Exploring torus orbit closures

by Prof. Eunjeong Lee (Chungbuk National University)

Thursday 23 Jan 2025, 08:30 → 10:30 Europe/Paris

Thursday 23 January 2025, 4:30 PM - 6:30 PM (Korea)

A toric variety is a normal algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety. Due to their rich symmetries, toric varieties establish a fruitful connection between geometry, topology, combinatorics, and representation theory. 

The first part of the talk will consider toric varieties and the above relations. We will then focus on a specific family of toric varieties living in a flag variety. A flag variety is a smooth projective homogeneous variety, denoted as G/B, where G is a semisimple algebraic group and B is a Borel subgroup. The maximal torus T of B acts on G/B via left multiplication. By examining the closures of torus orbits under this T-action, one can construct a family of toric varieties within G/B. For instance, a permutohedral variety can be obtained in this manner. We will explore these toric varieties in detail. This talk is based on several collaborations with Seonjeong Park and Mikiya Masuda. 

LINK FOR THE WEBINAR

https://cnrs.zoom.us/j/99325522412?pwd=BFaD8G2gkVmlvhEKPWPkfRhc5HzPw3.1

Eunjeong_Lee_recording_2025_Korea_France.mp4