SEMINARI DI GEOMETRIA

Kodaira fibrations with small signature

Tipo Seminario: 
Relatore: 
Sönke Rollenske

ABSTRACT:

 Kodaira fibrations are surfaces of general type with a non-isotrivial fibration, 
which are differentiable fibre bundles.  First examples were constructed by 
Kodaira and Atiyah to show that the signature need not be multiplicative in 
fibre bundles. 
We review approaches to construct such surfaces with focus on controlling the 
signature. From this we obtain new examples with signature 16. (Joint work 
with Ju A Lee and  Michael Lönne)

Data Seminario: 
Thursday, June 29, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 16:00
Affiliazione: 
Univ. Marburg (Germania)
Ora Inizio: 
0000 - 15:00

Elliptic diffeomorphisms of symplectic 4-manifolds

Tipo Seminario: 
Relatore: 
Gleb Smirnov

In his PhD thesis, Paul Seidel found examples of symplectomorphisms which are smoothly isotopic to the identity, but not isotopic to the identity within the symplectomorphism group.

Data Seminario: 
Wednesday, May 24, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 16:00
Affiliazione: 
International School for Advanced Studies (Trieste, Italy)
Ora Inizio: 
0000 - 15:00

Entropy and length rigidity of negatively curved manifolds of finite volume

Tipo Seminario: 
Relatore: 
Andrea Sambusetti

The problems of conjugacy rigidity and of entropy rigidity have a long history, with major breakthroughs in the last twenty years, for negatively curved compact manifolds and symmetric spaces. On the other hand, little is known for finite volume manifolds. I will survey the state of the art of these problems, and explain what can be generalized to finite volume manifolds, pointing out the main difficulties that arise in the non-compact case.

Data Seminario: 
Wednesday, March 22, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 16:00
Affiliazione: 
Roma La Sapienza
Ora Inizio: 
0000 - 15:00

Random groups and strong versions of Kazhdan’s Property (T)

Tipo Seminario: 
Relatore: 
Cornelia Drutu

Kazhdan's property (T) is a strong negation of amenability, relevant in the study of algebraic properties of groups, in the construction of expander graphs, in dynamics and in connection to the Baum-Connes conjectures. Various strengthened versions of property (T) have been formulated in recent years.

Data Seminario: 
Wednesday, May 17, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 16:00
Affiliazione: 
Oxford
Ora Inizio: 
0000 - 15:00

The universal quantum invariant and colored ideal triangulation

Tipo Seminario: 
Relatore: 
Sakie Suzuki

The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal R-matrix, and one can obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant of framed links is constructed using a ribbon Hopf algebra. In that construction, a copy of the universal R-matrix is attached to each crossing, and invariance under the Reidemeister III move is shown by the quantum Yang-Baxter equation of the universal R-matrix. On the other hand, R.

Data Seminario: 
Tuesday, February 14, 2017
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
0000 - 15:00
Affiliazione: 
RIMS - Kyoto
Ora Inizio: 
0000 - 14:00

Torsion in negative curvature

Tipo Seminario: 
Relatore: 
Roman Sauer

A classical theorem of Gromov states that the Betti numbers, i.e. the size of the free part of the homology groups, of negatively curved manifolds are bounded by the volume. We extend this theorem to the torsion part of the homology in all dimensions d > 3. From Gromov’s work it is known that in dimension 3 the size of torsion homology cannot be bounded in terms of the volume. In dimension 4 we give a somewhat precise estimate for the number of negatively curved manifolds of finite volume, up to homotopy, and in dimension d > 4 up to homeomorphism.

Data Seminario: 
Tuesday, April 11, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 16:00
Affiliazione: 
Karlsruhe Institute of Technology
Ora Inizio: 
0000 - 15:00

How to "synthesize" sub-fixed point sets into the global one just by looking inside groups?

Tipo Seminario: 
Relatore: 
Masato Mimura

Consider a group G action on a metric space X by isometries, and subgroups M_1,..., M_l. One interesting and important problem is to study conditions under which non-emptyness of each M_i-fixed points ensures that of global (G-)fixed points. One extreme case is where G is a simple Lie group, X is an origin-excluded Hilbert space, and the action is given by a (strongly continuous) unitary representation. Then, the Howe--Moore property, based on the Mautner phenomenon,  implies that for each(!) non-compact closed subgroup M, the existence of M-fixed points suffices that of G-fixed points.

Data Seminario: 
Thursday, January 12, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 17:00
Affiliazione: 
Tohoku university e EPF Lausanne
Ora Inizio: 
0000 - 16:00

On a proof to Shiota's conjecture to characterize Nash images of Euclidean spaces

Tipo Seminario: 
Relatore: 
José Fernando

In this work we characterize the subsets of R^n that are images of Nash maps f : R^m → R^n. We prove Shiota’s conjecture and show that a subset S ⊂ R^n is the image of a Nash map f : R^m → R^n if and only if S is semialgebraic, pure dimensional of dimension d ≤ m and there exists an analytic path α : [0, 1] → S whose image meets all the connected components of the set of regular points of S. Given a semialgebraic set S ⊂ R^n satisfying the previous properties, we provide a theoretical strategy to construct (after Nash approximation) a Nash map whose image is the semialgebraic set S.

Data Seminario: 
Wednesday, September 14, 2016
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 16:00
Affiliazione: 
Universidad Complutense de Madrid
Ora Inizio: 
0000 - 15:00

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