Xornada "Symmetry and shape"

ven., 16 set. 2022


Durante a 3ª semana de outubro, concretamente entre os días 13 e 16, celebrarase na Aula Magna da Facultade de Matemáticas da Universidade de Santiago de Compostela o Congreso "Symmetry and shape". O obxectivo desta xornada é reunir expertos no estudo da simetría en Xeometría Diferencial. A conferencia xirará arredor do estudo da curvatura, os espazos homoxéneos e simétricos, a xeometría de subvariedades riemannianas e outros temas relacionados en Xeometría Diferencial e Análise Xeométrica.

Segundo Felix Klein, a xeometría é o estudo daquelas propiedades no espazo que son invariantes baixo un grupo de transformación dado. Intuitivamente, a simetría é a correspondencia de forma en cada punto dun espazo. Un problema interesante en xeometría e moitas ciencias físicas é determinar as simetrías dun espazo a partir da súa forma.

Ó longo desta actividade contarase con ponencias e charlas dos diferentes invitados (actualizado a 19/09/2022):

Charlas

  • Christoph Böhm, Universität Münster, Germany.
  • Giovanni Catino, Politecnico di Milano, Italy.
    • Some canonical metrics on Riemannian manifolds: In this talk I will review recent results concerning the existence of some canonical Riemannian metrics on closed (compact with no boundary) smooth manifolds. The constructions of these metrics are based on Aubin's local deformations and a variant of the Yamabe problem which was first studied by Gursky.

  • Quo-Shin Chi, Washington University at St. Louis, USA.
    • Fano 3-folds and classification of constantly curved holomorphic 2-spheres of degree 6 in the complex Grassmannian G(2,5): Harmonic maps from the Riemann sphere to Grassmannians (and, more generally, to symmetric spaces) arise in the sigma-model theory in Physics. Such maps of constant curvature constitute a prototypical class of interest, for which Delisle, Hussin and Zakrzewski proposed the conjecture that the maximal degree of constantly curved holomorphic 2-spheres in the (complex) G(m,n) is m(n−m) and confirmed it when m=2 and n=4 or 5. Up to unitary equivalence, there is only one constantly curved holomorphic 2-sphere of maximal degree 4 in G(2,4) by Jin and Yu. On the other hand, up to now, the only known example in the literature of constantly curved holomorphic 2-sphere of maximal degree 6 in G(2,5) has been the first associated curve of the Veronese curve of degree 4. By exploring the rich interplay between the Riemann sphere and projectively equivalent Fano 3-folds of index 2 and degree 5, we prove, up to the ambient unitary equivalence, that the moduli space of (precisely defined) generic such 2-spheres is semialgebraic of dimension 2. All these 2-spheres are verified to have non-parallel second fundamental form except for the above known example.

  • Anna Fino, University of Torino, Italy.
  • Luis Guijarro, Universidad Autónoma de Madrid, Spain.
  • Michael Jablonski, University of Oklahoma, USA.
  • Andreas Kollross, Universität Stuttgart, Germany.
  • Adela Latorre, Universidad Politécnica de Madrid, Spain.
  • Carlos Olmos, Universidad Nacional de Córdoba, Argentina.
  • Marco Radeschi, University of Notre Dame, USA.
  • Uwe Semmelmann, Universität Stuttgart, Germany.
  • Joeri Van der Veken, University of Leuven, Belgium.

Posters

  • 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 [1]), from an algebraic perspective. In this poster we revisit these spaces from a more geometrical approach.

Bibliography:

  1. P. Benito, C. Draper, A. Elduque: Lie-Yamaguti algebras related to g2, J. Pure Appl. Algebra 202 (2005), 22-54.

Comité Organizador

  • José Carlos Díaz Ramos, investigador vinculado a CITMAga, Universidade de Santiago de Compostela
  • Miguel Domínguez Vázquez, investigador vinculado a CITMAga, Universidade de Santiago de Compostela
  • Eduardo García Río, investigador vinculado a CITMAga, Universidade de Santiago de Compostela
  • Victor Sanmartín López, Universidade de Santiago de Compostela
  • M. Elena Vázquez Abal, investigadora vinculada a CITMAga, Universidade de Santiago de Compostela


  • Fonte: http://xtsunxet.usc.es/symmetry2022/committees.html