Satya Mandal, The University of Kansas, KS, USA
Description
Speaker: Satya Mandal, The University of Kansas, KS, USA
Date/Time: 27 October 2020, 6:30pm IST/ 1:00pm GMT/ 9:00am EDT (joining
time: 6:15 pm IST - 6:30 pm IST)
Google meet link: meet.google.com/zcj-xnpb-ffo
Title: Quillen $K$-Theory: A reclamation in Commutative Algebra - Part 1
Abstract: In these two talks I take a pedagogic approach to Quillen
$K$-theory. What it takes to teach (and learn) Quillen $K$-theory? I am at
the tail end of completing a book on this, which would eventually be
available through some outlet. This is based on a course I taught. Current
version has nearly 400 pages, in eleven chapters. I finish with Swan’s
paper on quadrics. I tried to do it in a reader friendly way, and tried to
avoid expressions like “left to the readers”. I would give an overview and
a road map.
To justify the title, let me remind you that $K$-theory used to be part of
Commutative algebra. In this endeavor, I consolidate the background
needed, in about 100 pages, for a commutative algebraist to pick up the
book and give a course, or learn. There is a huge research potential in
this direction. This is because, with it, topologists have done what they
are good at. However, these higher $K$-groups have not been described in a
tangible manner. That would be the job of commutative algebraist, and
would require such expertise.