Lecture Notes taken by Nilufer Koldan In this lecture I will describe one of the most significant achievements of the second half of the XX century – the Atiyah-Singer index theorem. I will also discuss some more recent developments in the area as well as some open problems. 1. The definition of the index 1.1. The finite-dimensional case. Let A : V 1 → V 2 be a linear map between finite dimensi...

Potato virus Y (PVY) as one of the serious diseases on tobacco (Nicotiana tabacum L.), reduces leaf yield and its quality. Use of re-sistant genotypes is being considered as the most effective, economical and a safe way to reduce damages of the virus. In the present study, the response of 90 oriental and semi-oriental tobacco genotypes was evaluated against PVY using randomized complete block d...