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Algebraic Statistics |
| December 15, 2008 to December 18, 2008 |
| Organized By: Serkan Hosten (SFSU), Lior Pachter (UCB), Bernd Sturmfels (UCB) |
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| Return to Workshop Description |
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Towards the salmon conjecture
Tuesday December 16, 2008
02:20PM - 03:00PM
Speakers:
Luke Oeding
Abstract:
In 2007 E. Allman offered a prize of Alaskan smoked salmon for the answer to the following problem: Determine the defining ideal of the 4th secant variety to the Segre product of 3 copies of $\PP^{3}$. It is conjectured that the known generators in degrees 5,6 and 9 suffice. Although this variety is a classical object, recent interest spawned from the study of molecular phylogenetics and how DNA sequences can be related by evolutionary trees. Applications of classical representation theory and geometry have been keys to recent progress on this problem. In fact, Landsberg and Manivel have made a reduction to understanding a smaller secant variety. I will describe some of the theoretical and computational aspects of this approach, and discuss the status of the conjecture.
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