# NCMW - Representation theory and syzygies (2023)

## Venue: Chennai Mathematical Institute, Siruseri

## Dates: 18 Dec 2023 to 23 Dec 2023

**Convener(s)**

Name: |
Mandira Mondal | Manoj Kummini |

Mailing Address: |
INSPIRE Faculty Fellow, Indian Institute of Technology Jodhpur | Professor, Chennai Mathematical Institute |

Email: |
mandira at iitj.ac.in | mkummini at cmi.ac.in |

This workshop introduces representation-theoretic methods in the study of syzygies. One of the earliest milestones in this area is Lascoux’ description of the syzygies of the determinantal variety. This method (now of- ten called the ‘Kempf-Lascoux-Weyman technique’) was later expanded and used to provide the syzygies in many instances of geometric significance. An exposition of the technique and the pre-requisites needed from representation theory for proving Lascoux’ theorem forms the major part of this workshop.

In the mid 2000’s Boij and Soederberg proposed some conjectures on the numerical nature of free resolutions. Eisenbud-Floystad-Weyman proved one of these conjectures, by constructing free resolutions using Pieri maps between irreducible representations. A discussion of this construction forms the minor part of this workshop.

**Pre-requisites**: Free resolutions, Koszul complexes, depth, Auslander-Buchsbaum theorem,Hilbert syzygy theorem, divisors and line bundles, sheaf cohomology, higher direct image.