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Friday, October 6, 2017
Public Access

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8:00am [3:00pm]Dr. Satya P Singh 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. [3:30pm]Prof. M. S Raghunathan 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.