Perverse Sheaves and their Categorification in Geometry and Representation Theory

About

The use of perverse sheaves lies at the core of Geometric Representation Theory. It has allowed mathematicians to solve hard algebraic or representation-theoretic problems by identifying suitable spaces that encode crucial information and by using them to translate the initial problem into geometric terms.

Perverse schobers have found diverse applications across algebraic geometry, topology, and representation theory. For instance, they have been instrumental in the study of birational geometry and derived categories, particularly in the context of flops. They also play a key role in the study of the derived categories of quotient stacks from the viewpoint of Geometric Invariant Theory (GIT). Additionally, perverse schobers have been applied to classical problems, such as studying the non-rationality of certain varieties.

One of the most significant applications of perverse schobers lies in their connection to homological mirror symmetry, Fukaya categories, and cluster theory. These connections bridge algebraic geometry, symplectic geometry, and representation theory, revealing deep relationships between categorical structures and geometric phenomena. For example, perverse schobers provide a natural framework for understanding wall-crossing phenomena in mirror symmetry, further enriching the interplay between these fields

Course leader

Giovanna Carnovale (University of Padova), William Donovan (Tsinghua University), Francesco Esposito (University of Padova), Martina Lanini (Tor Vergata University of Rome), Francesco Sala (University of Pisa)

Target group

The Summer School is intended for PhD students, early postdoctoral fellows and junior researchers, working in areas related to Algebraic Geometry, Representation Theory, and Topology

Course aim

The aim of this Summmer School is to introduce graduate students working in Algebraic Geometry, Representation Theory, or Topology to perverse sheaves and their categorification (perverse schobers), and some of their recent important applications. The study of perverse sheaves, perverse schobers, and their interplay with geometry, algebra, and representation theory is currently an extremely vibrant and promising area of research. The techniques involved are highly sophisticated, making it challenging for early-career researchers to familiarize themselves with this rapidly evolving field without proper guidance

Fee info