During the 3rd week of October, specifically between the 13th and 16th, the Congress "Symmetry and shape" will be held in the Main Classroom of the Faculty of Mathematics of the University of Santiago de Compostela. The objective of this conference is to bring together experts in the study of symmetry in Differential Geometry. The conference will revolve around the study of curvature, homogeneous and symmetric spaces, the geometry of Riemann's submanifolds and other topics related to Differential Geometry and Geometric Analysis.
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 the shape at each point in a space. An interesting problem in geometry and many physical sciences is determining the symmetries of a space from its shape.
Throughout this activity, there will be presentations and talks by the different guests (updated on 09/19/2022):
- Local topological rigidity of 3-manifolds of hyperbolic type, Andrea Drago (Sapienza University of Rome, Italy).
We study systolic inequalities for closed, orientable, Riemannian 3-manifolds of bounded positive volume entropy. This allows us to prove that the class of atoroidal manifolds (i.e. that admit an hyperbolic metric) with uniformly bounded diameter and volume entropy is topologically rigid. In particular our main result is the following theorem:
Let X be a closed, orientable, atoroidal, Riemannian 3-manifold with Ent(X)<E and Diam(X)<D. Then there exist a function s(E,D) such that, if Y is closed, orientable, torsionless, Riemannian 3-manifold with Ent(Y)<E and dGH(X,Y)<s(E,D), then π1(X)≅π1(Y). In particular, X and Y are diffeomorphic.
- Homogeneous spaces of G2, Cristina Draper Fontanals (Universidad de Málaga, Spain).
Pilar Benito, Cristina Draper and Alberto Elduque study the reductive homogeneous spaces obtained as quotients of the exceptional group G2 in the Draper doctoral dissertation (see ), from an algebraic perspective. In this poster we revisit these spaces from a more geometrical approach.
- P. Benito, C. Draper, A. Elduque: Lie-Yamaguti algebras related to g2, J. Pure Appl. Algebra 202 (2005), 22-54.