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# Integrable systems methods for surfaces and new families of constant mean curvature surfaces in $\mathbb{R}^3$

## Eduardo Mota Sánchez University College Cork

THIS SEMINAR HAS BEEN POSTPONED BECAUSE OF THE UNIVERSITY POLICY CONCERNING THE CORONAVIRUS OUTBREAK. A NEW DATE WILL BE ANNOUNCED AS SOON AS POSSIBLE.

In this lecture I will outline the integrable systems technique for CMC surfaces, but with a view at some other cases. Then I will explain some recent developments in the construction of certain families of CMC surfaces using this setup. In particular, we start with a $2\times 2$ Cauchy problem to which we associate a scalar second order differential equation. The singularities in this ODE correspond to the ends in the resulting surface. Particularly, regular singularities produce asymptotically Delaunay ends while irregular singularities produce irregular ends. Our aim is to discuss global issues such as period problems and asymptotic behavior involved in the construction of CMC surfaces in $\mathbb{R}^3$ arising from the family of Heun's differential equations.

Seminario 1ª planta - IEMath-GR

# The Classification of Semigraphical Translators for Mean Curvature Flow

We say that a surface is semigraphical if it is properly embedded, and, after removing a discrete collection of vertical lines, it is a graph. In this talk, we provide a nearly complete classification of semigraphical translators.

Seminario de la primera planta, IEMath

# A gravitational collapse singularity theorem that improves Penrose's

## Ettore Minguzzi Università degli Studi di Firenze

The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penrose's theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in absence of predictability and hence compatibly with quantum field theory and black hole evaporation.

Seminario 1A Planta, IEMath

# Holomorphicity of real Kaehler submanifolds

## Sergio Chion Aguirre IMPA, Río de Janeiro

I will discuss the subject of real Kaehler submanifolds, that is, isometric immersions $f\colon M^{2n}\to\mathbb{R}^{2n+p}$ of a Kaehler manifold $(M^{2n},J)$ of complex dimension $n\geq 2$ into Euclidean space with codimension $p$. In particular, I will present a recent result that shows that for codimension $2p\leq 2n-1$ generic rank conditions on the second fundamental form of $f$ imply that the submanifold has to be minimal. In fact, for codimension $p\leq 11$ we have a stronger conclusion, namely, that $f$ must be holomorphic with respect to some complex structure in the ambient space.

This is joint work with A. de Carvalho and M. Dajczer.

# Dynamical Aspects of Pseudo-Riemannian Geometry

## Braga (Portugal)

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This conference will focus on recent progress in Pseudo-Riemannian Geometry and, in particular, in Lorentzian Geometry.

One of the goals of the conference is to explore the natural intervention/interaction of dynamical systems in several questions of Pseudo-Riemannian geometry.