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SUMMARY:Modular linear differential operators and their classification - D
 on Zagier (Max-Planck-Institut für Mathematik\, Bonn)
DTSTART:20220822T090000Z
DTEND:20220822T100000Z
UID:TALK177188@talks.cam.ac.uk
DESCRIPTION:Modular linear differential equations (MLDEs) have arisen in s
 everal different&nbsp\;contexts in mathematics and mathematical physics in
  recent years. &nbsp\;Perhapsthe first example\, which will be described b
 riefly\, was the second-order LDE&nbsp\;&nbsp\; &nbsp\; &nbsp\; f"(z) - (k
 +1)/6 E_2(z) f'(z) + k(k+1)/12 E_2'(z) f(z) = 0&nbsp\;that arose in work o
 f Kaneko and myself on supersingular j-invariants incharacteristi p\, but 
 more recently they have become important in thetheory of vertex operator a
 lgebras\, where they often give non-trivial&nbsp\;information about the pr
 operties (or sometimes non-existence) of VOAsof given type and given centr
 al charge. &nbsp\;The talk will describe recent jointwork with K. Nagatomo
  and Y. Sakai giving descriptions of all MLDOs (forthe full modular group 
 and other lattices in SL(2\,R) ) in terms of Rankin-Cohen brackets and in 
 terms of quasimodular forms. &nbsp\;All notions\, includingthe definitions
  of modular and quasimodular forms\, will be reviewed.
LOCATION:Seminar Room 1\, Newton Institute
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