# Riemann-Hilbert correspondence for classical and for twistor D-modules

## Speaker:

Teresa Monteiro Fernandes

## Date:

Friday, 18 November, 2016 - 15:30

## Venue:

Room 1.22

In this talk I will give an overview of the main concepts and results in D-module theory, and then switch to the notion of relative D-module. I will explain the main motivation for the study of holonomic relative modules given by Mochizuki's notion of mixed twistor D-module. We will explain the Riemann-Hilbert correspondence in this case as a joint work with Claude Sabbah.

# Computing lines in smooth cubic hypersurfaces and application to the irrationality problem

Xavier Roulleau

## Date:

Friday, 11 November, 2016 - 11:30

## Venue:

Room 0.30

A smooth cubic hypersurface X of dimension >1 is unirational. The variety of lines F(X) on these hypersurfaces is an essential tool to understand the geometry of X. In dimension 3, the study of F(X) enables to prove that X is always irrational.

In this talk we study the zeta function of F(X) and we obtain a simplified proof of the irrationality of a dense set of smooth cubic threefold. This is a joint work with D. Markouchevitch.

# Action of the mapping class group on character varieties and Higgs bundles

## Date:

Friday, 7 October, 2016 - 14:30

## Venue:

Room 1.22

We consider the action of the mapping class group of a compact  surface S of genus g>1 on the character variety of the fundamental group of S  in a connected semisimple real Lie group G.

# Complexified Hamiltonian symplectomorphisms and solutions of the homegeneous complex Monge-Ampere equation

José Mourão

## Date:

Friday, 23 September, 2016 - 14:30

## Venue:

Room 1.22

The geodesics for the Mabuchi metric on the space of Kaehler metrics on a manifold correspond to solutions of the homogeneous complex Monge-Ampere (HCMA) equation. We will describe a method for reducing the Cauchy problem for the HCMA equation with analytic initial data to finding a related Hamiltonian flow followed by a "complexification". Examples and applications will be discussed.

Work in collaboration with J.P. Nunes and T. Reis

# Stability conditions for (G,h)-constellations.

Alfonso Zamora

## Date:

Friday, 1 July, 2016 - 14:45

## Venue:

1.22

Given a reductive group G and an affine G-scheme X, constellations are G-equivariant sheaves over X such that their module of global sections has finite multiplicities. Prescribing these multiplicities by a function h, and imposing a stability condition $\theta$ there is a moduli space for $\theta$-stable constellations constructed by Becker and Terpereau, using Geometric Invariant Theory. This construction depends on a finite subset D of the set of irreducible representations of G.

# Nielsen-Olesen cosmic strings, the Einstein-Bogomol'nyi equations, and algebraic geometry

## Speaker:

Luis Álvarez-Cónsul

## Date:

Friday, 1 July, 2016 - 13:30

## Venue:

1.22

Y. Yang observed 20 years ago that the 2-sphere is the only compact orientable surface admitting solutions of the Einstein-Bogomol'nyi equations, coupling vortices with gravity, and obtained sufficient conditions for the existence of cosmic strings in this situation. In this talk, we will give an algebro-geometric interpretation of Yang's conditions, and explain why they are in fact necessary for the existence of solutions.

# TBA

Luís Diogo

## Date:

Wednesday, 22 June, 2016 - 13:30

DMAT-1.22

TBA

# The curvature veronese of a 3-manifold immersed in Euclidean space

## Speaker:

M. Carmen Romero Fuster

## Date:

Friday, 3 June, 2016 - 14:30

## Venue:

Room 1.22

The concept of curvature ellipse at a point of a surface immersed in 4-space has been known since a long time ago [2] and it has proven to be a useful tool in the study of the geometrical properties from both, the local and global viewpoint [1, 3, 4]. Its natural generalization to higher dimensional manifolds is given by the image of a convenient linear projection of a Veronese submanifold of order 2 in the normal space of the manifold at each point [3]. We call it the curvature locus or curvature veronese.

# Triples and Higgs bundles for the indefinite unitary group revisited

Peter Gothen

## Date:

Friday, 27 May, 2016 - 14:30

## Venue:

Room 1.22 - DM - FCUP

Holomorphic chains on a Riemann surface are sequences of holomorphic bundles, connected by holomorphic maps. Triples are chains of length one. Chains arise naturally as fixed points of the C^*-action on the moduli space of Higgs bundles.

# Nijenhuis forms on Lie-infinity algebras

Joana da Costa

## Date:

Friday, 20 May, 2016 - 14:30

## Venue:

Room 1.22

I will talk about Nijenhuis deformations of Lie-infinity algebras, a notion that unifies several Nijenhuis deformations, namely those of Lie algebras, Lie algebroids and Poisson structures. This is a Joint work with M. Azimi and C. Laurent-Gengoux.