Symmetry and shape

Ilka Agricola (Philipps-Universität Marburg, Germany)

Dmitri Alekseevsky (Higher School of Modern Mathematics MIPT, Russia)

Jürgen Berndt (King's College London, United Kingdom)

Antonio Di Scala (Politecnico di Torino, Italy)

Anna Fino (Università di Torino, Italy)

Claudio Gorodski (Universidade de São Paulo, Brazil)

Luis Guijarro (Universidad Autónoma de Madrid, Spain)

Jason Lotay (University of Oxford, United Kingdom)

Paolo Piccione (Universidade de São Paulo, Brazil)

Silvio Reggiani (Universidad Nacional de Rosario, Argentina)

Alberto Rodríguez Vázquez (Université Libre de Bruxelles, Belgium)

Evangelia Samiou (University of Cyprus, Cyprus)

Francisco Vittone (Universidad Nacional de Rosario, Argentina)

Equivariant Approximation Process of Currents and Spaces with Bounded Curvature

Andrés Ahumada Gómez (CUNEF Universidad, Spain)

In this talk (poster) we introduce actions of a compact Lie group in two regularization processes: in De Rham's approximation process of currents on a smooth manifold by smooth currents, and in a smoothing operator of Riemannian metrics of metric spaces with bounded curvature.

Bycicle tracks with hyperbolic monodromy

Luis Hernández-Lamoneda (Centro de Investigación en Matemáticas, A.C., México)

We find new necessary and sufficient conditions for the bicycling monodromy of a closed plane curve to be hyperbolic. The manin tool is the ''hyperbolic development'' of a euclidean plane curve in the hyperbolic plane.

Exterior Curvature in Hitchin's Generalised Geometry

Oskar Schiller (Universität Hamburg, Germany)

Generalised Geometry is concerned with the study of geometrical objects on the generalised tangent bundle $TM \oplus T^* M$ over a manifold $M$. The basic objects are generalised metrics, generalised connections, and divergence operators. From these, one can obtain other geometrical objects, such as the generalised Riemann tensor.

In this talk, which is based on joint work with Vicente Cortés, we consider an immersed manifold $N \hookrightarrow M$, and investigate how $TN \oplus T^*N$ inherits geometric structures defined on $TM \oplus T^*M$. Assuming $N$ is a hypersurface, we develop the notion of generalised exterior curvature, introducing the generalised second fundamental form and the generalised mean curvature. We present generalised versions of the Gauß-Codazzi equations, and discuss possible applications.