Sala Seminari (Dip. Matematica)

Rational homology cobordisms of plumbed 3-manifolds and arborescent link concordance

Tipo Seminario: 
Relatore: 
Paolo Aceto

We investigate rational homology cobordisms of 3-manifolds with non-zero first Betti number. This is motivated by the natural generalization of the slice-ribbon conjecture to multicomponent links.

Data Seminario: 
Wednesday, April 15, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 14:30
Affiliazione: 
Università di Firenze
Ora Inizio: 
Saturday, January 1, 0000 - 13:30

Seminari dei Baby-Geometri - Topological Quantum Field Theories

Relatore: 
Carlo Colllari

Abstract: Topological Quantum Field Theories (TQFTs for short) were
axiomatized by Atiyah in 1988 ([1]). Following his exposition, we will
define the concept of TQFT and give some examples. In particular, we will
describe the (1+1)-TQFTs and their algebraic counterparts, the Frobenius
algebras. Time permitting we will give some more examples in higher
dimension.

[1] M. Atiyah, Topological Quantum Field Theory, Publications
Mathématiques de l'IHÉS 68 (68): 175–186

Data Seminario: 
Wednesday, March 11, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Dipartimento di Matematica - Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Splice links and colored signatures

Tipo Seminario: 
Relatore: 
Ana G. Lecuona

The splice of two links is an operation defined by Eisenbund and Neumann which generalizes several other operations on links, such as the connected sum, the cabling or the disjoint union. The precise definition will be given in the talk but the rough idea goes as follows: the splice of the links L’ and L'' along the components K' and K'' is the link (L' \ K') U (L''\ K'') obtained by identifying the exterior of K' with the exterior of K''.

Data Seminario: 
Wednesday, May 6, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Université d'Aix-Marseille
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

On the existence of spherical metrics with conical singularities on a 2-sphere

Tipo Seminario: 
Relatore: 
Gabriele Mondello

A celebrated result by Poincaré states that a compact Riemann surface of positive genus has a conformal metric of constant curvature, unique up to rescaling. Clearly, the case of genus 0 is not so exciting: there is a unique complex structure and a unique metric of curvature 1 up to Möbius transformations.

Data Seminario: 
Wednesday, March 25, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Università di Roma "La Sapienza"
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Sets with few rational points

Tipo Seminario: 
Relatore: 
Georges Comte

In the spirit of famous papers by Pila & Bombieri and Pila & Wilkie, I will explain how to bound the number
of rational points, with respect to their height, in various kinds of sets, such as algebraic varieties of a given degree,
transcendental sets definable in some o-minimal (or not) structure over the real field, and, after joint work
with R. Cluckers and F. Loeser, also definable sets in non-archimedean contexts.
The talk will consist in a survey of results and I will go into some of the proofs only in order to give the main ideas relating

Data Seminario: 
Thursday, March 12, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:30
Affiliazione: 
Université de Savoie, Francia
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Korn-Poincaré inequalities for functions with a small jump set

Relatore: 
Antonin Chambolle

We show hos the gradient of SBD functions can control, on "most" of the domain, their global behaviour (up to a rigid motion), provided the jump set is not too large.
This is a joint work with Sergio Conti and Gilles Francfort.

Data Seminario: 
Thursday, February 26, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 17:00
Affiliazione: 
Ecole Polytechnique
Ora Inizio: 
Saturday, January 1, 0000 - 16:00

Counting self-intersecting multi curves

Tipo Seminario: 
Relatore: 
Viveca Erlandsson
I will describe some joint work in progress with Juan Souto studying the asymptotic growth on the number $n_k^S(L)$ of multicurves with $k$ self-intersections of length at most $L$ on a hyperbolic surface $S$. More concretely, I will show that for small $k$, $\frac{n_k^S(L)}{L^{6g-6}}$ has a limit as $L\to\infty$. Moreover, when $S$ is the punctured torus, this limit exists for any fixed $k$.
Data Seminario: 
Wednesday, March 18, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Aalto University
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Variational aspects of Toda systems

Tipo Seminario: 
Relatore: 
Andrea Malchiodi

We consider a coupled system of Liouville equations on compact surfaces motivated by the study of non-abelian Chern-Simons vortices, and also describing holomorphic curves in projective spaces. We will see how geometric inequalities à la Moser-Trudinger allow to study the variational features of the problem in terms of concentration of the components of the system at finitely-many points of the surface. Existence results can then be derived via min-max theory. These are joint works with L.Battaglia, A.Jevnikar, S.Kallel, C.Ndiaye and
D.Ruiz.

Data Seminario: 
Wednesday, February 25, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 17:30
Affiliazione: 
SNS
Ora Inizio: 
Saturday, January 1, 0000 - 16:30

Variations on the Bernstein problem in asymptotically flat spaces

Tipo Seminario: 

The Bernstein problem, namely the problem of classifying all entire minimal hypergraphs in Euclidean spaces has played a crucial role in the development of Analysis throughout the whole course of the twentieth century. In this talk, I will discuss its natural extension to asymptotically flat manifolds, where it is motivated by the study of the large-scale structure of initial data sets for the Einstein field equation. I will first present the basic non-existence result and its relation to the asymptotic Plateau problem and then mention the application of similar techniques to the study of 1) large CMC spheres and isoperimetric domains (C.-Chodosh-Eichmair), 2) marginally outer-trapped surfaces (C.) and 3) the zero set of static potentials (Galloway-Miao). 

Data Seminario: 
Wednesday, February 11, 2015
Relatore: 
Alessandro Carlotto
Ora Fine: 
Saturday, January 1, 0000 - 17:30
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 16:30

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