Title of Seminar: Algebraic Geometry Preprint Seminar 2023
Title of Talk: Phantoms on surfaces and mutations of exceptional collection
Speaker: Swarnava Mukhopadhyay, TIFR, Mumbai
Date: September 12, 2023
Time: 16:00:00 Hours
Venue: AG-77
Abstract: An admissible subcategory in a triangulated category is called a phantom if it has trivial Hochschild homology and Grothedieck group. In this talk, we will discuss the recent work of Johannes Krah (arXiv:2304.01269) on the existence of phantoms on a rational surface and discuss its implications on conjectures about the fullness of exceptional collections of maximal length and on transitivity of the action of the mutations and shifts on the set of maximal exceptional collections. If time permits we will discuss the origin of the example in Krah's preprint. This builds upon earlier works of Krah (arXiv:2211.07724), Elagin-Lunts (MR3598503), Kuznetsov (MR3691718), Orlov-Kuleshov (MR1286839), and Vial (MR3570150).
Title of Talk: Phantoms on surfaces and mutations of exceptional collection
Speaker: Swarnava Mukhopadhyay, TIFR, Mumbai
Date: September 12, 2023
Time: 16:00:00 Hours
Venue: AG-77
Abstract: An admissible subcategory in a triangulated category is called a phantom if it has trivial Hochschild homology and Grothedieck group. In this talk, we will discuss the recent work of Johannes Krah (arXiv:2304.01269) on the existence of phantoms on a rational surface and discuss its implications on conjectures about the fullness of exceptional collections of maximal length and on transitivity of the action of the mutations and shifts on the set of maximal exceptional collections. If time permits we will discuss the origin of the example in Krah's preprint. This builds upon earlier works of Krah (arXiv:2211.07724), Elagin-Lunts (MR3598503), Kuznetsov (MR3691718), Orlov-Kuleshov (MR1286839), and Vial (MR3570150).