Date and Time: 23 June 2020, 5:30 pm IST - 6:30 pm IST (joining time :
5:15 pm IST - 5:30 pm IST)
Google Meet Link:
https://meet.google.com/gkc-hydx-fkn
Speaker: Mitra Koley, TIFR Mumbai
Title: $F$-rationality of Rees algebras.
Abstract: In this talk we will discuss $F$-rationality of Rees algebras.
The study in this direction began when Singh gave an example of
$3$-dimensional hypersurface $F$-rational ring whose Rees algebra with
respect to a maximal ideal is Cohen-Macaulay and normal domain but not
$F$-rational. Motivated by this example Hara, Watanabe and Yoshida
investigated various questions regarding $F$-rationality of Rees algebras.
Using the notion of tight integral closure they gave a criterion for
$F$-rationality of Rees algebras of ideals primary to the maximal ideal of
a Cohen-Macaulay local ring. Their paper is of significant interest
because of some conjectures and some open questions. In a joint work with
Manoj Kummini we study these questions and conjectures and answer some of
them.