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Description: | Department Colloquium Speaker: CS Dalawat, Harish Chandra research Institute Date & Time: Tuesday, February 20, 2018, 16:00-17:00. Venue: Ramanujan Hall Title : Some footnotes to Galois's memoirs Abstract : In his first memoir, Galois gave a criterion for an irreducible equation of prime degree to be solvable by radicals. In the second memoir, he defined primitive equations and showed that if a primitive equation is solvable by radicals, then its degree is the power of a prime. His results can be reformulated in terms of extensions of fields. We will show how to extend this reformulation and parametrise all primitive solvable extensions of an arbitrary field. (An extension is called primitive if there are no intermediate extensions, and it is called solvable if the Galois group of its Galois closure is a solvable group). All these concepts will be recalled and illustrated through examples. If time permits, we will discuss an arithmetic application. The talk should be accessible to a wide audience, including students. |

Location: | Ramanujan Hall, Department of Mathematics |

Date: | Tuesday, February 20, 2018 |

Time: | 4:00pm-5:00pm IST |

Duration: | 1 hour |

Access: | Public |