Symmetry and shape

Celebrating Prof. J. Berndt's 60th birthday

28 - 31 October 2019, Santiago de Compostela, Spain


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According to Felix Klein, geometry is the study of those properties in space that are invariant under a given transformation group. Intuitively, symmetry is the correspondence of shape at every point of a space. An interesting problem in geometry and many physical sciences is to determine the symmetries of a space from its shape. In Riemannian geometry, the natural group to consider is the isometry group, that is, the group of transformations of a manifold that preserve distances.

The aim of this conference is to gather experts from around the world in the study of symmetry in submanifold geometry, whilst we celebrate Jürgen Berndt's 60th birthday. The conference will revolve around the study of homogeneous submanifolds, including cohomogeneity one and polar actions, their characterization via concepts like isoparametric submanifolds or singular Riemannian foliations and their interaction with other topics in Differential Geometry and Geometric Analysis.

Professor Jürgen Berndt

Jürgen Berndt

Jürgen Berndt obtained his Ph.D. in 1989 at the University of Cologne. He worked at the University of Cologne, the University of Hull, University College Cork, and since 2009 he is Professor of Mathematics at King's College London. His research mainly revolves around the themes of symmetry and shape. He is particularly interested in the geometry of submanifolds (e.g. submanifolds with constant principal curvatures, totally geodesic submanifolds) and isometric Lie group actions (e.g. cohomogeneity one actions, polar actions) on Riemannian symmetric spaces. By now he has published three research monographs and more than fifty research articles. Many of these publications were obtained in collaborations with colleagues (from 14 different countries).

Prof. J. Berndt's webpage

University of Santiago de Compostela

Fonseca library

With more than five centuries of tradition, the University of Santiago de Compostela is a historic institution that projects itself to the future and beyond its frontiers, always attentive to the different demands of society, where it stands as an important academic frame of reference and where it develops its academic and research work. Centuries of history give the University an special capacity to merge the experience, security and confidence with present and future challenges.

The roots of the University go back to 1495, when the Santiago de Compostela solicitor López Gómez de Marzoa founds, with the help of the San Martiño Piñeiro abbot, a school for the poor known as "Grammatic Academy" in the monastery of San Paio de Antealtares.


Santiago's cathedral

Santiago de Compostela is the capital of the Autonomous Community of Galicia; declared a World Heritage City by UNESCO thanks to its monumental beauty, extraordinary conservation and as the final destination of a thousand-year-old pilgrim route: the Way of St. James, which, since the 9th century, has transformed this finis terrae into a meeting place of Western faith and thinking.

Obradoiro square

Santiago de Compostela is a stone apparition in the midst of the green forests of Northwest Spain and the nearby Galician “rias”. It was originally a stopping point on a Roman road, but the discovery of the Apostle James’ tomb at the beginning of the 9th century gave rise to a place of workshop in the corner of the Iberian Peninsula, which was then dominated by the Moors. From then on all of Europe started walking towards Santiago, a holy city of Christendom where the grace of plenary absolution awaited them. A Romanesque cathedral then arose there, with the following centuries adding the sobriety of the Renaissance style and the majesty of a Baroque style that eventually characterised the city’s monumental image, made from the granite of its monasteries, its pilgrim hospitals, its numerous churches, its stately houses and its squares, where time stands still.


Facultade de Matemáticas, Universidade de Santiago de Compostela