Toric Geometry

 

In the summer term, the lecture Toric Geometry will be given by Christian Steinert for 6 credit points (4h per week). The lecture is designed for Bachelor and Master students of mathematics. The content of the lectures Linear Algebra I and II is required.

Toric varieties are a special class of algebro-geometric objects whose properties are completely determined by the combinatorics of polyhedral objects (cones, fans, polytopes). Although these varieties are interesting on their own, we will mostly use them to study connections between algebraic geometry, representation theory and discrete mathematics – especially via so called Newton–Okounkov bodies and toric degenerations. After an introduction to fundamental concepts of algebraic geometry, we will mainly move along certain examples that appear regularly in other lectures of the Chair (knowledgs of these terms is not required at all): the Lie algebra of (traceless) complex quadratic matrices, flag and Grassmann varieties, the polytopes of Gelfdand and Tsetlin, the polytopes of Feigin, Fourier and Littelmann and further polytopes if time permits. We will also encounter the possibly acquainted theory of Eugène Ehrhart.

The lecture will be structured as an "inverted classroom". Each week covers a section of the script and contains one exercise and one revision meeting. The respective contents will be acquired before the exercise meeting using script and videos, deepened in small groups during the exercise meeting and finally reinforced through questions and discussions in the revision meeting.

Physical meetings will take place Mondas and Wednesdays from 14:30 to 16:00 Uhr. The location will be announced at a later date.

Registration will be done via RWTHonline at the beginning of the semester. Upon registration one automatically enters the learning space in RWTHmoodle, where exercises will be organized and further information can be found.