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www.galoisrepresentations.com | ||
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totallydisconnected.wordpress.com
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| | | | | $latex \bullet$ Let $latex f$ be some cuspidal Hecke eigenform, with associated Galois representation $latex \rho_{f}:G_{\mathbf{Q}}\to \mathrm{GL}_2(\overline{\mathbf{Q}_p})$. A notorious conjecture of Greenberg asserts that if $latex \rho_{f}|G_{\mathbf{Q}_p}$ is abelian (i.e. is a direct sum of characters), then $latex f$ is a CM form, or equivalently $latex \rho_f$ is induced from a character. At some point... | |
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www.jeremykun.com
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| | | | | Last time we defined and gave some examples of rings. Recapping, a ring is a special kind of group with an additional multiplication operation that "plays nicely" with addition. The important thing to remember is that a ring is intended to remind us arithmetic with integers (though not too much: multiplication in a ring need not be commutative). We proved some basic properties, like zero being unique and negation being well-behaved. | |
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gilkalai.wordpress.com
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| | | | | Topology Quasi-polynomial algorithms for telling if a knot is trivial Marc Lackenby announced a quasi-polynomial time algorithm to decide whether a given knot is the unknot! This is a big breakthrough. This question is known to be both in NP and in coNP. See this post, and updates there in the comment section. Topology seminar,... | |
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nobsstats.com
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