Tue, February 20, 2018
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February 2018
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11:00am [11:45am] Madhusudan Manjunath
Commutative algebra seminar Speaker: Madhusudan Manjunath Date and time : Tuesday 20 Feb, 11.30am-1.00pm Venue: Room 215 Title: Groebner bases of Toric Ideals. Abstract: This is the first of two lectures where we'll cover Groebner bases of toric ideals. We start with an introduction to toric ideals and then study their Grobener bases. Our main goal will be a theorem of Bernd Sturmfels from 1991 that relates (certain) initial ideals of toric ideals to regular triangulations of an associated point configuration. The lectures are based on Chapters 4 and 8 of the book ``Groebner Bases and Convex Polytopes'' by Sturmfels.

4:00pm [4:00pm] Department Colloquium
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.