Additional Information

What can we say about (or using) immersions of 1-manifolds into 2-manifolds? Perhaps surprisingly, quite a lot! Specific directions will be negotiated between the instructor and the participants, but may include: (1) The geometry and topology of the curve complex, including applications to understanding the mapping class group of a surface; (2) Gabai's proof of the Simple Loop Conjecture for maps between surfaces, and other forms of the Simple Loop Conjecture; (3) Calegari's work on stable commutator length; (4) Determining minimal intersection and self-intersection of curves on surfaces. Since this is a Berstein seminar, almost all the presentations will be given by the participants. A student who has taken the first year courses in topology and algebra will be well-prepared for this course.