# Prossimi seminari del Dipartimento di Matematica

25
Nov

Lunedì
Victor Kac
Complexity of representations of quivers

seminario interdisciplinare

ore 15:30
presso Aula Pincherle

25
Nov

Lunedì
Victor Kac
Complexity of representations of quivers

nell'ambito della serie: COLLOQUIO DI DIPARTIMENTO

seminario interdisciplinare

ore 15:30
presso Aula Pincherle

26
Nov

Martedì
Alessio Savini
Euler number for measurable cocycles of surface groups

nell'ambito della serie: TOPICS IN MATHEMATICS 2019/2020

seminario di algebra e geometria

ore 11:00
presso Seminario II
A quite useful philosophy in mathematics is to use the sharpness of an inequality regarding the "shape" of a topological space in order to detect a precise geometry on it: more precisely, the maximal value of the inequality usually allows to identify a specific geometric structure. Think for instance either to the applications of arithmetic/geometric mean inequality or to the isoperimetric inequality on the plane. Something similar happens in the world of Zimmer's cocycle theory. In this seminar we are going to focus our attention on Zimmer's cocycles associated to the fundamental group a surface S with genus bigger than or equal to 2. If such a measurable cocycle admits a (generalized) boundary map, one can define the notion of Euler number. The latter well behaves along cohomology classes and its absolute value is bounded by the modulus of the Euler characteristic of S. Remarkably the maximal value is attained if and only if the cocycle is cohomologous to a hyperbolization. The first part of the talk will be a gentle introduction to measurable cocycles and boundary theory. Then, we are going to introduce the orientation cocycle on the circle. Finally we will define the Euler number of a measurable cocycle and we will discuss its rigidity property. This is a joint work with Marco Moraschini.

26
Nov

Martedì
Emanuele Delucchi
Abelian arrangements, 4

seminario di algebra e geometria

ore 14:00
presso Aula Vitali

28
Nov

Giovedì
Conferenzieri e organizzatori del convegno Two Days on CalcVar&PDEs
Tavola rotonda I parte: regolarità nel calcolo delle variazioni

seminario di analisi matematica

ore 08:45
presso Seminario I

28
Nov

Giovedì
Paolo Marcellini (U. Firenze)
Some remarks in the calculus of variations

seminario di analisi matematica

ore 14:30
presso Aula Vitali
We will discuss some examples, problems and remarks related to the calculus of variations and to partial differential equations.

28
Nov

Giovedì
Bernard Dacorogna
Symplectic factorization, Darboux theorem and ellipticity

seminario di analisi matematica

ore 15:10
presso Aula Vitali

28
Nov

Giovedì
Gioconda Moscariello
TBA
ore 15:50
presso Aula Vitali
TBA

28
Nov

Giovedì
Cristiana De Filippis (U. Oxford)
TBA

seminario di analisi matematica

ore 17:00
presso Aula Vitali
I will discuss some recent results on a class of non-uniformly elliptic problems modelled upon the double phase energy

28
Nov

Giovedì
Luca Lussardi (Politecnico di Torino)
On the Kirchhoff–Plateau problem

seminario di analisi matematica

ore 17:40
presso Aula Vitali
The Kirchhoff–Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. We establish the existence of an equilibrium shape that minimizes the total energy of the system under the physical constraint of non-interpenetration of matter, but allowing for points on the surface of the bounding loop to come into contact. In our treatment, the bounding loop retains a finite cross-sectional thickness and a nonvanishing volume, while the liquid film is represented by a set with finite two-dimensional Hausdorff measure. Moreover, the region where the liquid film touches the surface of the bounding loop is not prescribed a priori. Our mathematical results substantiate the physical relevance of the chosen model. Indeed, no matter how strong is the competition between surface tension and the elastic response of the filament, the system is always able to adjust to achieve a configuration that complies with the physical constraints encountered in experiments. In this seminar I will present some results concerning the Kirchhoff-Plateau problem obtained in collaboration with Eliot Fried, Giulio Giusteri, Giulia Bevilacqua and Alfredo Marzocchi.

29
Nov

Venerdì
Antonia Passarelli di Napoli (U. Napoli "Federico II")
Regularity for minimizers of a class of degenerate convex functionals

seminario di analisi matematica

ore 09:30
presso Aula Enriques

29
Nov

Venerdì
Michela Eleuteri (U. Modena e Reggio Emilia)
Lipschitz regularity results for variational models with non standard growth

seminario di analisi matematica

ore 10:10
presso Aula Enriques
In this talk we are going to present some recent Lipschitz regularity results for functionals and systems with non standard growth, without further structure conditions on the integrand, both in the scalar and in the vector case. This is a joint project with Paolo Marcellini and Elvira Mascolo. In the last part of the talk, we will complement these results by dealing with obstacle problems. This is a joint project with Antonia Passarelli di Napoli and Michele Caselli.

29
Nov

Venerdì
Cristina Marcelli (U. Politecnica delle Marche)
Coercivity of integral functionals of non-everywhere superlinear lagrangians

seminario di analisi matematica

ore 11:20
presso Aula Enriques
TBA

29
Nov

Venerdì
Ermanno Lanconelli (U. Bologna)
On the stability of the Gauss mean value formula for harmonic functions

seminario di analisi matematica

ore 12:00
presso Aula Enriques
Among the various rigidity properties of the Euclidean balls one of the best known examples is the Gauss mean value formula for harmonic functions. This property raises the question of its stability. i.e. : if $D$ is an open set with finite measure and $x_0$ is a point of $D$ such that $u(x_0)$ is close to the average of $u$ on $D$ for every integrable harmonic functions $u$ in $D$, is it true that $D$ is close to a ball centered at $x_0$? In this talk we present some positive answers to this question, obtained in collaboration with Giovanni Cupini, Nicola Fusco and Xiao Zhong

29
Nov

Venerdì
The basic problem of the calculus of variations: some recent results for nonautonomous Lagrangians that are highly discontinuous in the state or velocity variable

seminario di analisi matematica

ore 14:00
presso Aula Enriques

29
Nov

Venerdì
Stable minimizers of functionals of the gradient

seminario di analisi matematica

ore 14:40
presso Aula Enriques
Let $\Omega\subset \mathbb{R}^n$ be a bounded Lipschitz domain. Let $L:\mathbb{R}^n\rightarrow \bar{\mathbb{R}}=\mathbb{R}\cup \{+\infty\}$ be a continuous function with superlinear growth at infinity, and consider the functional $\mathcal{I}(u)=\int_\Omega L(Du)$, $u\in W^{1,1}(\Omega)$. We provide necessary and sufficient conditions on $L$ under which, for all $f\in W^{1,1}(\Omega)$ such that $\mathcal{I}(f)<+\infty$, the problem of minimizing $\mathcal{I}(u)$ with the boundary condition $u_{|\partial\Omega}=f$ has a solution which is stable, or -- alternatively -- is such that all of its solutions are stable. By stability of $\mathcal{I}$ at $u$ we mean that $u_k\rightharpoonup u$ weakly in $W^{1,1}(\Omega)$ together with $\mathcal{I}(u_k)\to \mathcal{I}(u)$ imply $u_k\rightarrow u$ strongly in $W^{1,1}(\Omega)$. This extends to general boundary data some results obtained by Cellina and Cellina and Zagatti. Furthermore, with respect to the preceding literature on existence results for scalar variational problems, we drop the assumption that the relaxed functional admits a continuous minimizer. The results are contained in a joint paper with G. Colombo, Dipartimento di Matematica, University of Padova and M. Sychev, Sobolev Institute of Mathematics, Novosibirsk.

29
Nov

Venerdì
Nicola Fusco (U. Napoli "Federico II")
TBA

seminario di analisi matematica

ore 15:20
presso Aula Enriques
TBA

29
Nov

Venerdì
Conferenzieri e organizzatori del convegno Two Days on CalcVar&PDEs
Tavola rotonda II parte: regolarità nelle PDEs

seminario di analisi matematica

ore 18:00
presso Seminario II

05
Dic

Giovedì
Chiara Guidi
Characterization of the Palais-Smale sequences for the fractional CR Yamabe functional

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

seminario di analisi matematica

ore 16:00
presso Seminario II

10
Dic

Martedì
Counting problems in infinite measure.

seminario interdisciplinare

ore 11:00
presso Seminario II
Given a group Γ acting properly discontinuously and by isometries on a metric space X, one can wonder how grows the orbit of a given point. More precisely, given two points x, y ∈ X and ρ > 0, we define the orbital function as NΓ(x, y, ρ) := #(Γ · y ∩ B(x, ρ)) , where B(x, ρ) denotes the ball centred at x of radius ρ. A counting problem con- sists to estimate the orbital function when ρ → ∞. In the setting of groups acting on hyperbolic spaces this question was widely in- vestigated for decades, with mainly two different approaches: an analytical one relying on Selberg’s pre-trace formula, due to Huber in the 50’s, and a dynami- cal one relying on the mixing of the geodesic flow, due to Margulis in the late 60’s. During the talk, we shall describe Margulis’ dynamical method in order to mo- tivate the introduction of the Brownian motion. Combined with the use of the pre-trace formula, we shall establish a counting theorem linking the heat kernel of the quotient manifold and the orbital function. If the time allows it, we also shall review a couple of corollaries of the approach.

18
Dic

Mercoledì
Berardo Ruffini
TBA

nell'ambito della serie: TOPICS IN MATHEMATICS 2019/2020

ore 10:30
presso Seminario I