Differential Geometry Seminar Schedule for
Fridays 3:00 - 3:50pm, SH 6635
1/19 Hanming Zhou, UCSB "Lens
Rigidity for a Particle in a Yang-Mills Field"
Abstract: In this talk, we consider an inverse problem related to
the motion of a classical colored spinless particle under the influence
of an external Yang-Mills potential $A$ on a compact manifold with
boundary of dimension $\geq 3$. We show that under suitable convexity
assumptions, one can recover the potential $A$, up to gauge
transformations, from the lens data of the system, namely, scattering
data plus travel times between boundary points. The talk is based on
joint work with Gabriel Paternain and Gunther Uhlmann.
1/26 Changliang Wang, McMaster University,"Perelman's functionals on compact manifolds with
isolated conical singularities"
Abstract: We extend the theory of the Perelman's functionals on compact
smooth manifolds to compact manifolds with isolated conical
singularities. For the lambda-functional, this is essentially an
eigenvalue problem for a Schrodinger operator with singular potential.
We obtain a certain asymptotic behavior of eigenfunctions near the
singularities. This asymptotic behavior plays an important role for
deriving the variation formulas of the lambda-functional and other
applications. Moreover, we show that the infimum of the W-functional
over a suitable weighted Sobolev space on compact manifolds with
isolated conical singularities is finite, and the minimizing function
exists. We also obtain a certain asymptotic behavior for the minimizing
function near the singularities. This is a joint work with Professor
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