Geometry and Topology

Some surfaces with canonical map of degree 16

Speaker: 

Carlos Rito (CMUP)

Date: 

Friday, 17 April, 2015 - 14:30

Venue: 

FC1 - 0.06

It is known since Beauville (1979) that if the canonical image $\phi(S)$ of a surface of general type $S$ is a surface, then the degree $d$ of the canonical map $\phi$ satisfies $d\leq 36-9q$, where $q$ is the irregularity of $S$. Beauville has constructed families of examples with holomorphic Euler characteristic $\chi$ arbitrarily large for $d\leq 8$, but for $d\geq 9$ only three examples are known: $d=K^2=9, q=0$ (Tan), $d=K^2=12, q=0$ (Rito) and $d=K^2=16, q=0$ (Persson), where $K$ is a canonical divisor of $S$.

 

C^0-rigidity phenomena in symplectic topology

Speaker: 

Rémi Leclercq

Date: 

Friday, 13 March, 2015 - 15:30

Venue: 

Room 0.07, FC1

A celebrated theorem due to Gromov and Eliashberg states that the C^0-limit of a se­quence of sym­plec­to­mor­phisms is sym­plec­tic (if smooth). This rigid­ity phe­nom­e­non mo­ti­vated the study of C^0 sym­plec­tic geom­e­try which is con­cerned with con­tin­u­ous analogs of clas­si­cal notions. In joint works with V. Hu­milière and S. Sey­fad­dini, we showed that coisotropic submanifolds together with their characteristic foliations are also C^0 rigid.

Stratifications on the Moduli Space of Higgs Bundles

Speaker: 

Ronald Zúñiga-Rojas (CMUP, CIMM-Universidad de Costa Rica)

Date: 

Friday, 6 March, 2015 - 15:30

Venue: 

Room 0.06, FC1

The work of Hausel proves that the Bialynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. These two stratifications do not coincide in general. Here we give an approach for the rank three case of the classification of the Shatz stratification in terms of the Bialynicki-Birula stratification.

Toric constructions of monotone Lagrangian submanifolds in $\mathbbCP^2$ and $\mathbbCP^1 \times \mathbbCP^1$

Speaker: 

Agnès Gadbled (CMUP)

Date: 

Friday, 16 January, 2015 - 15:30

Venue: 

Room 0.04, FC1

In a previous paper, I proved that two very different constructions of monotone Lagrangian tori are Hamiltonian isotopic inside $\mathbb{CP}^2$ by comparing both of them to a third one called modified Chekanov torus. This modified Chekanov torus has an interesting projection under the standard moment map of $\mathbb{CP}^2$ and motivates a method of construction of (monotone) Lagrangian submanifolds in symplectic toric manifolds. I will explain how this method gives some old and new monotone examples in $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$.

Hölder conditions for endomorphisms of hyperbolic groups

Speaker: 

Pedro V. Silva (CMUP)

Date: 

Friday, 6 February, 2015 - 11:00

Venue: 

M006

Hyperbolic groups were introduced by Mikhail Gromov in the 80s by considering the geometry of Cayley graphs, viewed as geodesic metric spaces. One important feature of hyperbolic groups is the concept of boundary, which can be defined through the topological completion for an appropriate metric (such as the visual metrics), and has the advantages of compacteness.

Tight contact structures on connected sums which are not contact connected sum.

Speaker: 

Paolo Ghiggini (Nantes)

Date: 

Friday, 24 April, 2015 - 14:30

Venue: 

FC1 - 0.06

It is well known that, in dimension three, every tight contact structure on a connected sum is a contact connected sum. I will show that the same statement is not true in dimension five. This is a joint work with Klaus Niederkrüger and Chris Wendl.

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