## Events at Physics |

**Chaos & Complex Systems Seminar**

**Computational complexity theory -- The world of P and NP**

**Date:**

**Tuesday, September 11th**

**Time:**12:05 pm

**Place:**4274 Chamberlin (refreshments will be served)

**Speaker:**Jin-Yi Cai, UW Department of Computer Science

**Abstract:**Computational Complexity Theory is the study of intrinsic difficulties of computational problems. The most prominent open problem is the conjecture that P is not equal to NP. In essense this conjecture states that it is intrinsically harder to find proofs than to verify them. It has a fundamental importance in many areas from computer science to mathematics, to our basic understanding of nature.<br>

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Valiant's new theory of holographic algorithms is one of the most beautiful ideas in algorithm design in recent memory. It gives a new look on the P versus NP problem. In this theory, information is represented by a superposition of linear vectors in a holographic mix. This mixture creates the possibility for exponential sized cancellations of fragments of local computations. The underlying computation is done by invoking the Fisher-Kasteleyn-Temperley method for counting perfect matchings for planar graphs (Dimer Problem). Holographic algorithms challenge our conception of what polynomial time computation can do, in view of the P vs. NP question.<br>

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In this talk we will survey the developments in holographic algorithms. No specialized background is assumed.

**Host:**Sprott