May 13, 2019 - May 17, 2019
Public Access Category: All |
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- Time:
- 4:30pm-5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Commutative Algebra Seminar.
Speaker: Jyoti Singh.
Affiliation: Visvesvaraya National Institute of Technology, Nagpur.
Date and Time: Tuesday 14 May, 4:30 pm - 5:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Strongly generalized Eulerian $D$-modules.
Abstract: Let K be a field of characteristic zero and A_n(K) be the nth-Weyl
algebra over K. In this talk, we discuss strongly generalised Eulerian
$A_n(K)$-modules and their properties. We prove that if M is a strongly
generalized
Eulerian $A_n(K)$-module, then so is the graded Matlis dual of M. We also
prove that
Ext functor of strongly generalized Eulerian modules is strongly generalized
Eulerian $A_n(K)$-module. As a consequence, we prove the following
conjecture:
Let M and N be non-zero, left, holonomic, graded generalized Eulerian
$A_n(K)$-modules. Then the graded K-vector space $Ext^i_{A_n(K)}(M, N)$ is
concentrated in degree zero for any i >=0.
- Time:
- 3:30pm-4:30pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Statistics Seminar.
Speaker: Raj Kamal Maurya.
Affiliation: IIT Patna.
Date and Time: Thursday, 16 May, 3:30 pm - 4:30 pm.
Venue: Room 216, Department of Mathematics.
Title: Some Problems of Estimation and Prediction under Progressive
Censoring.
Abstract: We have considered the problem of making statistical inferences for different lifetime
models on the basis of progressive type-II censored samples. In particular, we have
derived various estimates of parameters using both classical and Bayes methods. The
associated MLEs are computed using the EM algorithm. We also compute the ob-
served Fisher information matrices and based on these computations, the asymptotic
confidence intervals of parameters are constructed. Bootstrap intervals are also dis-
cussed. We also derive Bayesian estimates of parameters against different loss func-
tions. Most of these estimates appear in analytically intractable forms and so we
have used different approximation methods like importance sampling, Lindley, Tier-
ney and Kadane procedures to compute the Bayes estimates. In sequel, we have also
constructed highest posterior density intervals of parameters. We have also derived
predictive inference for censored observations under frequentist and Bayesian frame-
works. In particular, we obtain best unbiased predictor, conditional median predictor
from frequentist perspective. Among prediction intervals, we construct pivotal in-
terval, highest conditional density interval, equal tail interval and HPD interval for
future observations. Determination of optimal plans is one of the primary objective
in many life test studies. We have obtained such plans again using both frequentist
and Bayesian approaches under progressive censoring. We also consider estimation
of multicomponent stress-strength reliability under progressive censoring. We have
numerically compared the proposed methods using simulations for each problem. We
have also discussed real life examples in support of studied methods. We have provided
relevant information in each chapter of the thesis.
- Time:
- 3:30pm-4:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebra Seminar.
Speaker: Satya Mandal.
Affiliation: University of Kansas.
Date and Time: Thursday 16 May, 3:30 pm - 4:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Homotopy obstructions for Projective Modules.
Abstract: The Theory for vector bundles in topology shaped the research in
projective modules in algebra, consistently. This includes Obstruction
Theory. The
algebra has always been trying to catch up. To an extent, this fact
remained under
appreciated.
For an affine scheme $X=\spec{A}$, and a projective $A$-module $P$, our
objective
would be to define an obstruction class $\varepsilon(P)$ in a suitable
obstruction
house (preferably a group), so the triviality of $\varepsilon(P)$ would
imply $P
\equiv Q \oplus A$. One would further hope the obstruction house is an
invariant of
$X$; not of $P$. We would report on what is doable. We detect splitting $P
\equiv Q
\oplus A$ by homotopy.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.
Speaker: R. Parimala.
Affiliation: Emory University.
Date and Time: Friday 17 May, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Norm equations and local-global principles.
Abstract: Let L be a cyclic extension of a number field K. Hasse’s theorem
says that
an element of K is a norm from L if it is a norm locally at all
completions of K.
Examples of failure of similar local global principle if L is not cyclic
were also
known. We survey recent results on obstructions to local global principle
for norm
equations over number fields.