October 2, 2017 - October 6, 2017
Public Access Category: All |
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
- Time:
- 9:30am-10:25am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Neeraj Kumar
Title: Linear resolutions of monomial ideals - II
Abstract: Consider a graded ideal in the polynomial ring in several
variables. We shall discuss criterion for the graded ideal and its power
to have linear resolution. Then we focus our attention
to study linear resolution of monomial ideals.
Monomial ideals are the bridge between commutative algebra and the
combinatorics. Monomial ideals are also significant because they appear as
initial ideals of arbitrary ideals. Since many properties of an initial
ideal are inherited by its original ideal, one often adopt this strategy
to decipher properties of general ideals. The first talk is meant for
covering the preliminary results on resolution and regularity of monomial
ideal.The aim of this series of talk is to present the result in
arXiv:1709.05055
- Time:
- 10:30am-11:25am
- Description:
- Speaker: Kriti Goel
Title: Huneke-Itoh Intersection Theorem and its Consequences - III
Abstract: Huneke and Itoh independently proved a celebrated result on
integral closure of powers of an ideal generated by a regular sequence. As
a consequence of this theorem, one can find the Hilbert-Samuel polynomial
of the integral closure filtration of I if the normal reduction number is
at most 2. We prove Hong and Ulrich's version of the intersection theorem.
- Time:
- 11:00am-12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: A Sum Product theorem over finite fields
Abstract: Let A be a finite subset of a field F. Define A+A and AA to
be the set of pairwise sums and products of elements of A,
respectively. We will see a theorem of Bourgain, Katz and Tao that
shows that if neither A+A nor AA is much bigger than A, then A must be
(in some well-defined sense) close to a subfield of F.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Dr. Rashmi Tiwari, Department of Mathematics IIT Bombay
Title: SOME ASPECTS OF MOMENTS OF ORDERED STATISTICS
Abstract: Recurrence relations of moments which are useful to reduce
the amount of direct computations quite considerably and usefully
express the higher order moments of order statistics in terms of the
lower order moments and hence make the evaluation of higher order
moments easy. We have derived recurrence relations for single, double
(product) and higher moments of various ordered random variables, like
ordinary order statistics, progressively censored order statistics,
generalized order statistics and dual generalized order statistics
from some specific continuous distributions. It also deals with
L-moments and TL-moments which are analogous of the ordinary moments.
We have derived L-moments and TL-moments for some continuous
distributions. These results have been applied to find the L-moment
estimators and TL-moment estimators of the unknown parameters for some
specific continuous distributions.
- Time:
- 3:00pm-4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Dr. Satya P Singh,
Department of Statistics University of Haifa Israel
Title: Some issues in the design of experiments with ordered
experimental treatments
Abstract: There are many situations where one expects an ordering
among K>2 experimental groups or treatments. Although there is a
large body of literature dealing with the analysis under order
restrictions, surprisingly very little work has been done in the
context of the design of experiments. Here, we provide some key
observations and fundamental ideas which can be used as a guide for
designing experiments when an ordering among the groups is known in
advance. Designs maximizing power as well as designs based on single
and multiple contrasts are discussed. The theoretical findings are
supplemented by numerical illustrations.
- Time:
- 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Title: Kodaira's theorem: criterion for embedding a compact Kahler
manifold in projective space (Lecture 2)
Abstract: Let $M$ be a compact Kahler manifold and $\Omega (M)$ the
canonical $2$-form on $M$. When $M$ is projective $n$-spce $\P^n(\C)$ ,
$H^2(M,\C)$
is of dimension 1. It follows that for any Kahler metric on the projective
space, the cohomology class $[\Omega (M)$ of the canonical $2$-form is a
multiple of the (unique up to sign) of a generator of $H^2(M,\Z)$. It is
immediate from this that if $M$ is a complex sub-manifold of $\P^n(\C)$ for
some $n$, then for the Kahler metric on $M$ induced from one on $\P^n(\C)$,
it is clear that $[\Omega(M)] \in $\C \cdot H^2(M, Z)$. Kodaira's theorem
is a converse to this fact: If a complex manifold $M$ admits a Kahler
metric such that the class of $\Omega(M)$ is a multiple of an integral
class, then $M$ can be embedded in some projective space. This result was
conjectured by W V D Hodge.