| 29 September |
Speaker: Yaroslav Kurylev (UCL)
Title: Inverse spectal problems: uniqueness and stability
Abstract:
We consider the inverse problems of the reconstruction of a
Riemannian manifold from its spectral data (say, heat kernel) given on a
part of the boundary or internal subdomain.
In the first part of the talk we discuss the uniqueness in this problem
while in the second part consider the question of stability and its
relations to the issue of geometric convergence in proper classes of
Riemannian manifolds.
|
| 6 October |
Speaker: No Seminar
Title: No Seminar
Abstract:
No Seminar
|
| 13 October |
Speaker: Jeff Streets (Princeton)
Title: Geometric Flows in Complex Geometry
Abstract:
I will introduce a geometric evolution equation for Hermitian metrics on non-Kahler manifolds generalizing the Kahler Ricci flow. I will show some regularity theorems for the flow, and exhibit recently discovered Perelman-type functionals. Finally I will discuss optimal regularity conjectures for this flow, and the applications to the topology of complex surfaces.
|
| 20 October |
Speaker: Mohammad Ghomi (Ga. Tech)
Title: Spherical images of closed hypersurfaces
Abstract:
Given any finite subset $X$ of the sphere $S^n$,
$n>1$, which includes no pairs of antipodal points,
we explicitly construct smoothly immersed closed
orientable hypersurfaces in Euclidean space
$R^{n+1}$ whose Gauss map misses $X$. In
particular, this answers a question of M. Gromov.
Furthermore, we discuss the problem of
characterizing subsets $A$ of $S^n$ which may
contain the image of the Gauss map of a closed
hypersurface.
|
| 27 October |
Speaker: No Seminar
Title: No Seminar (Chern-Simons Symposium)
Abstract:
|
| 3 November |
Speaker: Felix Schulze (FU Berlin)
Title: On short time existence of the network flow.
Abstract:
I will report on joint work with T. Ilmanen and A. Neves on how to prove the existence of an embedded,
regular network moving by curve shortening flow in the plane, starting from a non-regular initial network.
Here a regular network consists of smooth, embedded line-segments such that at each endpoint, if not infinity,
there are three arcs meeting under a 120 degree angle. In the non-regular case we allow that an arbitrary number
of line segments meet at an endpoint, without an angle condition.
The proof relies on gluing in appropriately scaled self-similarly expanding solutions and a new monotonicity formula,
together with a local regularity result for such evolving networks.
This short time existence result also has applications in extending such a flow of networks through singularities.
|
| 10 November |
Speaker: Jaigyoung Choe (KIAS)
Title: Higher dimensional minimal submanifolds arising from the
catenoid and helicoid
Abstract:
For each m-dimensional minimal submanifold N of S^n we construct
an (m+1)-dimensional complete minimal immersion of N × R into
R^{n+2} and (m +1)-dimensional minimal immersions of N × R into
R^{2n+3} , H^{2n+3} and S^{2n+3}. Also from the Clifford torus N = S^k
(1/√2) × S^k (1/√2) we construct a (2k+2)-dimensional
complete minimal helicoid in R^{2k +3} . (Joint work with J. Hoppe)
|
| 17 November |
Speaker: Nicos Kapouleas (Brown)
Title: Recent progress on gluing constructions for minimal surfaces.
Abstract:
I will discuss recent progress on gluing constructions
for minimal surfaces including the doubling construction for
the equatorial two-sphere inside the round three-sphere.
I will also discuss related open questions.
|
| 24 November |
Speaker: No Seminar (Thanksgiving)
Title: No Seminar
Abstract:
No Seminar
|
| 1 December |
Speaker: Jacob Bernstein (Stanford)
Title: A Variational Characterization of the Catenoid
Abstract:
We show that the catenoid is the unique surface of least area (suitably understood) within a geometrically natural class of minimal surfaces.
The proof relies on techniques involving the Weierstrass representation used by Osserman and Schiffer to show the sharp isoperimetric inequality
for minimal annuli. An alternate approach that avoids the Weierstrass representation will also be discussed. This latter approach depends on a
conjectural sharp eigenvalue estimate for a geometric operater and has interesting connections with spectral theory. This is joint work with C. Breiner.
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