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SUMMARY:BPS cohomology and BPS categories [Lecture]
DTSTART:20260120T090000Z
DTEND:20260120T094500Z
DTSTAMP:20260308T040700Z
UID:indico-event-1025@math-events.uni-bonn.de
DESCRIPTION:Speakers: Tudor Padurariu (Bonn)\n\nModuli spaces of bundles o
 n complex curves and surfaces are central objects in algebraic geometry an
 d related fields. A fundamental problem is the computation of their Betti 
 numbers\, dating back to the work of Harder-Narasimhan and Atiyah-Bott. Cl
 osely related is the question of how the Betti numbers of different moduli
  spaces are related. An important tool is the existence of dualities betwe
 en certain moduli spaces\, such as moduli spaces of Higgs bundles on a cur
 ve\, which can manifest as equalities of Betti numbers. Establishing such 
 dualities is interesting in its own right\, as it provides evidence for du
 alities of gauge theories.\nIn this talk\, I will introduce BPS cohomology
  (joint with Chenjing Bu\, Ben Davison\, Andrés Ibáñez Núñez\, and Ta
 suki Kinjo\, building on earlier work of Davison et.al.\, Kontsevich-Soibe
 lman\, and Joyce et.al.) and BPS categories (joint with Yukinobu Toda) for
  certain singular spaces\, both refinements of the BPS invariants of inter
 est in physics. These constructions apply to a variety of settings\, inclu
 ding moduli spaces of coherent sheaves on Calabi-Yau threefolds\, moduli o
 f local systems on three-manifolds\, and moduli spaces of representations 
 of quivers with potential. They are well-behaved replacements of more clas
 sical cohomology theories or of the derived category of coherent sheaves o
 n such spaces.\nI 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.\n\nhttps://math-events.uni-bonn.de
 /event/1025/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1025/
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