Triangle Seminars
Tuesday, 15 Dec 2009
The archaeology of unipotent radicals of the exceptional algebraic groups
David Stewart
(Imperial College London)
Abstract:
We want to know all reductive subgroups of the five exceptional algebraic groups. In low characteristic some unusual subgroups appear which are contained inside parabolic subgroups. I will show how to find these by an archaeological dig.
We want to know all reductive subgroups of the five exceptional algebraic groups. In low characteristic some unusual subgroups appear which are contained inside parabolic subgroups. I will show how to find these by an archaeological dig.
Posted by: KCL
Thursday, 17 Dec 2009
Cosmological quantum billiards
Hermann Nicolai
(MPI, Potsdam)
Abstract:
The mini-superspace quantization of D=11 Supergravity is
equivalent to the quantization of a E10-K(E10) coset
space sigma model when the latter is restricted to the E10 Cartan
subalgebra. As a consequence, the wavefunctions solving the relevant
mini-superspace Wheeler-DeWitt equation involve automorphic (Maass wave)
forms under the modular group W+(E10) cong PSL2(O). Using Dirichlet
boundary conditions on the billiard domain a general inequality for the
Laplace eigenvalues of these automorphic forms can be derived, which
implies that the wave function of the universe is generically complex
and always tends to zero when approaching the initial singularity. The
potential significance of these properties for the question of
singularity resolution in quantum cosmology is discussed, also in
comparison with other approaches. The present approach offers
interesting new perspectives on some long-standing issues in canonical
quantum gravity.
The mini-superspace quantization of D=11 Supergravity is
equivalent to the quantization of a E10-K(E10) coset
space sigma model when the latter is restricted to the E10 Cartan
subalgebra. As a consequence, the wavefunctions solving the relevant
mini-superspace Wheeler-DeWitt equation involve automorphic (Maass wave)
forms under the modular group W+(E10) cong PSL2(O). Using Dirichlet
boundary conditions on the billiard domain a general inequality for the
Laplace eigenvalues of these automorphic forms can be derived, which
implies that the wave function of the universe is generically complex
and always tends to zero when approaching the initial singularity. The
potential significance of these properties for the question of
singularity resolution in quantum cosmology is discussed, also in
comparison with other approaches. The present approach offers
interesting new perspectives on some long-standing issues in canonical
quantum gravity.
Posted by: IC