[cmi-seminar-external] LECTURE ANNOUNCEMENT

[VIJAYALAKSHMI V]

LECTURE SERIES

``There will be a series of research talks by mathematics faculty,
post-docs and graduate students during 3rd-7th February. The details are at
<http://www.cmi.ac.in/~mathsem/feb2014.txt>.''

Sd/=
Seminar Coordinator

Schedule of Talks
Monday 3rd February 2014:
14:00 M Sundari, TBA (This talk is earlier than usual.)
16:00 S Sundar, TBA

Tuesday 4th February 2014:
15:00 Narasimha Chary, Automorphism group of a BSDH variety.
16:00 T R Ramadas, Rational and global forms of certain Chiral Conformal Field Theories; Vertex Algebras I

Wednesday 5th February 2014:
15:00 Sourish Das, Bayesian Solution to Some Ill-Posed Problems
16:00 K V Subrahmanyam, TBA

Thursday 6th February 2014:
15:00 Priyavrat Deshpande, Reflections on manifolds & generalized Artin groups.
16:00 Sukhendu Mehrotra, TBA.

Friday 7th February 2014:
14:00 B V Rao, TBA (This talk is earlier than usual.)


Titles/Abstracts

Narasimha Chary, Tue 04-02-2014 15:00
Title: Automorphism group of a BSDH variety.
Abstract: Let G be a simple, simply connected algebraic group over the
field of complex numbers. Let B be a Borel subgroup of G containing a
maximal torus T of G. Let X(w) be the Schubert variety in G/B
corresponding to an element w of the Weyl group W. In general Schubert
varieties are not smooth. Demazure constructed for each reduced expression
of w, a desingularization Z(w) of the Schubert variety X(w), which is now
known as Bott-Samelson-Demazure-Hansen variety (for short BSDH variety).
Unlike Schubert varieties it is not clear from the construction of BSDH
varieties whether they are independent of the reduced expression of w. In
this talk, we will discuss the automorphim groups of BSDH varieties. More
precisely, we will show that the connected component of the identity
element of the automorphism group of Z(w) is a parabolic subgroup of G
either if G is simply laced and the action of B on X(w) is faithful or
X(w)=G/B. We will also describe explicity this parabolic subgroup. In
particular, we will see examples of BSDH varieties corresponding to
different reduced expressions for the same Weyl group element having
different non-isomorphic automorphism groups and hence the BSDH varieties
do depend on the reduced expressions under consideration. (joint work with
S.S Kannan and A.J Parameswaran).

Sourish Das, Wed 05-02-2014 15:00
Title: Bayesian Solution to Some Ill-Posed Problems
Abstract: When the problem Xb=y, is not well-posed (means either
non-existence or non-uniqueness) of b, ordinary least square method does
not yield required solution. Such problem is typically known as ill-posed
problems or ill-posed systems. In statistics, this problem is known as
either "Large-P, small N" or "Multicollinearity" problem. In order to
prefer particular solution with desirable properties, a TikhonovÂ’s
regularization term can be included in the objective function. It turns out
that TikhonovÂ’s regularization yields a Bayesian solution popularly
known as Ridge Regression. In recent times, some variant Bayesian solution
like ‘LASSO’ and ‘Elastic Net’ is being proposed. On the same
ill-posed systems, multiple testing problems can be considered and nice
Bayes solution is available. Similarly, in functional data analysis, Bayes
solution is achievable with Gaussian process prior. Finally if time
permits, we will present some empirical results on the application of
multiple testing in Finance.

Priyavrat Deshpande, Thu 06-02-2014, 15:00
Title : Reflections on manifolds and generalized Artin groups.
Abstract: The Artin groups form an interesting class of groups as they
appear in the study of various areas like mapping class groups,
configuration spaces, moment angle complexes, reflection groups and
hyperplane arrangements. Moreover, these groups have intriguing properties;
most of them are torsion-free, have trivial center, have solvable word
problem and in general are bi-automatic. The study of Artin groups display
a rich interplay between algebra, combinatorics and topology. In this talk
I will begin with an introduction to these groups, describe some of their
interesting properties and discuss several instances where they appear
naturally. Finally I will propose a generalization of these groups and
ongoing work to understand the aspects of so-called K(\pi, 1) problem.

Sukhendu Mehrotra, Thu 06-02-2014 16:00
Title: TBA
Abstract: TBA

T R Ramadas, Tue 04-02-2014 16:00
Title: Rational and global forms of certain Chiral Conformal Field Theories; Vertex Algebras I
Abstract: By rational forms we mean constructions on the complex projective
line that replace power series, formal or otherwise, by rational functions.
By global forms we understand extensions to smooth projective curves of
arbitrary genus. I will show how definitions and basic results around
vertex algebras are made simple when power seris are replaced by rational
expressions.

B V Rao, Fri 07-02-2014 14:00 (This talk is earlier than usual.)
Title: TBA
Abstract: TBA

K V Subrahmanyam, Wed 05-02-2014 16:00
Title: TBA
Abstract: TBA

S Sundar, Mon 03-02-2014 16:00
Title: TBA
Abstract: TBA

M Sundari, Mon 03-02-2014 14:00 (This talk is earlier than usual.)
Title: TBA
Abstract: TBA

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