Invited Speakers
Titles and Abstracts
Nikhil Srivastava
UC Berkeley, USA ![]() |
TBAAbstract: TBA
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Rekha R. Thomas
University of Washington, USA ![]() |
Classical Invariant Theory in Computer VisionAbstract: Invariant theory arises naturally in reconstruction problems in computer vision because most common models of cameras are defined up to some group action. In this talk I will explain some fundamental questions that arise in the reconstruction of 3d scenes from images in two cameras, where the invariant theory of point sets in the projective plane play a major role. They come hand in hand with classical constructions in algebraic geometry such as cubic surfaces and their 27 lines and related objects. |
Frank Vallentin
Universität zu Köln, Germany ![]() |
Least Distortion Euclidean Embeddings of Flat ToriAbstract: Lattices (discrete subgroups of $n$-dimensional Euclidean spaces) are ubiquitous objects in mathematics. One typical algorithmic problem for lattices is the closest vector problem (given a lattice and a point in Euclidean space, which lattice vector is closest to this given point?). In general the closest vector problem is NP-hard. One potential approach to derive efficient approximation algorithm the closest vector problem could go via the concept of least distortion metric embeddings. In this talk I will derive and analyze an infinite-dimensional semidefinite program which computes least distortion embeddings of flat tori $R^n/L$, where $L$ is an $n$-dimensional lattice, into Hilbert spaces. This enables us to provide a very simple, constant factor improvement over the previously best known lower bound on the minimal distortion of an embedding of an $n$-dimensional flat torus. As further applications we prove that every $n$-dimensional flat torus has a finite dimensional least distortion embedding, and we derive some optimal embeddings of flat tori given by certain important lattices. |