GEOMETRY AND TOPOLOGY

Mise à jour le   13/05/2024

Shortcode : CONTENAIR BOX

Team and research areas

The “Geometry and Topology” team is made up of 23 teacher-researchers and 7 doctoral students. The team's activity is organized around four main axes:

  • Differential geometry
  • Algebra and geometry
  • Quantum and differential topology
  • Discrete geometry

(6 PR, 16 MCF, 1 PRAG, 7 doctorants, responsable de l'équipe : Gaël Meigniez)

Differential geometry:

   Analysis on Riemannian varieties: harmonic, p-harmonic and bi-harmonic applications; GJMS operators and conformal geometry; geometric flows; extreme metrics.
   General relativity and Lorentzian geometry: black holes; scattering; Goursat problem.
   Complex differential geometry: twistor theory; holomorphic foliations; Kähler geometry.
   Functions of several complex variables: distribution of complex values; uniqueness theorems for meromorphic applications; logarithmic jet fibers.

Algebra and geometry:

   Algebraic geometry: Classification of general type varieties; algebraic curves and surfaces; caustics; Plücker formulas; theory of invariants.
   Real algebraic geometry: topology and geometry of real algebraic varieties, vector bundles, moduli spaces.
   Formal computing: modeling; Gröbner bases; correction codes.
   Representation theory: Lie groups and algebras; non-commutative algebra; invariant distributions.
   Arithmetic: Waring problem; perfect polynomials; finished bodies.

Quantum and differential topology: quantum groups; TQFT (topological quantum field theory); nodes; homotopic and geometric theory of foliations.

Discreet geometry: Immeubles de Tits; discrete groups; real trees; combinatorial fields; visual recognition of objects.

Seminars and working groups:

   seminar in Brest: Friday at 2 p.m. in the conference room (building H, UBO Brest)

   seminar in Vannes: Friday at 11 a.m. in room B133 of the LMBA (UBS, Yves Coppens building located in the Tohannic Research center in Vannes)

   The joint UBO Brest and UBS Vannes meetings in Quimper, which began on May 25, 2012, have since 2014 become the Quimperiodic seminar, of regional importance, bringing together three times a year in Quimper, for two days, under the patronage of four UMR CNRS and from the Center Henri Lebesgue, the surveyors of Brittany and Pays de Loire.

   “gauge theory” working group on Friday at 11 a.m., twice a month, in the conference room (building H, UBO Brest)

Participation in national and international research networks:

   GDR “Plato”
   GDRE “Geometric Analysis”
   ANR “Emarks”
   ANR “Flows and geometric operators”
   GDR “Mathematical Computing”
   GDR “Braids”
   GDR “Quantum Dynamics”
   ANR “Geometry and representations of Cherednik algebras, and O categories”
   GDR “Algebraic and Geometric Lie Theory”
   GDR “Number Theory”
   GDR “Structuring Number Theory”
   GDR “Algebraic Geometry and Complex Geometry”
   EAGER (European algebraic geometry research training network)
   RAAG (European research training network real algebraic and analytic geometry)
   LIA CNRS “Format Vietnam”

Recently organized conferences:

   “Supersymmetry” fall school, Aber Wrac’h, September 2015.
   International workshop “H-principle Houat”, Houat Island, June 15 to 19, 2015.
   Autumn school “Quantum field theory”, Aber Wrac’h, September 2014.
   International conference “Real vector bundles”, Brest; from July 7 to 11, 2014.
   International conference “Geometric Analysis at Roscoff”, Roscoff from June 16 to 20, 2014.
   GDR DynQua meeting, Roscoff from February 5 to 7, 2014.
   Tri-annual seminar “Quimperiodic Seminar”, Quimper.
   Conference "Crossed perspectives on random walks and the geometry of groups in honor of Emile Le Page", Berder Island (Gulf of Morbihan), from September 26 to 30, 2011.
   “Geometric Analysis” Days, Brest, March 24 and 25, 2011.
   Conference “Black holes, general relativity, waves”, Roscoff, from November 8 to 10, 2010.
   Thematic school "Geometric analysis", Roscoff, from October 18 to 22, 2010.
   Conference “Conformal Geometry: invariant theory and the variational method”, Roscoff from June 30 to July 4, 2008.
   Conference "Effective aspects of complex hyperbolic varieties", September 10-14, 2007, Aber Wrac'h.

Recent visitors:

   Andrew Clarke (UFRJ, Brazil), January 2014.
   Mario Garcia-Fernandez (ICMAT, Spain), January 2014.
   Rod Gover (University of Auckland, New Zealand), May 2012.
   Yoshihiko Mitsumatsu (Chow University, Tokyo, Japan and ENS Lyon), April 2012.
   Do Duc Thai (Hanoi National University of Education, Vietnam), September 2007, April 2012.
   Radu Pantilie (IMAR, Bucharest, Romania), CNRS Researcher April-June 2012.
   Nathan Geer (Utah State University, Logan USA), May-June 2011, March 2012.
   Ester Vergara-Diaz: European Commission Research Directorate, Marie Curie intra-European fellowship for career development, 2008-2010.
   Mike Eastwood (MSRI, Canberra, Australia), Apr 2007 and July 2008.
   Seiki Nishikawa (Tohoku University, Sendai, Japan), May 2005 and October 2010.
   Cezar Oniciuc (Iasi, Romania), May-June 2005, CNRS Researcher March-June 2008, 2015.
   Radu Slobodeanu (University of Bucharest, Romania), Postdoctoral researcher, 2005-2006, visiting professor June 2007, 2008, 2010 and 2011.

Keywords :

Application (p)-harmonic, harmonic morphism, conformal structure, geometric flow, black hole, relativity, extremal metrics, foliations, twistors, moduli spaces, real algebraic geometry, complex hyperbolic manifold, jet metric, distribution of values, algebra of Lie, Lie group, quantum group, knot, discrete group, correction code, Waring problem, perfect polynomials.