Campuses:

geometry

Thursday, May 21, 2015 - 9:00am - 9:50am
Fitting a low-rank matrix to data is an inherently non-convex problem; correspondingly, an increasingly common instinct has been to relax the rank constraint to a convex one, with the resulting estimator shown to be consistent under further statistical/structural assumptions.

However, this approach is rarely taken in practice, because it wastefully increases both the computational complexity and the search space of solutions.
Wednesday, October 22, 2014 - 1:45pm - 2:30pm
Thomas Hughes (The University of Texas at Austin)
Ten years ago last May, I presented a lecture entitled “Consider a Spherical Cow – Conservation of Geometry in Analysis: Implications for Computational Methods in Engineering” during the IMA Workshop Compatible Spatial Discretizations for Partial Differential Equations (May 11-15, 2004). In that lecture I coined the term Isogeometric Analysis [1,2], a pithy terminology for my vision of how to address a major problem in Computer Aided Engineering (CAE). The motivation was as follows: Designs are encapsulated in Computer Aided Design (CAD) systems.
Wednesday, March 5, 2014 - 11:30am - 12:20pm
Michael Farber (University of Warwick)
I will discuss several probabilistic models producing simplicial complexes, manifolds and discrete
groups. Random simplicial complexes are high dimensional analogues of random graphs and can be
used for studying the behaviour of large systems or networks depending on many random
parameters. We are interested in properties of random spaces which are satisfies with probability
tending to one. Using probabilistic models one may also test probabilistically the validity of open
Monday, March 3, 2014 - 11:30am - 12:20pm
Alberto Speranzon (United Technologies Corporation)
In this talk we will describe methodologies to localize both a single and a team of vehicles navigating in a complex environment without GPS. During the first part of the talk, we will consider the situation when vehicles (or a single vehicle navigating in an environment with multiple beacons) can measure their relative (inter-vehicle) distances. In this case, the problem can be posed as a distributed graph embedding problem.
Thursday, October 10, 2013 - 10:15am - 11:05am
Monica Nicolau (Stanford University)
I will discuss the effect of geometric transformations on the topology of data. Geometric transformations are central in highlighting characteristics in the data that extract information. A common feature is that the same data set can provide answers to multiple problems. Thus the choice of underlying geometry is crucial in highlighting the answers to the correct problem. There will be many examples from systems biology.
Monday, October 7, 2013 - 9:00am - 9:50am
Gunnar Carlsson (Stanford University)
We will give a summary of the topological methods for understanding complex data sets. We will discuss the persistent homology theme as well as the theme which deals with geometric representations of data.
Tuesday, July 26, 2011 - 9:00am - 9:30am
Anton Leykin (Georgia Institute of Technology)
Overview of the numerical algebraic geometry group agenda
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