


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, 2:303.45 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 BuchstaberPanov'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 wellknown examples of random divergencefree vector fields. The first one is the alternating shear flow model proposed by Pierrehumbert, in which case we set up a dynamicsbased framework to construct such spacetime 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. 45 pm
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Venue: Ramanujan Hall
Host: Tony Puthenpurakal
Speaker: R. V. Gurjar, IIT Bombay
Title: BrieskornPham 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) BrieskornPham, 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 3dimensional BP singularities that admit a nontrivial 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 3dimensional BP 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.