Consider a polynomial differential operator in one variable, depending on a small parameter (Planck constant). Under appropriate conditions, the low-energy spectrum admits an asymptotic expansion in hbar.
I will present a way to calculate such a series via a purely "commutative problem", a mixture of variations of Hodge structures and of the Stirling formula. This result came from discussions with A.Soibelman. It seems that we obtain an explanation of an old observation by J.Zinn-Justin of the 

 universal appearance of Bernoulli numbers.


Talk Number 21110011
Speaker Profile Maxim Kontsevich
Perimeter Institute Recorded Seminar Archive