Nori proved that a vector bundle on a projective variety satisfies a polynomial equation with integral coefficients if and only if its pullback to a finite cover is trivial. I shall talk about an extension of this result to Gauduchon astheno-Kahler manifolds. This is joint work with Indranil Biswas.

Abstract and title are attached.

This is the first of two lectures where we'll cover Groebner bases of toric ideals. We start with an introduction to toric ideals and then study their Grobener bases. Our main goal will be a theorem of Bernd Sturmfels from 1991 that relates (certain) initial ideals of toric ideals to regular triangulations of an associated point configuration. The lectures are based on Chapters 4 and 8 of the book ``Groebner Bases and Convex Polytopes'' by Sturmfels.

This is a study on unbiased estimation of the reliability R(t) = exp(-t / lambda) based on a random sample of size n from an exponential population with unknown mean lambda where t ( > 0 ) is given. We focus on unbiased estimation of R(t) based on (i) Complete Sample, (ii) Failure-Truncated Sample, (iii) Time-truncated Sample. Time permitting, we also discuss about the problem of Prediction of Future Observation(s) Based on Exponential Samples.

This talk will discuss the question of fixing the sign of certain arithmetic quantities and its connection to the so called congruent number problem - one of the oldest open problems in mathematics.

The abstract for his talk is given in the attachment.

The abstract for his talk is given in the attachment.

The abstract for his talk is given in the attachment.

Theme.....as is told by a participant in a recent presentation of this talk..... "When I first heard about such a "show", just the very idea of it seemed to be intriguing to me. I immediately made up my mind to witness it, given an opportunity. Fortunately, the opportunity came soon and almost at my next door. It was an engaging experience overall - the fundamental concepts of "odd - man - out" were exemplified in front of the young eyes almost tangibly. The enactment that followed took us right to the birthplace of probability – the games of chance and maximizing wins. The presentation aspect was captivating – with your throwing questions, salvaging the confounded youngsters and a continuous stream of wits – how lively the session was! When you declared the “game” to be over… the magical journey was short – was possibly my only complaint !!!