Monday, December 2, 2013, 4:00 p.m., B239 VV  
Math Department Colloquium
Simon Marshall (Northwestern University)

Semiclassical estimates for eigenfunctions on locally symmetric
spaces.


Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace
eigenfunction on M.  If p > 2, a theorem of Sogge tells us how large the L^p
norm of f can be in terms of its Laplace eigenvalue.  For instance, when p
is infinity this is asking how large the peaks of f can be.  I will present
an analogue of Sogge's theorem for eigenfunctions of the full ring of
invariant differential operators on a locally symmetric space, and discuss
some links between this result and number theory.