Is P the same as NP?

P is the set of problems whose solution times are proportional to polynomials involving N’s. NP (which stands for nondeterministic polynomial time) is the set of problems whose solutions can be verified in polynomial time. But as far as anyone can tell, many of those problems take exponential time to solve.

Is NP harder than P?

The P versus NP problem is a major unsolved problem in computer science. If it turned out that P ≠ NP, which is widely believed, it would mean that there are problems in NP that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time.

How is GCT used to solve the P vs NP problem?

This series of three talks will give a nontechnical, high level overview of geometric complexity theory (GCT), which is an approach to the P vs. NP problem via algebraic geometry, representation theory, and the theory of a new class of quantum groups, called nonstandard quantum groups, that arise in this approach.

Which is the best approach to P vs NP?

Geometric complexity theory (GCT) is an approach towards the P vs. NP and related problems [C, Kp, Le, V] initiated in [GCTpram] with a proof of a special case of the P 6= NCconjecture and developed in a se- ries of articles [GCT1]-[GCT8] and [GCTflip], with further developments in [Bu, BLMW, Ku, LMR].

How is the P vs NP problem related to Riemann hypothesis?

In particular, GCT suggests that the P vs. NP problem in characteristic zero is intimately linked to the Riemann Hypothesis over finite fields. No background in algebraic geometry, representation theory or quantum groups would be assumed.

Which is the most comprehensive book on arithmetic curves?

I–IV” (EGA I–IV), the most comprehensive and detailed elaboration of the theory of algebraic schemes available in (text-)book form, whereas the second, merely arithmetic part provides the very first systematic and coherent introduction to the advanced theory of arithmetic curves and surfaces at all.