Fri, October 6, 2017
Public Access Category: All |
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- 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.