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| Mathematics Department Colloquium |
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| Start Date: | 3/17/2011 | Start Time: | 4:00 PM |
| End Date: | 3/17/2011 | End Time: | 5:00 PM |
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Event Description
Roger Brockett
An Wang Professor of Computer Science and Electrical Engineering
Harvard University
"Sorting and merging via stochastic differential equations: new models for some problems in statistical mechanics"
Recent publications in the condensed matter physics literature consider randomized algorithms for sorting a list of numbers as possible models for experimental results showing a type of "memory" associated with nonequilibrium processes such as the cooling of glass. On the other hand, it was observed more than twenty years ago that there are certain dynamical systems, e.g. the Toda lattice, that can be viewed as continuous versions of bubble sort, an elementary sorting algorithm often taught in beginning computer science classes. Although less well known, there are stochastic versions of these continuous sorting algorithms, naturally defined by a certain Lie algebraic structure in concert with the Ito calculus. In some cases these differential equation versions have explicitly computable invariant measures; this is best appreciated by realizing that the Toda lattice can be considered to be a gradient flow, distinct from its more widely appreciated Hamiltonian structure. In this talk we will attempt to weave together these threads and relate them, at least in a loose way, to the experimental observations mentioned above. At the same time, we will discuss how Lie theory suggests a wider class of dynamical systems, apparently not directly related to Hamiltonian mechanics, but still having the potential to describe the phenomena in question. |
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Remarks:
Tea at 3:30 in SAS 4104 |
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