Sala Seminari (Dip. Matematica)

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

Polynomial-Exponential Equations

Tipo Seminario: 
Relatore: 
Ayhan Günaydin

We consider polynomial‐exponential equations over the complex
numbers where
the variables run through the rational numbers. Classically, the integer
solutions of
such equations are considered and there are several finiteness results in the
literature for those solutions. We present a method to reduce the rational
solutions to integer ones and give a description of them using the earlier
results.  As a corollary, we get a finiteness result. If time permits,
we will present

Data Seminario: 
Friday, January 23, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
MSGSU Istanbul, Turchia
Ora Inizio: 
Saturday, January 1, 0000 - 09:30

Decomposition of quantum representations into irreducible factors

Tipo Seminario: 
Relatore: 
Julien Korinman

 I will define two families of representations of the mapping class group of surfaces, namely the Weil and Reshetikhin-Turaev representations. Then I will state some results concernings the (in)finiteness of their image and their decomposition into irreducible factors.

Data Seminario: 
Wednesday, January 28, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Université de Grenoble
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

The l-infinity-semi-norm on uniformly finite homology

Tipo Seminario: 
Relatore: 
Clara Loeh
(joint work with Francesca Diana)

Uniformly finite homology is a coarse homology theory, defined via chains that satisfy a uniform boundedness condition. Byconstruction, uniformly finite homology carries a canonical $\ell^\infty$-semi-norm. We show that, for UDBG spaces, this semi-norm on uniformly finite homology in degree~$0$ with $\mathbb Z$-coefficients allows for a new formulation of Whyte's rigidity result. In contrast, we prove that this semi-norm is trivial on uniformly homology in higher degrees with $\mathbb R$-coefficients.

Data Seminario: 
Wednesday, March 4, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Regensburg
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Quasimorfismi e coomologia limitata

Tipo Seminario: 
Relatore: 
Cristina Pagliantini

Nel seminario presenteremo la relazione tra coomologia limitata e
quasimorfismi di un gruppo.
Ci concentreremo poi sui quasimorfisimi mediani e daremo una
caratterizzazione delle azioni su alberi che inducono quasimorfismi mediani non banali.

Data Seminario: 
Wednesday, February 18, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Regensburg
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Relative Bounded Cohomology for groupoids

Tipo Seminario: 
Relatore: 
Matthias Blank

Bounded cohomology is a functional analytic modification of
regular cohomology, with applications to geometry, topology and (geometric) group theory. After giving a very short introduction to groupoids, I will present our construction of (relative) bounded cohomology for (pairs) of groupoids. This includes a natural setting for bounded cohomology relative to a family of subgroups. Finally, I will discuss a relative version of Gromov's mapping Theorem in this context.

Data Seminario: 
Wednesday, February 11, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Regensburg
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Volume and homology growth

Tipo Seminario: 
Relatore: 
Roman Sauer

Consider a tower of finite coverings of a closed manifold.
We usually assume that the fundamental group is residually finite and that the tower corresponds to a residual chain of the fundamental group.

We then ask: How does the size of the k-th homology group grow as we go up in the tower?

By size we mean the rank or the cardinality of the torsion subgroup.
We connect the homology growth for aspherical Riemannian manifolds in the above sense to the volume of balls. 

Data Seminario: 
Wednesday, May 27, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Karlsruhe Institute of Technology
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

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