Fri, October 30, 2020
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6:00pm [6:30pm] Satya Mandal, The University of Kansas, KS, USA
Speaker: Satya Mandal, The University of Kansas, KS, USA Date/Time: 30 October 2020, 6:30pm IST/ 1:00pm GMT/ 9:00am EDT (joining time: 6:15 pm IST - 6:30 pm IST) Google meet link: Title: Quillen $K$-Theory: A reclamation in Commutative Algebra - Part 2 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.