Tue, February 20, 2018
Public Access Category: All |
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- Time:
- 11:45am
- Location:
- Room No 215, Department of Mathematics
- Description:
- 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.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- 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.