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SUMMARY:Soheyla Feyzbaksh (Imperial College London)
DTSTART:20210326T170000Z
DTEND:20210326T183000Z
DTSTAMP:20260423T040411Z
UID:CAGS/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAGS/8/">App
 lication of a Bogomolov-Gieseker type inequality to counting invariants</a
 >\nby Soheyla Feyzbaksh (Imperial College London) as part of Columbia alge
 braic geometry seminar\n\n\nAbstract\nIn the preliminary talk\, I will fir
 st explain the notion of (weak) Bridgeland stability conditions on the bou
 nded derived category of coherent sheaves on a smooth projective threefold
 . Then I will discuss the Bogomolov-Gieseker conjecture of Bayer-Macrì-To
 da.\n\nIn the main talk: I will work on a smooth projective threefold $X$ 
 which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda\, s
 uch as the projective space $\\mathbb P^3$ or the quintic threefold. I wil
 l show certain moduli spaces of 2-dimensional torsion sheaves on $X$ are s
 mooth bundles over Hilbert schemes of ideal sheaves of curves and points i
 n $X$. When $X$ is Calabi-Yau this gives a simple wall crossing formula ex
 pressing curve counts (and so ultimately Gromov-Witten invariants) in term
 s of counts of D4-D2-D0 branes. In the end\, I will sketch how we can gene
 ralise this method to higher ranks to express DT invariants counting Giese
 ker semistable sheaves of any rank $> 1$ on $X$ in terms of those counting
  sheaves of rank 0 and pure dimension 2. This is joint work with Richard T
 homas.\n
LOCATION:https://researchseminars.org/talk/CAGS/8/
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