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5:00pm 
[5:30pm] Neena Gupta, ISI Kolkata
 Description:
 Date and Time: Friday 31 July 2020, 5:30 pm IST / 12:00 GMT / 08:00am EDT
(joining time : 5:15 pm IST  5:30 pm IST)
Google Meet link: https://meet.google.com/xxmcidryqa
Speaker: Neena Gupta, ISI Kolkata.
Title: On the triviality of the affine threefold $x^my = F(x, z, t)$ 
Part 2.
Abstract: In this talk we will discuss a theory for affine threefolds of
the form $x^my = F(x, z, t)$ which will yield several necessary and
sufficient conditions for the coordinate ring of such a threefold to be a
polynomial ring. For instance, we will see that this problem of four
variables reduces to the equivalent but simpler twovariable question as
to whether F(0, z, t) defines an embedded line in the affine plane. As one
immediate consequence, one readily sees the nontriviality of the famous
RussellKoras threefold x^2y+x+z^2+t^3=0 (which was an exciting open
problem till the mid 1990s) from the obvious fact that z^2+t^3 is not a
coordinate. The theory on the above threefolds connects several central
problems on Affine Algebraic Geometry. It links the study of these
threefolds with the famous AbhyankarMoh “Epimorphism Theorem” in
characteristic zero and the SegreNagata lines in positive characteristic.
We will also see a simplified proof of the triviality of most of the
Asanuma threefolds (to be defined in the talk) and an affirmative solution
to a special case of the AbhyankarSathaye Conjecture. Using the theory,
we will also give a recipe for constructing infinitely many counterexample
to the Zariski Cancellation Problem (ZCP) in positive characteristic. This
will give a simplified proof of the speaker's earlier result on the
negative solution for the ZCP.


6:00pm 

