A Hitchhiker’s Guide to Joyce Structures

Abstract: Joyce structures were introduced by Tom Bridgeland in the context of stability conditions and were constructed in close analogy to Frobenius structures introduced in Topological Field Theories. The main motivation behind them was the similarity between the Iso-Stokes condition and the Kontsevich-Soibelman Wall Crossing Formula. Since then, Joyce structures have exhibited not only a rich analytical side but also an extremely interesting geometric structure.

In this seminar, I will introduce these works, starting with the definition and motivation of Joyce structures and then moving to the formulation of the Riemann-Hilbert-Birkhoff problem. After discussing an explicit solution, I will conclude by exploring the geometric side and interpreting all the concepts in this new setting. Given the variety of topics, I will make an effort to provide specific examples.

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon