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Differential Geometry Seminar Schedule for Winter 2018

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 Xianzhe Dai.

2/16 Distinguished Lecture by Prof. Gunther Uhlmann


 2/23 TBA,  " "

Abstract:

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