[Colloquium] Combinatorics & Theory Speaker

[Donna Brooms]

Combinatorics & Theory Seminar Today:

Today, Thursday, May 26, 2016

Ry. 251 @ 3pm

Nathan Linial (Hebrew University)

Title: Quantum matching problems

 Abstract:

We describe two algorithmic problems, both of which can be viewed as quantum analogues of the perfect matching problem on bipartite graphs. Given several square matrices, we are asked to:

(1) decide if there is a full-rank matrix in their linear span

(2) decide if there is a shrunk subspace, that is a subspace U, s.t. the union of the images under these matrices is of smaller dimension than U.

The first problem is the well-known polynomial identity testing problem, for which a deterministic efficient solution implies a strong arithmetic circuit lower bound. The second problem has a rich history and has appeared in various forms in a remarkable number of mathematical and computational areas. For example, it is a key problem in the theory of non-commutative arithmetic circuits with divisions, as recently studied by Hrubes and Wigderson.

After introducing these problems, we will present a couple of ingredients in our recent deterministic efficient algorithm for the second problem.  These include a polynomial degree upper bound on generating the ring of matrix semi-invariants, and a linear algebraic analogue of the augmenting path technique.

Based on joint works with Gabor Ivanyos and K. V. Subrahmanyam, arXiv:1508.00690 and arXiv:1512.03531. Another recent paper on this topic is arxiv:1511.03730.

Host: Prof. Babai

Refreshments will be served before the talk in Ry 255. 













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