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SUMMARY:Adeel Khan (Academia Sinica)
DTSTART:20231108T060000Z
DTEND:20231108T070000Z
DTSTAMP:20260423T035916Z
UID:MAC8028/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAC8028/9/">
 The derived Bézout theorem</a>\nby Adeel Khan (Academia Sinica) as part o
 f Trends in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n
 \nAbstract\nGiven two smooth algebraic curves of degrees $d$ and $e$ in th
 e complex projective plane\, Bezout’s theorem is a classical result asse
 rting that the intersection consists of either infinitely many or exactly 
 $d\\cdot e$ points\, counted with multiplicities.  Generalizing this formu
 la to intersections in higher-dimensional projective space was a task that
  fuelled much of 20th century algebraic geometry\, eventually culminating 
 in J.-P. Serre’s solution in 1958.\n\nWe will review some of this histor
 y before presenting a 21st century point of view on Bézout’s theorem.  
 Specifically\, we will see that the modern language of derived algebraic g
 eometry allows us to give a simple definition of intersection multipliciti
 es\, which unlike Serre’s formula applies even to non-proper intersectio
 ns\, and yields a vast generalization of Bézout theorem for arbitrary int
 ersections of projective hypersurfaces.\n
LOCATION:https://researchseminars.org/talk/MAC8028/9/
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