Our research seminar is devoted to the many connections between convex and algebraic geometry. This interaction has many important applications in various areas of mathematics: combinatorics, representation theory, mathematical physics to name a few. A classical and one of the most well-known examples is the combinatorial description of an important class of algebraic varieties - the so-called toric varieties - in terms of polytopes and fans (collections of cones). Yet another recent and up-to-date application is the theory of Newton-Okounkov bodies. Participants will tell about recent papers that they find important on
http://arxiv.org/find/grp_math/1/AND+cat:+math.AG+all:+polytope/0/1/0/all/0/1 and
http://arxiv.org/find/grp_math/1/AND+cat:+math.RT+all:+polytope/0/1/0/all/0/1,
providing extensive background material for those less familiar with the subject.
Geometrically oriented 2nd year students and higher are welcome.
https://docs.google.com/document/d/1l47Wj3EoNNR8eDZfvYvgsVswbgm-S-W4qdwc4aJ0LkA/edit