Topology and combinatorics of the complex of flags

Seminar
Speaker
Roy Meshulam (Technion)
Date
16/12/2018 - 15:30 - 14:00Add to Calendar 2018-12-16 14:00:00 2018-12-16 15:30:00 Topology and combinatorics of the complex of flags Let V be an n-dimensional space over a fixed finite field. The complex of flags X(V) is the simplicial complex whose vertices are the non-trivial linear subspaces of V, and whose simplices are ascending chains of subspaces. This complex, also known as the spherical building associated to the linear group GL(V), appears in a number of different mathematical areas, including topology, combinatorics and representation theory. After recalling the classical homological properties of X(V), we will discuss some more recent results including: 1. Minimal weight cocycles in the Lusztig-Dupont homology. 2. Coding theoretic aspects of X(V) and the existence of homological codes. 2. Coboundary expansion of X(V) and its applications. Room 201, Math and CS Building (Bldg. 216) אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Room 201, Math and CS Building (Bldg. 216)
Abstract

Let V be an n-dimensional space over a fixed finite field. The complex of flags X(V) is the simplicial complex whose vertices are the non-trivial linear subspaces of V, and whose simplices are ascending chains of subspaces. This complex, also known as the spherical building associated to the linear group GL(V), appears in a number of different mathematical areas, including topology, combinatorics and representation theory. After recalling the classical homological properties of X(V), we will discuss some more recent results including:

1. Minimal weight cocycles in the Lusztig-Dupont homology.

2. Coding theoretic aspects of X(V) and the existence of homological codes.

2. Coboundary expansion of X(V) and its applications.

תאריך עדכון אחרון : 11/12/2018