Prossimi seminari del Dipartimento di Matematica

Martedì
18 giugno
This seminar addresses the problem of image segmentation through an accurate high-order scheme based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function, but the velocity that drives the curve to the boundary of the object has been modified in order to obtain a new velocity with additional properties that are extremely useful to develop a more stable high-order approximation with a small additional cost. The approximation scheme proposed here is the 2D version of an adaptive “filtered” scheme, which combines two building blocks (a monotone scheme and a high-order scheme) via a filter function and smoothness indicators that allow one to detect the regularity of the approximate solution adapting the scheme in an automatic way. Some numerical tests on synthetic and real images confirm the accuracy of the proposed method and the advantages given by the new velocity.
Mercoledì
19 giugno
Domenico Scopelliti
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario interdisciplinare
ore 11:00
presso Aula Arzelà
Optimization and equilibrium problems have been extensively studied when the involved preference relations admit a representation by means of realvalued functions. Although these problems have been analyzed under very minimal assumptions on the representation function, this context could appear to be quite restrictive in some practical situations. The aim of this talk is to present a new study of preference relations in topological spaces and to analyze, in Banach spaces, a suitable concept of a normal operator to upper contour set. In doing this, we propose the concept of weak upper continuity for preference relations and we compare it with the other continuity-like notions available in the literature. As an application of our theoretical developments, we analyze a preference equilibrium problem by using a suitable quasi-variational inequality formulation: as an example, a preference allocation problem (possibly under time and uncertainty) is also considered.
Mercoledì
19 giugno
Katia Colaneri
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di probabilità
ore 12:00
presso Aula Seminario VIII piano
We study the problem of a profit maximizing electricity producer who has to pay carbon taxes and who decides on investments into technologies for the abatement of carbon emissions in an environment where carbon tax policy is random and where the investment in the abatement technology is divisible, irreversible and subject to transaction costs. We consider two approaches for modelling the randomness in taxes. First we assume a precise probabilistic model for the tax process, namely a pure jump Markov process (so-called tax risk); this leads to a stochastic control problem for the investment strategy. Second, we analyze the case of an {uncertainty-averse} producer who uses a differential game to decide on optimal production and investment. We carry out a rigorous mathematical analysis of the producer's optimization problem and of the associated nonlinear PDEs in both cases. Numerical methods are used to study quantitative properties of the optimal investment strategy. We find that in the tax risk case the investment in abatement technologies is typically lower than in a benchmark scenario with deterministic taxes. However, there are a couple of interesting new twists related to production technology, divisibility of the investment, tax rebates and investor expectations. In the stochastic differential game on the other hand an increase in uncertainty might stipulate more investment. This presentation is based on joint works with Rüdiger Frey and Verena Köck.
Mercoledì
19 giugno
Francesco Galuppi
Seminario di algebra e geometria
ore 14:00
presso Seminario II
To each smooth path it is possible to associate a sequence of tensors that encode its geometric features. These signature tensors are powerful tools in stochastics analysis and data analysis, and recently they started attracting the geometers' attention. In this talk I will present the algebraic geometry viewpoint on signature tensors: the varieties they parametrize, their rank and their symmetries.
Giovedì
20 giugno
Simone Ciani
Seminario di analisi matematica
ore 16:00
presso Aula Vitali
seminario on line • collegamento al meeting
We present a recent study on the boundary behavior of solutions to parabolic double-phase equations, through the celebrated Wiener’s sufficiency criterion. The analysis is conducted for cylindrical domains and the regularity up to the lateral boundary is shown in terms of either its p or q capacity, depending on whether the phase vanishes at the boundary or not. Eventually we obtain a fine boundary estimate that, when considering uniform geometric conditions (as density or fatness), leads us to the boundary Holder continuity of solutions. In particular, the double-phase elicits new questions on the definition of an adapted capacity. This is a joint work in collaboration with Eurica Henriques and Ihor Skrypnik.
Venerdì
21 giugno
We establish local well-posedness in the sense of Hadamard for the higher-order nonlinear Schrödinger equation with a general power nonlinearity formulated on the half-line. We consider two different scenarios of certain parameters, one of which is associated with a single boundary condition, and the other case requires the use of two boundary conditions. We assume general nonhomogeneous Dirichlet and/or Neumann boundary conditions. Our functional framework centers around fractional Sobolev spaces with respect to the spatial variable. We treat both high regularity and low regularity solutions: in the former setting, the relevant nonlinearity can be handled via the Banach algebra property; in the latter setting, however, this is no longer the case and, instead, delicate Strichartz estimates must be established. This task is especially challenging in the framework of nonhomogeneous initial-boundary value problems, as it involves proving boundary-type Strichartz estimates that are not common in the study of Cauchy (initial value) problems. The linear analysis, which forms the core of this work, crucially relies on a weak solution formulation defined through the novel solution formulae obtained via the Fokas method (also known as the unified transform) for the associated forced linear problem. In this connection, we note that the higher-order Schrödinger equation comes with an increased level of difficulty due to the presence of more than one spatial derivatives in the linear part of the equation. This feature manifests itself via several complications throughout the analysis, including (i) analyticity issues related to complex square roots, which require careful treatment of branch cuts and deformations of integration contours; (ii) singularities that emerge upon changes of variables in the Fourier analysis arguments; (iii) complicated oscillatory kernels in the weak solution formula for the linear initial-boundary value problem, which require a subtle analysis of the dispersion in terms of the regularity of the boundary data. *This is a joint work with A. Alkın (Iztech) and D. Mantzavinos (Univ. of Kansas).
24/06/2024
28/06/2024
Conference
da lunedì 24 giugno 2024 a venerdì 28 giugno 2024
Parabolic dynamics has undergone a revolution in the last twenty-five years through the use of renormalization methods. This meeting will showcase many of the recent developments of the field and its many applications to other areas. We will take the opportunity to celebrate Giovanni Forni's 60th birthday and his pioneering contributions to the field.
24/06/2024
28/06/2024
Conference
da lunedì 24 giugno 2024 a venerdì 28 giugno 2024
Noncommutativity is a broad term that occurs in many areas of mathematics. Recently, there have been major developments around noncommutative phenomena related to all fundamental aspects of mathematics. The aim of the conference is to bring together experts in these diverse areas to share new ideas, discuss major recent advances and propose possible future directions.
Kähler geometry lies in the intersection of complex geometry, Riemannian geometry and symplectic geometry. From the complex geometric point of view, it is therefore natural to consider special non-Kähler Hermitian metrics on complex manifolds. Among them, pluriclosed metrics deserve particular attention. These metrics always exist on compact complex surfaces but the situation in higher dimension is very different. We will discuss several properties concerning these metrics also in relation with the Bismut connection having Kähler-like curvature. This is joint work with G. Barbaro and F. Pediconi.
Martedì
25 giugno
We revisit the well-known Curve Shortening Flow for immersed curves in the d-dimensional Euclidean space. We exploit a fundamental structure of the problem to derive a new global construction of a solution, that is, a construction that is valid for all times and is insensitive to singularities. The construction is characterized by discretization in time and the approximant, while still exhibiting the possibile formation of finitely many singularities at a finite set of singular times, exists globally and is well behaved and simpler to analyze than a solution of the CSF. Estimates for a natural (geometric) norm involving length and total absolute curvature allow passage to the limit. Many classical qualitative results about the flow can be recovered by exploiting the simplicity of the approximant and new ones can be proved. The construction also suggests a numerical procedure for the computation of the flow which proves very effective.
Giovedì
27 giugno
By using a Pizzetti's 1909 idea for the classical Laplacian, we introduced a notion of asymptotic average solutions. This notion enables the pointwise solvability of every Poisson equation Lu(x)=−f(x) with continuous data f, where L belongs to a class of hypoelliptic linear partial differential operators whose classical solutions can be characterized in terms of mean value formulae.
Mercoledì
10 luglio
Christopher Eur
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
ore 14:30
presso - Aula Da Stabilire -
Matroids combinatorially abstract the ubiquitous notion of "independence" in various contexts such as linear algebra and graph theory. Recently, an algebro-geometric perspective known as "combinatorial Hodge theory" led by June Huh produced several breakthroughs in matroid theory. We first give an introduction to matroid theory in this light. Then, we introduce a new geometric model for matroids that unifies, recovers, and extends various results from previous geometric models of matroids. We conclude with a glimpse of new questions that further probe the boundary between combinatorics and algebraic geometry. Joint works with Andrew Berget, Alex Fink, June Huh, Matt Larson, Hunter Spink, and Dennis Tseng.
12/09/2024
13/09/2024
Conference
Differential evolutive models in spaces with singularities
da giovedì 12 settembre 2024 a venerdì 13 settembre 2024
The scope is to present recent advances in geometric analysis in spaces with singularities, with particular emphasis on sub-Riemannian and degenerate structures, PDEs in this setting, and applications to vision, cognition, and biological problems.
Giovedì
26 settembre
Lorenzo Brasco
TBA
Seminario di analisi matematica
ore 16:00
presso - Aula Da Stabilire -
seminario on line •
TBA