David Roe.
Berkovich Spaces
Berkovich spaces provide an analytification of p-adic varieties. By adding additional points, the natural p-adic topology on the points of a variety transforms from totally disconnected to uniquely path connected. I will describe the construction of the Berkovich affine line, as well as the definitions of analytic spaces that provide the foundation for rigid cohomology.
The alcove seminar's name originates from the traditional venue for it's meetings: the small alcoves spotting the halls of the math department. The seminar is aimed at being more approachable than the department number theory seminar.