Phase transition

Thursday, January 18, 2018 - 2:00pm - 2:50pm
Daniel Beller (Brown University)
In thermotropic smectic-A liquid crystals, the strong energetic preference for constant layer spacing often results in the spontaneous formation of focal conic domains (FCDs) to resolve large distortions. Collections of many FCDs self-organize into arrangements such as 2D lattices and polygonal textures, whose packing geometries involve beautiful geometric matching rules to ensure that smectic layers remain smooth. However, strong confinement can frustrate the typical FCD self-organization principles. I will discuss three such scenarios:
Thursday, January 28, 2016 - 3:15pm - 4:05pm
Weiyu Xu (The University of Iowa)
In this talk, we explore the performance limits of recovering structured signals from low-dimensional linear projections, using tools from high dimensional convex geometry. In particular, we focus on two signal reconstruction applications: a total variation minimization for recovering gradient-sparse signals and a low-rank Hankel matrix completion for super-resolution of spectrally sparse signals. Using the tool of Gaussian width, we obtain counter-intuitive performance bounds on the sample complexity for these two applications.
Wednesday, October 9, 2013 - 2:00pm - 2:50pm
Omer Bobrowski (Duke University)
In manifold learning, one wishes to infer geometric and topological features of an unknown manifold, embedded in a d-dimensional Euclidean space, from a finite (random) point cloud. One topological invariant of a considerable interest is the homology of the underlying space.
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