Alexey Ananyevskiy (St. Petersburg): Non-vanishing sections of algebraic vector bundles and characteristic classes

In the talk I will discuss the cohomological interpretation of the existence of a nowhere vanishing section of a rank n vector bundle over a smooth algebraic variety of dimension n. I will briefly cover the classical statement for projective varieties involving the top Chern class and describe the approach to the affine case involving the techniques from the motivic homotopy theory and the motivic Euler class. Then I will discuss some special cases when the vanishing of the top Chern class yields the vanishing of the Euler class.