Lecture series on Hodge Theory

9 Nov., Thu.  at 11.30 am
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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: V. Srinivas, IIT Bombay

Title: Some elements of variation of Hodge structures

Abstract: I will touch on some aspects of variations of Hodge structure, finishing up my series of lectures for this semester.

Topology and Related Topics Seminar 

Thursday, 9  November 2023, 2:30-3.45  pm

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Venue: 215

Host: Rekha Santhanam

Speaker: Navnath Daundkar

Affiliation: IIT Bombay

Title: Cohomology of moment angle complexes - III

Abstract: In this talk, we will present the proof of Buchstaber-Panov's theorem, which describes the cohomology ring of a moment angle complex associated with a simplicial complex K as the tor algebra of K.

Analysis of PDE Seminar

Thursday, 09 November 2023, 02:15 pm

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Venue: Room 216, Department of Mathematics

Host: Harsha Hutridurga

Speaker: Rishabh Gvalani

Affiliation: Max Planck Institute, Leipzig.

Title: Exponential mixing by random velocity fields

Abstract: We establish exponentially fast mixing for passive scalars driven by two well-known examples of random divergence-free vector fields. The first one is the alternating shear flow model proposed by Pierrehumbert, in which case we set up a dynamics-based framework to construct such space-time smooth universal exponential mixers. The second example is the statistically stationary, homogeneous, isotropic Kraichnan model of fluid turbulence. In this case, the proof follows by a new explicit identity for the evolution of negative Sobolev norms of the scalar. This is based on joint works with Alex Blumenthal (Georgia Tech)
and Michele Coti Zelati (ICL), and Michele Coti Zelati and Theodore Drivas (Stony Brook).

Commutative algebra Seminar

Thursday, 9 Nov. 4-5 pm

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Venue:  Ramanujan Hall

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.

Analysis and PDE seminar

Thursday, 9th Nov. 5:15 pm - 6:15 pm

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Host: Chandan Biswas

Venue: Ramanujan Hall

Speaker: Chandan Biswas, IIT Bombay

Title: A basic introduction to Fourier restriction estimates

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