BPS cohomology and BPS categoriesLecture

by Tudor Padurariu (Bonn)

Tuesday Jan 20, 2026, 10:00 AM → 10:45 AM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Moduli spaces of bundles on complex curves and surfaces are central objects in algebraic geometry and related fields. A fundamental problem is the computation of their Betti numbers, dating back to the work of Harder-Narasimhan and Atiyah-Bott. Closely related is the question of how the Betti numbers of different moduli spaces are related. An important tool is the existence of dualities between certain moduli spaces, such as moduli spaces of Higgs bundles on a curve, which can manifest as equalities of Betti numbers. Establishing such dualities is interesting in its own right, as it provides evidence for dualities of gauge theories.

In this talk, I will introduce BPS cohomology (joint with Chenjing Bu, Ben Davison, Andrés Ibáñez Núñez, and Tasuki Kinjo, building on earlier work of Davison et.al., Kontsevich-Soibelman, and Joyce et.al.) and BPS categories (joint with Yukinobu Toda) for certain singular spaces, both refinements of the BPS invariants of interest in physics. These constructions apply to a variety of settings, including moduli spaces of coherent sheaves on Calabi-Yau threefolds, moduli of local systems on three-manifolds, and moduli spaces of representations of quivers with potential. They are well-behaved replacements of more classical cohomology theories or of the derived category of coherent sheaves on such spaces.

I will explain how BPS cohomology and BPS categories shed new light on classical moduli spaces, such as the moduli of Higgs bundles on curves, and how they provide a general framework for formulating and studying the dualities mentioned above.