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SUMMARY:Yifeng Huang (University of Michigan)
DTSTART:20211201T200000Z
DTEND:20211201T210000Z
DTSTAMP:20260420T053048Z
UID:NYC-NCG/81
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/81/"
 >Point count of the variety of modules over the quantum plane over a finit
 e field</a>\nby Yifeng Huang (University of Michigan) as part of Noncommut
 ative geometry in NYC\n\n\nAbstract\nIn 1960\, Feit and Fine gave a formul
 a for the number of pairs of commuting n by n matrices over a finite field
 . We consider a quantum deformation of the problem\, namely\, counting pai
 rs (A\,B) of n by n matrices over a finite field that satisfy AB=qBA for a
  fixed nonzero scalar q. We give a formula for this count in terms of the 
 order of q as a root of unity\, generalizing Feit and Fine's result. In th
 is talk\, after explaining the title and the results\, we will discuss a c
 urious phenomenon that one sees when comparing the commutative case (q=1) 
 and the general case from a geometric viewpoint.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/81/
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