratified fluid which is transported by the velocity field. The velocity field is connected to the temperature via Riesz-transform, which are singular integral operators. It has applications in both meteorological and oceanic flows, while in mathematics it is often used as a toy model for the 3D Euler equations due to some structural similarities of these equations.
We consider two prototype classes of McKean-Vlasov (mean-field) SDEs with
In the first case, the coefficient is assumed to be affine in the
state-variable, only measurable in the law, and the dynamics allow for Lévy
jumps. We study the equivalent functional fixed-point equation for the
unknown time-dependent coefficients of the associated Markovian SDE. By
proving a contraction property for the functional map in a suitable normed
space, we infer existence and uniqueness results for the MK-V SDE, and
A degenerate reason why trivial is not always good
Abstract: In this talk, we focus on degeneration of low dimensional Calabi-Yau varieties. All the mysterious words in this abstract will be explained.
The talk is divided in two main parts. The first one is focused on
(generalized) companion pencils, which are strong linearizations and
they present a template involving no arithmetic operations at all. In
addition, we are mainly interested in sparse (generalized) companion
pencils and then, we determine the smallest number of nonzero entries of
a particular class of companion pencils. In the case of generalized
companion pencils, we should impose natural conditions on its entries.
Large Data Solutions for Fractional Higher Order Nonlinear Equations.
Titolo: Classificazione di Enriques delle superfici algebriche
Prerequisiti: geometria algebrica di base e teoria dei fasci
Nella prossima lezione studieremo alcuni dei risultati dell'articolo di
Bondal e Orlov che ci permettono di ricostruire una varietà liscia e
proiettiva con fascio (anti)canonico ampio dalla sua categoria derivata.