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[2:30pm] Dilip P Patil, IISc Bangalore
 Description:
 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
 Description:
 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
onedimensional 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 wellknow and
classical results.
[4:30pm] Parthanil Roy:Parthanil Roy:Mathematics Colloquium
 Description:
 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 GaltonWatson 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 lightertailed case, however, the behaviour is much more
subtle, and the scaling of the position of the rightmost particle in the
nth 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.


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