Sala Seminari (Dip. Matematica)

Minimal volume hyperbolic 4-manifolds

Tipo Seminario: 

Since the volume of a hyperbolic manifold is often regarded as a measure of its complexity, it is interesting to study the examples of minimal volume.
The 2 and 3-dimensional cases are well understood.
In dimension four there is an abundance of examples, but we are far from classifying them. In this talk, we will survey all known examples of minimal volume hyperbolic 4-manifolds and prove that these fall into three commensurability classes. This is joint work with Stefano Riolo.
 

Relatore: 
Leone Slavich
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

A Hele-Shaw tumor growth model as a gradient flow.

Relatore: 
Simone Di Marino
Abstract. In 2014 Perthame, Quiroz and Vasquez unite two types of modeling of tumor growth into a unique framework of reaction-diffusion type where the diffusive term is $\Delta p(\rho)$ and $p(\rho)=\rho^m$. The stiff limit $m \to \infty$ is in particular a Hele-Shaw type problem: we find a gradient flow formulation of this problem, namely it is the gradient flow of the negative mass with respect to the Wasserstein-Fisher-Rao distance, discovered simultaneously by many authors in the last years.
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Scuola Normale Superiore
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

On Aharonov-Bohm operators with moving poles

Relatore: 
Veronica Felli

In this talk, I will present some results in collaboration with L. Abatangelo
(Milano-Bicocca), L. Hillairet (Orléans), C. Léna (Torino),  B. Noris
(Amiens), M. Nys (Torino), concerning the behavior of the eigenvalues of
Aharonov-Bohm operators with one moving pole or two colliding
poles. In both cases of poles moving inside the domain and approaching
the boundary, the rate of the eigenvalue variation is estimated in
terms of the vanishing order of some limit eigenfunction. An accurate

Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 14:00
Affiliazione: 
Università di Milano bicocca
Ora Inizio: 
Saturday, January 1, 0000 - 13:00

Liouville-type problems on compact surfaces: a variational approach

Abstract. A class of Liouville equations and systems on compact surfaces is considered: we focus on the Toda system which is motivated in mathematical physics by the study of models in non-abelian Chern-Simons theory and in geometry in the description of holomorphic curves. We discuss its variational aspects which yield existence results.
Relatore: 
Aleks Jevnikar
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Backward error analysis for polynomial rootfinders

Relatore: 
Leonardo Robol

The most common methods to compute roots of polynomials is to rephrase the problem in linear algebra terms: one constructs a companion matrix (or pencil) that has the roots of the polynomial as eigenvalues.
However, even when the eigenvalue method used is backward stable, it's non-trivial to map the backward error back on the polynomial. This problem has been studied extensively in the past and it has been shown that relying on the QR method does not provide a normwise backward-stable rootfinder. For this reason, one needs to rely on QZ + appropriate scaling.

Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
ISTI--CNR Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Morfismo traccia e deformazioni di coppie (varieta', fascio coerente).

Tipo Seminario: 
Relatore: 
Marco Manetti

Dato un fascio coerente F su una varieta' liscia proiettiva X, viene determinata l'algebra di Lie differenziale graduata che controlla le deformazioni della coppia (X,F). Viene poi introdotto un morfismo di traccia tra opportuni fasci di operatori differenziali mediante il quale viene esteso un classico risultato di Artamkin sulle deformazioni di fasci.

Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
Universita' di Roma "La Sapienza"
Ora Inizio: 
Saturday, January 1, 0000 - 14:00

Equivariant hyperbolization and applications

Tipo Seminario: 
Relatore: 
Danny Ruberman

Given a closed 3-manifold Y with the action of a finite group G, we show how to find a closely related hyperbolic G-manifold Y’. The two manifolds are related by an invertible equivariant homology cobordism; a cobordism from Y to Y’ is invertible if there is a second cobordism from Y’ to Y such that the union of the two along Y’ is a product cobordism.  I will give a collection of applications in 3 and 4-dimensional topology. (Joint work with Dave Auckly, Hee Jung Kim, and Paul Melvin.)

Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 17:00
Affiliazione: 
Brandeis University
Ora Inizio: 
Saturday, January 1, 0000 - 16:00

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