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[7:00pm] Ben Briggs, University of Utah
 Description:
 15 September 2020, 7:00 pm IST/ 1:30 pm GMT/ 09:30 am EDT (joining time :
6:45 pm IST  7:00 pm IST) Please note the unusual time
Google meet link: https://meet.google.com/adatdggryd
Speaker: Ben Briggs, University of Utah
Title: On a conjecture of Vasconcelos  Part 1
Abstract: These two talks are about the following theorem: If $I$ is an
ideal of finite projective dimension in a ring $R$, and the conormal
module $I/I^2$ has finite projective dimension over $R/I$, then $I$ is
locally generated by a regular sequence. This was conjectured by
Vasconcelos, after he and (separately) Ferrand established the case that
the conormal module is projective.
The key tool is the homotopy Lie algebra, an object sitting at the centre
of a bridge between commutative algebra and rational homotopy theory. In
the first part I will explain what the homotopy Lie algebra is, and how it
can be constructed by differential graded algebra techniques, following
the work of Avramov. In the second part I will bring all of the
ingredients together and, hopefully, present the proof of Vasconcelos'
conjecture.

