# Toric topology of the Grassmann manifolds

Date:

Time:

2021 03 29

15:30 (GMT+0)

Speaker:

Svjetlana Terzi ́c

Knots and representation theory

It is a classical problem to study the canonical action of the compact torus $T^{n}$ on a Grassmann manifold $G_{n,2}$ which is connected to a series of problems in modern algebraic topology, algebraic geometry and mathematical physics.

The aim of the talk is to present the recent results which are concerned with the description of the orbit space $G_{n,2}/T^n$ in term of the new notions:

1. universal space of parameters $\mathcal{F}_{n}$;

2. virtual spaces of parameters $\widetilde{F}_{\sigma}\subset \mathcal{F}_{n}$ which correspond to the strata $W_{\sigma}$ in stratification $G_{n,2} = \cup _{\sigma} W_{\sigma}$ defined in terms of the Pl\"ucker coordinates;

3. projections $\widetilde{F}_{\sigma}\to F_{\sigma}$ for the spaces of parameters $F_{\sigma}$ which correspond to the strata $W_{\sigma}$.

In the course of the talk it will be described the chamber decomposition of the hypersimplex $\Delta _{n,2}$ which is defined by the special arrangements of hyperplanes and represents one of the basic tools for the description of the orbit space $G_{n,2}/T^n$ in terms of the given notions.

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