Aditya Sarma Phukon, Temple University
This is a continuation of the series of meetings on algebraic groups. For an algebraic subgroup $H$ of a larger group $G$, we will define what a reasonable quotient $G/H$ should be. We shall justify when these quotients, called Homogeneous spaces, have a variety and, even better, an affine $k$-group structure. Towards this, we shall use representation machinery introduced before by Vasily and apply a neat trick of placing $G$ in a projective space and looking at particular orbits. We will end on a few remarks on cross-sections and, if time permits, on a closely related type of quotient called categorical quotient.