29. Algebraic geometry – Categorizing schemes in the wild (Nickolas Rollick)

Speaker: Nickolas Rollick

The talk was given at the algebraic geometry working seminar on July 20th, 2017 (Department of Pure Mathematics, University of Waterloo)

Abstract: Last time, we laid the groundwork necessary to make sense of the category of schemes. This week, we get a feel for this category via some examples and structural facts. In particular, we will learn what the final object is, construct non-trivial morphisms from a one-point scheme to itself, and look at the seemingly odd notion of scheme-valued points of a scheme. It’s truly a wild world these schemes live in…

Following the notes of Ravi Vakil, available at http://math.stanford.edu/~vakil/216blog/index.html.

Video 28 is missing. Please refer to the notes.

Diophantine Approximation and Algebraic Curves Workshop

Last week, I got back from the workshop at Banff on Diophantine approximation and algebraic curves. All recorded videos are available here. Here I will post some of my most favorite lectures.

Cameron L. Stewart (University of Waterloo), On k-free integers represented by binary forms.

Jan-Hendrick Evertse (University of Leiden), S-parts of values of binary forms and decomposable forms.

Yann Bugeaud (Université de Strasbourg), On the digital representation of smooth numbers.

Benjamin Matschke (University of Bordeaux), Solving S-unit, Mordell, Thue, Thue–Mahler and generalized Ramanujan–Nagell equations via Shimura–Taniyama conjecture.

Beth Malmskog (Villanova University), Solving S-unit equations in Sage and Applications to Algebraic Curves.

Fabien Pazuki (University of Copenhagen), Elliptic curves and isogenies.