Abstract: We will continue with the material in Chapter 1 in Cassels and
Frohlich.
Time:
4:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Speaker: Eknath Ghate, TIFR Mumbai
Title: Reductions of Galois Representations: Act 1.5
Abstract: We shall describe recent progress on the question of writing
down the reductions of certain local Galois representations. We shall
focus on the case of half integral slopes (especially slope 3/2)
where the behaviour of the reduction is both more complicated and
more interesting.
Our proof uses the mod p Local Langlands Correspondence to reduce the
problem to computing the reductions of certain locally algebraic
representations of GL_2 of the p-adics on certain functions on
the underlying tree
Time:
3:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Rational Singularities.
We will define special singularities of algebraic or analytic varieties
called rational singularities introduced my M. Artin. After discussing
some equivalent criterion for rationality we will give many naturally
occuring examples.
Next, we will describe the results of Artin in dimension 2.
Important results due to Brieskorn, Lipman, Mumford, Tjurina,...
will be mentioned.
If time permits some results by Spivakovsky, Le dung Trang-M. Tosun,
Gurjar-Wagh,...will be mentioned.
No proofs wil be given.