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SUMMARY:The loop-nilpotent cohomological Hall algebra and integral forms o
 f Yangians [Oberseminar Darstellungstheorie]
DTSTART:20261104T090000Z
DTEND:20261104T110000Z
DTSTAMP:20261029T070200Z
UID:indico-event-1722@math-events.uni-bonn.de
DESCRIPTION:Speakers: Shivang Jindal (EPFL Lausanne)\n\nGiven a quiver wit
 h potential\, Kontsevich and Soibelman defined its cohomological Hall alge
 bra (CoHA) as a mathematical model for the algebra of BPS states. Since th
 en\, CoHAs have been found to have connections with several areas of mathe
 matics\, including cohomological Donaldson–Thomas theory\, quantum group
 s\, non-abelian Hodge theory\, and cluster algebras. In certain cases\, di
 mensional reduction identifies the CoHA with a preprojective CoHA\, an alg
 ebra that appears naturally in the Schiffmann–Vasserot proof of the AGT 
 conjecture and in the study of Nakajima quiver varieties.\nIn this talk\, 
 I will introduce an algebra combining features of these constructions\, wh
 ich we call the loop nilpotent CoHA. will describe this algebra as a sub
 algebra of a shuffle algebra\, characterised by certain integral wheel con
 ditions. I will then explain how\, for quivers of finite type\, this algeb
 ra can be identified with the positive half of the Drinfeld–Gavarini dua
 l of the Yangian. We will also see how this description leads to a charact
 erisation of the Kac polynomials of a quiver in terms of dimensions of spa
 ces of symmetric polynomials satisfying explicit degree and divisibility c
 onditions. If time permits\, I will explain how the loop-nilpotent CoHA ad
 mits a surjective homomorphism onto the positive half of the corresponding
  quantized Coulomb branch algebra.\nThis talk is based on joint work with 
 Andrei Neguț.\n\nhttps://math-events.uni-bonn.de/event/1722/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1722/
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