| 28/11/17 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Antonio Marigonda | Universita' di Verona | A comparison principle for viscosity solutions of an Hamilton-Jacobi Equation in Wasserstein spaces
In this talk we present recent results about the existence and uniqueness of the viscosity solution for a certain classes on Hamilton-Jacobi Equations in the Wasserstein space of probability measure, arising in problem of mean field control of multi-agent systems. We consider a multi-agent system subject to a centralized controller aiming to minimize a cost function. The microscopic dynamics of each agent is given by a differential inclusion. We model the distribution of agents by a probability measure, and formulate the minimization problem as a Mayer problem for a dynamics in the Wasserstein space represented by a controlled continuity equation decribiing the macroscopical evlution of the system. We prove that the value function V of the problem solves a Hamilton-Jacobi equation in the Wasserstein space in a suitable viscosity sense, and prove a comparison principle for such an equation, thus characterizing V as the unique viscosity solution of the Hamilton-Jacobi equation associated to the problem. |
| 21/11/17 | Seminario | 15:00 | 16:00 | 1101 D'Antoni | Giulio Ciraolo | Universita' di Palermo | Stime quantitative per ipersuperifici a curvatura media quasi costante
Discuteremo alcune versioni quantitative del Teorema di Alexandrov della bolla di sapone, che afferma che le sfere sono le sole ipersuperfici chiuse embedded a curvatura media costante. In particolare, considereremo ipersuperfici con curvatura media vicina ad una costante e descriveremo in maniera quantitativa la vicinanza ad una singola sfera o ad una collezione di sfere tangenti di raggio uguale in termini dell'oscillazione della curvatura media. Inoltre considereremo il problema analogo in ambito nonlocale, mostrando come l'effetto nonlocale implichi una maggiore rigidità del problema e prevenga la formazione di più bolle. |
| 17/11/17 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Michael Ehrig | University of Sydney | Functoriality of link homologies and higher representation theory
In this talk, we will discuss the notion of functoriality of link
homologies defined by Khovanov and Khovanov-Rozansky. These link
homologies are categorifications of the link invariants defined by
Reshetikhin-Turaev in case of the special linear group.
We will discuss why functoriality is an important notion and how to show
it. The latter will include the equivariant geometry of Grassmannians
and partial flag varieties as well as higher representation theory. |
| 14/11/17 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Annalisa Massaccesi | Universitat Zurich | Partial regularity for the hyperdissipative Navier-Stokes equations
In this joint work with Maria Colombo and Camillo De Lellis we prove a space-time partial regularity result à la Caffarelli-Kohn-Nirenberg for suitable weak solutions of the hyperdissipative Navier-Stokes equations. |
| 07/11/17 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Paolo Caldiroli | Universita' di Torino | Embedded tori with prescribed mean curvature
According to a famous result by A.D. Alexandrov, the only embedded, oriented, compact, constant mean curvature (CMC) surfaces in the Euclidean 3-space are round spheres. In particular there is no CMC embedded torus. We investigate the problem of embedded tori for a class of radially symmetric, prescribed mean curvature functions converging to a constant at infinity. Under suitable conditions, we construct a sequence of embedded tori. Such surfaces are close to sections of unduloids with small necksize, folded along circumferences centered at the origin and with larger and larger radii. The construction involves a deep study of the corresponding Jacobi operators, an application of the Lyapunov-Schmidt reduction method and some variational argument. This is a joint work with Monica Musso (Pontificia Universidad Católica de Chile). |
| 24/10/17 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Daniele Castorina | John Cabot University (Roma) | Ancient solutions of superlinear heat equations on Riemannian manifolds.
We study the qualitative properties of ancient solutions of superlinear heat equations in a Riemannian manifold, with particular attention to positivity and triviality in space. This is joint work with Carlo Mantegazza (Napoli ''Federico II'')
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| 17/10/17 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Carlo Nitsch | Universita' di Napoli | Problemi di ottimizzazione in isolamento termico
In questo seminario affrontiamo il problema di isolare
termicamente un corpo conduttore di calore dall'ambiente circostante,
avendo a disposizione una certa quantità di isolante da distribuire sulla
sua superficie. La definizione di "isolamento ottimo" dipenderà dalla
presenza o meno di una sorgente di calore e darà luogo a due formulazioni
distinte. Dimostreremo che la maniera migliore di disporre l'isolante
sulla superficie del conduttore non è sempre ovvia e a volte addirittura
controintuitiva. Anche nel caso più semplice, in cui il conduttore sia una
palla, e ci troviamo in assenza di sorgente di calore, distribuire
l'isolante uniformemente sulla superficie sferica non é sempre la cosa
migliore da fare. |
| 10/10/17 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Roberto Peirone | Universita' di Roma "Tor Vergata" | Existence of self-similar energies on finitely ramified fractals
An important problem in analysis on fractals is the construction of a self-similar energy on the fractal. An old conjecture is whether on a specific important class of finitely ramified self-similar fractals there exists a self-similar energy.
In this talk, it is shown a recent example where we have no self-similar energy. On the other hand, a self-similar energy always exists if the
self-similarity is considered with respect to a suitable set of maps that define the fractal. |
| 10/10/17 | Seminario | 13:00 | 14:00 | 1201 Dal Passo | Israel Vainsencher | Universidade Federal de Minas Gerais | Counting singular surfaces
How many surfaces of a given degree present singularities of some specified type and pass through an appropriate number of points?
We focus on counting singular surfaces with certain non isolated singularities: e.g., Whitney's umbrella, quartics singular along atwisted cubic, etc. We give a proof for the polynomial nature of the formulae and make it explicit in a few cases. Conjecturally the degree of the formula is twice the dimension of the family of curves imposed in the singular locus. We manage to bound it by thrice that dimension. We draw essentially from previous joint work with Angelo Lopez and Fernando Cukierman. |
| 03/10/17 | Seminario | 16:00 | 17:00 | 1101 D'Antoni | Peter Heinzner | Ruhr-Universitaet Bochum | KAEHLERIAN REDUCTION
In this talk we will consider Hamiltonian actions of groups of holomorphic Kaehler
isometries on Kaehlerian manifolds. In the rare cases where the orbit spaces are
smooth it is well known that the corresponding quotient spaces in the sense of Marsen
Weinstein are Kaehler manifolds as well.
We will show that in the general case the quotient has a natural structure of a
Kaehler space. The main tool in the proof is the construction of invariant Kaehler
potentials for not necessarily compact group actions.
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