Coloquio del Departamento de Matemáticas

20 de marzo de 2025. 11:30 hrs. Auditorio José Adem, Cinvestav-IPN

Próxima conferencia

20 de marzo de 2025. 11:30 hrs. Auditorio José Adem, Cinvestav-IPN

Unirse a Zoom
ID de la reunión: 857 5227 6523
Contraseña: 250580

Dr. Sudhir R. Ghorpade
Indian Institute of Technology Bombay

Grassmannians, Schubert Varieties and Linear Error Correcting Codes

Resumen: A Grassmannian may be defined as a collection of subspaces of a fixed dimension of a finite dimensional vector space over a field. It embeds naturally into a large projective space, via the so-called Plucker embedding, and as such it can be viewed as a projective algebraic variety. This Grassmann variety has a distinguished class of closed subvarieties known as Schubert varieties, and any such Schubert variety in a Grassmannian has a natural nondegenerate embedding in a subspace of the Plucker projective space. When the base field is finite, these varieties give rise to an interesting class of linear codes. These codes have been of considerable interest in the past few decades. In this talk, we shall provide a gentle introduction to these codes after a quick review of the relevant background, and then describe some of the known results and open problems.