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Representation theory transforms abstract algebra groups into things like simpler matrices. The field’s founder left a list of 43 problems for others to study, iterate on, and prove.
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
For most abelian varieties, the algebra Hdg*(X) is generated in degree one, so the Hodge conjecture holds. In particular, the Hodge conjecture holds for sufficiently general abelian varieties, for products of elliptic curves, and for simple abelian varieties of prime dimension.
Organic and baby carrots sold at grocery stores across the US have been recalled after an E. coli outbreak that has killed one person. So far, 15 people are in hospital and 39 cases have been ...
Larry Mullen Jr. has always found it difficult to comprehend arithmetic, and now he knows why.. After years of struggling with numeracy skills such as adding and counting, the U2 drummer, 63, has ...
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