ISL Algebra (2012)

In this school, a semester long course on basic abstract algebra will be covered. It will have 12 lectures each on important topics in the theory of groups, rings, fields and Galois theory. A brief syllabus is: group actions, groups of symmetries of Platonic solids, Sylow theorems, gen-eral linear group, special linear group, orthogonal and unitary groups, unique factorization domains, principal ideal domains, modules over them and their application to abelian groups and canonical forms, basic notions of field extensions, fundamental theorem of Galois theory and its applications to ruler and compass constructions.The school will emphasize problem solving and connections with other branches of mathematics such as number theory, geometry and topology.

Module 1: Group Theory - I --- Chanchal Kumar, IISER, Mohali

Symmetry, group actions, class equation, Sylow Theorems, groups of order 12.

Module 2: Group Theory – II ---- A. J. Prameswaran, TIFR, Mumbai

Classical linear groups, SU(2), SL(2), SO(3), Simple groups.

Module 3: Ring Theory - I ---- Manoj Kummni, CMI, Chennai

Integral domains and fraction fields, maximal ideals, Nullstellensatz, UFD, PID, Euclidean domains, Gauss

Lemma.

Module 4: Ring Theory - II --- K. V. Subrahmanyam, CMI, Chennai

Noetherian Rings, Hilbert Basis Theorem, Structure Theorem for modules over PID's,

Module 5: Field Theory ---- N. Raghavendra, HRI, Allahabad

Degree of a field extension, ruler and compass constructions, splitting fields, finite fields,

separable extensions, normal extensions, primitive element theorem.

Module 6: Basic Galois Theory ---- K. N. Raghavan, IMSc, Chennai

Fundamental Theorem of Galois theory, cubic equations, symmetric functions, fundamental Theorem of algebra.

Time-Table

Notice:

1. Selected candidates are requested to confirm their participation in this school positively by 31st January so that accommodation is arranged accordingly. Confirmation should be conveyed by E-mail to : drhsdhami at gmail.com or profdhami at rediffmail.com
2. Those participants who need the letter of participation should write e-mail to drhsdhami at gmail.com or profdhami at rediffmail.com It will be sent to them by E-mail as well as by post.

Almora is a hill station. There are trains from Delhi up to Haldwani/Kathgodam. The names of trains are  Ranikhet Express, Uttaranchal Sampark Kranti Express and AC express from Ananad Vihar in Delhi. Air  service is also available for Pantnagar from Delhi but one will have to check whether the facility is available 

on the days of journey. Taxi shall be available from Kathgodam or Haldwani which can be arranged for the  experts after knowing their itinerary.