HEGL Community Seminar SoSe 2026

Except otherwise indicated, the Seminar takes place on Tuesdays at 13:00 in Seminar Room C of the Mathematikon.

30.06.2026

Speaker: Vincent Pecastaing (Université Côte d’Azur)

Title: Visualizing the spherical geometry of the variety of complete flags of $\mathbb R^3$

Abstract:

Flag manifolds are a class of compact homogeneous spaces generalizing projective spaces, which arise naturally as boundaries of symmetric spaces. They attract interest from several communities, including algebraic geometry, representation theory, and the study of rigidity phenomena for discrete group actions.
n this talk, I will illustrate one of the most classical examples of such manifolds: the variety of complete flags of $\mathbb R^3$. By definition, it is the space of all pointed projective lines in $\mathbb RP^2$. It is homogeneous under the action of $PGL(3,\mathbb R)$ and admits an 8-fold covering by the 3-sphere. Using stereographic projection, we will see that intrinsic objects of the flag manifold, such as its Schubert cell decomposition, are closely related to familiar objects in the 3-sphere, notably Clifford tori and the Hopf fibration.
These visualizations, which arose at the beginning of an ongoing joint project with Thang Nguyen, were aimed at developing intuition for a completeness problem about compact manifolds locally modeled on the variety of complete flags of $\mathbb R^n$, which I will briefly discuss.

09.06.2026

Speaker: Lael Costa (PSU)

Title: Dynamical Systems on Polygons
Time: 13:00.

Abstract:

In this talk, I will discuss several loosely related dynamical systems. In particular, I will speak about some variants of mathematical billiards and associated tilings and fractals. The talk will also explore a novel system which has ties to both billiards and the famous pentagram map. I will state and prove a few results, but much of the time will be dedicated to interactive software demonstrations. Audience participation will be encouraged!

26.05.2026

Speaker: Bram Bekker (TU Delft)

Title: Visualizing buildings
Time: 13:00.

Abstract:

Buildings are combinatorial and geometric objects invented to better understand the structure of matrix groups. The Buildings Gallery is a web application that shows several visualizations of these buildings, bringing to life a topic that has played an important role in geometric group theory since the 1960’s. We will explore some of the techniques behind these images, and discuss what parts of the group structure they help explain.