Postdoctoral fellows and postgraduate students

Postdoctoral fellows and postgraduate students

Postdoctoral Fellows

Dr. José Carlos Díaz-Ramos, July 2006 - February 2009
Carlos obtained his doctorate degree in December 2005 at the University of Santiago de Compostela in Spain under the supervision of Eduardo García-Rio and myself. From July 2006 until February 2009 Carlos was a postdoctoral fellow at University College Cork supported first by a fellowship from the Irish Research Council for Science, Engineering and Technology and later by a two-year Marie Curie Fellowship from the European Community.
Our project is on Shape and Symmetry. The major aim of the project is to investigate geometric structures from the viewpoint of their symmetries, and to characterize them by some distinguished features. More precisely, we investigate the shape of submanifolds of spaces equipped with a Riemannian structure that are invariant under a subgroup of the isometry group of the space. A particular objective is to study polar actions on symmetric spaces of noncompact type and characterize their orbits by geometric data.
Current address: Department of Geometry and Topology, University of Santiago de Compostela, Spain
E-mail: josecarlos.diaz@usc.es
Joint publications:

Homogeneous polar foliations of complex hyperbolic spaces, preprint arXiv:1107.0688v1.

Hyperpolar homogeneous foliations on noncompact symmetric spaces (with Hiroshi Tamaru), J. Differential Geom. 86 (2010), 191-235.

Homogeneous hypersurfaces in complex hyperbolic spaces, Geom. Dedicata 138 (2009), 129-150.

Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane, Proc. Amer. Math. Soc. 135 (2007), 3349-3357.

Real hypersurfaces with constant principal curvatures in complex hyperbolic spaces, J. London Math. Soc. 74 (2006), 778-798.

Dr. Sebastian Klein, October 2006 - September 2008
Sebastian obtained his doctorate degree in 2005 at the University of Cologne in Germany under the supervision of Helmut Reckziegel. He was a postdoctoral fellow at University College Cork supported by a two-year fellowship from the German Academic Exchange Service (DAAD).
The project is on Totally geodesic submanifolds in Riemannian symmetric spaces and in pseudo-Riemannian symmetric spaces. In understanding the geometry of Riemannian symmetric spaces, the knowledge of their totally geodesic submanifolds plays an important role. Whereas there are already classification results for totally geodesic submanifolds in certain Riemannian symmetric spaces, such results still lack completely for Riemannian symmetric spaces, although there has been large progress in the structure theory of the latter in recent years. The objectives of the research project are (1) to obtain results concerning the existence of totally geodesic submanifolds in certain classes of Riemannian symmetric spaces, and (2) to classify totally geodesic submanifolds in some specific Riemannian symmetric spaces.
Current address: Department of Mathematics, University of Mannheim, Germany
E-mail: s.klein@math.uni-mannheim.de
Publications:

Totally geodesic submanifolds of the exceptional Riemannian symmetric spaces of rank 2, Osaka J. Math. 47 (2010), 1077-1157.

Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram, Geom. Dedicata 138 (2009), 25-50.

Totally geodesic submanifolds of the complex and the quaternionic 2-Grassmannian, Trans. Amer. Math. Soc. 361 (2009), 4927-4967,.

Dr. Hiroshi Tamaru, March 2000 - February 2001
Hiroshi obtained his doctorate degree in 1997 at Sophia University, Tokyo, Japan, under supervision of Tadashi Nagano. His main research interests are symmetric spaces, homogeneous spaces, nilpotent Lie groups and graded Lie algebras. The aim of our project is to classify all cohomogeneity one actions on Riemannian symmetric spaces of noncompact type. Hiroshi is now Associate Professor at Hiroshima University.
Address: Hiroshima University, Department of Mathematics, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan
E-mail: tamaru@math.sci.hiroshima-u.ac.jp
WWW: http://www.math.sci.hiroshima-u.ac.jp/~tamaru/
Joint publications:

Cohomogeneity one actions on symmetric spaces of noncompact type, preprint arXiv:1006.1980v1.

Hyperpolar homogeneous foliations on symmetric spaces of noncompact type (with José Carlos Díaz-Ramos), J. Differential Geom. 86 (2010), 191-235.

Cohomogeneity one actions on noncompact symmetric spaces of rank one, Trans. Amer. Math. Soc. 359 (2007), 3425-3438.

Cohomogeneity one actions on noncompact symmetric spaces with a totally geodesic singular orbit, Tohoku Math. J. (2) 56 (2004), 163-177.

Homogeneous codimension one foliations on noncompact symmetric spaces, J. Differential Geom. 63 (2003), 1-40.

Dr. Evangelia Samiou, February - June 1999
Evangelia obtained her doctorate degree in 1997 at Augsburg University in Germany under supervision of Professor Jost-Hinrich Eschenburg. She is interested in problems relating rank and rigidity of Riemannian manifolds. During her visit we constructed a counterexample to the local version of the Rank Rigidity Conjecture. We also studied an infinitesimal version of k-flat homogeneity. Evangelia is now Assistant Professor at the University of Cyprus.
Address: University of Cyprus, Department of Mathematics and Statistics, P.O.Box 20537, 1678 Nicosia, Cyprus.
E-mail: samiou@ucy.ac.cy
WWW: http://www.ucy.ac.cy/~samiou
Joint publications:

Rank rigidity, cones, and curvature-homogeneous Hadamard manifolds, Osaka J. Math. 39 (2002), 383-394.

On infinitesimally k-flat homogeneous spaces, Bull. Belg. Math. Soc. Simon Stevin 8 (2001), 61-66.

PhD Students

Thomas Murphy, January 2008 - June 2011
Thomas graduated with a BA in Mathematics at University College Cork in Summer 2005. He then continued his studies for two further years with an MA in Mathematics. In his first year of the MA he took several advanced courses in Mathematics at University College Cork. For his second year he obtained a one-year scholarship from University College Cork for continuing his studies at the University of California in Berkeley. He wrote his MA thesis on Manifolds with positive sectional curvature. Thomas was then awarded a 3-year postgraduate research scholarship from the Irish Research Council for Science, Engineering and Technology. After I moved from Cork to King's College London, Thomas joined me shortly afterwards in London. His PhD thesis is on curvature-adapted foliations of symmetric spaces. He passed his viva voce examination on 3 June 2011. In November 2011 he will start with a postdoctoral position in the Differential Geometry and Algebra group at the Free University of Brussels.
Email: twjmurphy@gmail.com

José Carlos Díaz-Ramos, July 2003 - December 2005
Carlos graduated at the University of Santiago de Compostela in June 2001 and obtained his MSc degree in July 2003 for his work on Characterization of Riemannian manifolds by means of total curvatures of geodesic spheres. As a PhD student, Carlos was supervised jointly by Eduardo Garcí'a-Rio at the University of Santiago de Compostela and myself. Most of the time Carlos worked in Santiago. For the joint supervision he visited me at the University of Hull for two months in Winter/Spring 2004, and at University College Cork for three months in Summer/Autumn 2004 and for two months in Summer 2005. In his PhD thesis Carlos investigated three topics:

Geometric consequences of algebraic properties of the curvature tensor;
Curvature invariants of geodesic spheres and geodesic celestial spheres;
Real hypersurfaces in the complex hyperbolic space.

We mainly worked on the third part of the thesis. His main result in this part is the classification of all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of complex dimension greater than two.
Email: jc.diazramos@ucc.ie
PhD Thesis:

Geometric consequences of intrinsic and extrinsic curvature conditions, University of Santiago de Compostela, 2005.

Daria Osipova, September 1997 - February 2001
Daria graduated in 1997 with Professor Victor Pliss in the Department of Differential Equations at St. Petersburg State University in Russia. She came to Hull in September 1997 and worked for three years in the Department of Mathematics as a Graduate Teaching Assistant. In her research she studied symmetric submanifolds of symmetric spaces. Her main result is an explicit construction of non-totally geodesic symmetric submanifolds in Riemannian symmetric spaces of non-compact type and of rank greater than one. Further such examples were constructed by Jost-Hinrich Eschenburg (Augsburg), and Kazumi Tsukada (Tokyo) found a unifying description of all these examples. She presented her results on the following occasions:

Nowton Court, Bury St. Edmunds, England, Second UK-Japan Winter School, January 2000
University Of Warwick, Brussels-Warwick Differential Geometry Seminar, May 2000
Sophia University, Tokyo, Japan, Seminar, July 2000
University of Tokyo, Japan, Integrable Systems in Differential Geometry, July 2000

In July 2000 she was invited guest researcher at the Tokyo Metropolitan University for one month, where she also discovered many of the wonderful features of Japanese culture and hospitality. A hint: some of here favourites are Sashimi and Sake. She passed the examination for her doctorate on 24 November 2000, examined by Professor Dmitri Alekseevsky (Hull) and Professor James Eells (Cambridge). She worked here until 28 February 2001 as a research assistant. Afterwards she spent one year as a postdoctoral research fellow at the Ecole Normale Superieure de Cachan in France, funded by the Centre National de la Recherche Scientifique. Then she left the academic world to start a career in business.
Email: sulamifka@mail.ru and dkachakhidze@scor.com
Publications:

D. Osipova: Symmetric submanifolds in symmetric spaces, Differential Geom. Appl. 16 (2002), 199-211.

D. Osipova: Symmetric submanifolds in symmetric spaces, PhD Thesis, University of Hull, 2000.

Return to homepage

Last update: 15 July 2011