Date and Time: Monday 30 September, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: P. Samuel's descent theorem.
Abstract: Let R be a normal noetherian domain with a finite group of
automorphisms G. Samuel's result says that the kernel of the natural
homomorphism Cl(R^G)\to Cl(R) is a subgroup of H^1(G,U), where U is the
group of units in R.
If R is divisorially unramified over R^G then the kernel is isomorphic to
H^1(G,U). This enables us to find the divisor class groups of rings of
invariants of finite group actions on polynomial or power series rings. If
time permits two general constructions of cyclic unramified coverings of
normal varieties will be discussed.
Time:
3:00pm-4:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Probability and Statistics seminar (It will be a talk by videoconference).
Speaker: Priyanka Majumder.
Affiliation: Indian Institute of Engineering Science and Technology, Shibpur.
Date and Time: Tuesday 01 October, 3:00 pm - 4:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: On Certain Probabilistic and Inferential Aspects of Reliability
Theory.
Abstract: Several nonparametric ageing classes have been established in
literature based on the various reliability characteristics. The talk will
cover certain probabilistic issues such as, reliability bound, moment
bound, closure under the formation of weak limits, characterisation
theorem, etc., which have been hitherto unknown in the literature, for the
New Better than Average Failure Rate (NBAFR) class of life distributions.
We further explore the validity of these results in the context of a more
general ageing class related to NBAFR family.
In the inferential part of my presentation, I will discuss a problem of
testing exponentiality against an alternative which is dened based on the
Laplace-Stieltjes transform, namely the so-called L-class. The asymptotic
distributions of our scale-invariant test statistics are derived and
consistency of the test established. General expressions of the local
approximate Bahadur eciencies for the test statistics are obtained and
evaluated for typical alternatives. The performance of the test is
assessed by means of a simulation study and through application to some
real life data sets.
Time:
4:30pm-5:30pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Coding Theory seminar.
Speaker: Prasant Singh.
Affiliation: Arctic University of Norway, Tromso.
Date and Time: Thursday 03 October, 4:30 pm - 5:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Decoding Grassmann codes using lines in Grassmannians.
Abstract: The talk is based on my joint work with Prof Peter Beelen. In
this talk, we recall the notion of Majority logic decoding for binary
codes introduced by Reed in the late 60s. We also recall some basic
notions of coding theory, construction of Grassmann codes and its basic
parameters. Lines in Grassmannians are closely related to parity checks of
Grassmann codes. We exploit this property of Grassmann codes together with
several other properties of point-line geometry of Grassmannian to
construct certain kind of parity checks for these codes. In the end, we
use these parity checks and the idea of Reed's majority logic decoding to
correct certain errors for Grassmann codes.