Analysis and PDE seminar

Thursday 16th Nov, 2023, 3.30-4.30 pm

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Venue: Ramanujan Hall

Host: Chandan Biswas

Speaker : Chandan Biswas, IIT Bombay

Title: A basic introduction to Fourier restriction estimates

Abstract: This is the sixth talk of the series. We will finish our discussion on Fourier restriction to the moment curve.

Commutative algebra Seminar

Thursday  16 Nov 4-5 pm

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Venue:  Room 215

Host: Tony  Puthenpurakal

Speaker: R. V. Gurjar, IIT Bombay

Title:  Brieskorn-Pham Singularities.

Abstract: Let  B=k[X_1,...,X_{n+1}]/(X_1^{a_1}+...+X_{n+1}^{n+1}) where k is the field of complex numbers and X the corresponding affine variety. These have been studied from many angles: (1) Brieskorn-Pham, Milnor, (2) from the topological viewpoint, giving rise to exotic spheres. (3) Storch for calculating the divisor class group of B (4) Flenner, Keichi Watanabe for characterizing rational singularities among them. (4) Recently Michael Chitayat wrote a beautiful thesis at Univ. of Ottawa characterizing 3-dimensional B-P singularities that admit a non-trivial locally nilpotent derivation (which is equivalent to having a G_a action on X). He has solved a conjecture about this completely. (5) I asked Michael which of the 3-dimensional B-P singularities define rational varieties in the sense of function field. Using ideas in his thesis he answered this completely.