The Real Story of Linear Series on P¹

    Real algebraic geometry is a difficult subject. Basic questions about some of the most elementary objects may not have answers that seem satisfactory when compared to the answers obtained in classical algebraic geometry. Nevertheless, it is a well-developed subject and an important one as applications demand real solutions. There are also many hidden gems in the subject.

    This talk will try to illustrate these remarks in a corner of the subject that I know well---real linear series on P¹. For a preview of some of the talk, below are pictures of linear series on P¹ of dimension 3 and degree 4 with simple real ramification.