Wed, September 11, 2019
Public Access

Category: All

September 2019
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2:00pm [2:30pm] Dilip P Patil, IISc Bangalore
Speaker: Dilip Patil. Affiliation: IISc, Bangalore. Date and Time: Wednesday 11 September, 2:30 pm - 3:30 pm. Venue: Room 215, Department of Mathematics. Title: Formal Smoothness and Cohen Structure Theorems. Abstract: We shall introduce smooth and formally smooth morphisms and study their basic properties. We shall complete the proof of CST (Cohen’s structure theorem for complete local rings).

[3:30pm] Jaikrishnan Janardhanan : IIT Madras
Analysis seminar. Speaker: Jaikrishnan Janardhanan. Affiliation: IIT Madras. Date and Time: Wednesday 11 September, 3:30 pm - 4:30 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: Holomorphic mappings into the symmetric product of a Riemann surface. Abstract: The symmetric product is an interesting and important construction that is studied in Algebraic Geometry, Complex Geometry, Topology and Theoretical Physics. The symmetric product of a complex manifold is, in general, only a complex space. However, in the case of a one-dimensional complex manifold (i.e., a Riemann surface), it turns out that the symmetric product is always a complex manifold. The study of the symmetric product of planar domains and Riemann surfaces has recently become very important and popular. In this talk, we present two of our recent contributions to this study. The first work (joint with Divakaran, Bharali and Biswas) gives a precise description of the space of proper holomorphic mappings from a product of Riemann surfaces into the symmetric product of a bordered Riemann surface. Our work extends the classical results of Remmert and Stein. Our second result gives a Schwarz lemma for mappings from the unit disk into the symmetric product of a Riemann surface. Our result holds for all Riemann surfaces and yet our proof is simpler and more geometric than earlier proved special cases where the underlying Riemann surface was the unit disk or, more generally, a bounded planar domain. This simplification was achieved by using the pluricomplex Green's function. We will also highlight how the use of this function can simplify several well-know and classical results.

[4:30pm] Parthanil Roy:Parthanil Roy:Mathematics Colloquium
Mathematics Colloquium. Speaker: Parthanil Roy. Affiliation: ISI Bangalore. Date and Time: Wednesday 11 September, 4:30 pm - 5:30 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: How to tell a tale of two tails? Abstract: We study the extremes of branching random walks under the assumption that underlying Galton-Watson tree has infinite progeny mean. It is assumed that the displacements are either regularly varying or have lighter tails. In the regularly varying case, it is shown that the point process sequence of normalized extremes converges to a Poisson random measure. In the lighter-tailed case, however, the behaviour is much more subtle, and the scaling of the position of the rightmost particle in the n-th generation depends on the family of stepsize distribution, not just its parameter(s). In all of these cases, we discuss the convergence in probability of the scaled maxima sequence. Our results and methodology are applied to study the almost sure convergence in the context of cloud speed for branching random walks with infinite progeny mean. The exact cloud speed constants are calculated for regularly varying displacements and also for stepsize distributions having a nice exponential decay. This talk is based on a joint work with Souvik Ray (Stanford University), Rajat Subhra Hazra (ISI Kolkata) and Philippe Soulier (Univ of Paris Nanterre). We will first review the literature (mainly, the PhD thesis work of Ayan Bhattacharya) and then talk about the current work. Special care will be taken so that a significant portion of the talk remains accessible to everyone.