May 2019
Public Access Category: All |

- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic K-Theory Seminar:

Speaker: Manoj Keshari.

Date and Time: Friday 03 May, 3:30 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: K_0 of an exact and Waldhausen category.

- 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.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Seminar: CACAAG.

Speaker: Srikanth Srinivasan.

Time: 4pm, Monday 20 May, 2019.

Venue: Ramanujan Hall.

Title: Algebraic complexity theory and connections to Hilbert functions.

Abstract: In a few lectures, I will introduce some of the main

problems in Algebraic Complexity theory and some of the techniques

that have been used to make progress on them. The techniques are

closely related to Hilbert functions and Young flattenings.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Srikanth Srinivasan.

Time: Thursday, 30 May, 4pm.

Venue: Ramanujan Hall.

Title: Algebraic complexity theory and connections to Hilbert functions

(Lecture II).

Abstract: In a few lectures, I will introduce some of the main

problems in Algebraic Complexity theory and some of the techniques

that have been used to make progress on them. The techniques are

closely related to Hilbert functions and Young flattenings.