| DATE: | Friday, February 16, 2001 |
| TIME: | |
| PLACE: | LN 2205 |
| SPEAKER: | Laura Anderson, Texas A&M |
| TITLE: | Combinatorial differential manifolds and matroid bundles |
This talk will discuss a combinatorial model for differential manifolds and vector bundles, due to Gelfand and MacPherson, which leads to an intriguing interplay between topology and combinatorics. A combinatorial differential manifold is essentially a simplicial complex together with a combinatorial model for a differential structure. Any real differential manifold can be "combinatorialized" into a combinatorial differential manifold. More generally, a real vector bundle has an analogous "combinatorial vector bundle", or matroid bundle. This "combinatorialization" leads to elegant combinatorial analogs to classical topological ideas, and to new combinatorial methods for topology. The road between topology and combinatorics runs both ways. While this model is inspired by real manifolds and vector bundles, in fact it extends further: various combinatorial objects with no obvious relation to topology have natural "combinatorial vector bundle" structures. The topological perspective this lends leads to surprising results in combinatorics.