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Finding rank-1 tensors via computing intersection of conic varieties and linear subspaces, and further directions
Student-Run Research Seminar| Speaker: | Jeshu Dastidar, UC Davis |
| Location: | 3106 MSB |
| Start time: | Wed, Jun 5 2024, 12:10PM |
In this talk, I will describe an algorithm of Johnston-Lovitz-Vijayaraghavan that computes the intersection of an arbitrary conic variety X and a linear subspace U, both living in some ambient vector space V. We will in particular focus on when the intersection is {0} and determinantal varieties of rank 1, and in this case, the algorithm works under the assumption that the dimension of U is at most (1/4)*dim(V) asymptotically. We investigate whether this constant of 1/4 is optimal and show that the algorithm fails if dim(U) > 1/sqrt(2)*dim(V) asymptotically. Lastly, I will talk about the broader implications of this and future directions.
Free pizzas! :)