Time: June 18th, 20th, 22th, 10:00-11:30am.

Abstract: An invertible nxn matrix is totally positive (resp. totally nonnegative) if all the minors are positive (resp. nonnegative). This definition is introduced by Schoenberg in the 30's. The systematic study of the total positivity is due to Lusztig in the 90's. In this mini-course, we will give an overview of the total positivity for GL_n (the group of invertible nxn matrices) and its Grassmannian, and its flag varieties. If time allows, we will talk about a recent conjecture of Arkani-Hamed, Witten, et. al. on the total positivity of the Grassmannian of GL_n.