Brave New Rings seminar 2009

Future seminars:

See also the Topology seminar page.

Past seminars:

• Friday January 23rd at 10.15 - 12.00 in room B63
  JOHN ROGNES:
  Differential geometry of gerbes and 2-vector bundles

  This spring we plan to go through parts of J.-L. Brylinski's book "Loop spaces, characteristic classes and geometric quantization", aiming to see how to extend the differential geometry of gerbes to 2-vector bundles of higher rank. For U(1)-gerbes, M. K. Murray's paper "Bundle gerbes" provides a more concrete approach. It is extended to non-abelian gerbes in P. Ascieri, L. Cantini and B. Jurco's paper "Nonabelian bundle gerbes, their differential geometry and gauge theory". The 2-vector bundles of N. A. Baas, B. I. Dundas and J. Rognes' paper "Two-vector bundles and forms of elliptic cohomology" generalize U(1)-gerbes in a different direction. We will to outline the relation between these notions, suggest how to define a connection in a 2-vector bundle, and explain how parallel transport with respect to such a connection may give rise to a conformal field theory.

  Here are the rough seminar notes.

• Friday February 6th at 10.15 - 12.00 in room B63
  SVERRE LUNØE-NIELSEN:
  Descent theory for sheaves

  (Brylinski, 5.1)

• Wednesday February 11th at 14.15 - 16.00 in room B63
  SVERRE LUNØE-NIELSEN:
  Descent theory for sheaves, II

• Friday February 13th at 10.15 - 12.00 in room B63
  THOMAS KRAGH:
  Sheaves of groupoids and gerbes

  (Brylinski, 5.2)

• Friday February 20th at 10.15 - 12.00 in room B63
  THOMAS KRAGH:
  Sheaves of groupoids and gerbes, II

• Friday February 27th at 10.15 - 12.00 in room B63
  JOHN ROGNES:
  Connective structure on gerbes and two-vector bundles

  (Brylinski, 5.3)

• Friday March 6th at 10.15 - 12.00 in room B63
  JOHN ROGNES:
  Connective structure on gerbes and two-vector bundles, II

  We associate a sheaf of groupoids (= a stack) to each 2-vector bundle, show that a connective structure on a 2-vector bundle gives rise to a connective structure on the associated stack, and discuss the existence of such connective structures.

• Wednesday March 18th at 14.15 - 16.00 in room B63
  THOMAS KRAGH:
  The determinant gerbe and connective structures

• Wednesday March 25th at 14.15 - 16.00 in room B63
  SVERRE LUNØE-NIELSEN:
  The holonomy line bundle

  (Brylinski, 6.2)

• Friday April 3rd at 10.15 - 12.00 in room B63
  JOHN ROGNES:
  Group completion of GL_n(N_0)

• Wednesday April 15th at 14.15 - 16.00 in room B63
  THOMAS KRAGH:
  The determinant gerbe and connective structures, II

• Wednesday May 13th at 14.15 - 16.00 in room B63
  THOMAS KRAGH:
  Bipermutative structures on Z x BU(1)

• Friday May 15th at 10.15 - 12.00 in room B63
  JOHN ROGNES:
  E_\infty ring structures on Z x BU(1)

Past years:

YFF home page:

Brave New Rings