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September 19, 2022 / Alexander Gaifullin (Steklov Inst., Skoltech, Moscow Univ.) = = = 27-vertex triangulations of 16-manifolds like the octonionic projective plane September 26, 2022 / Alexander Gaifullin (Steklov Inst., Skoltech, Moscow Univ.) = = = Combinatorial formulae for Pontryagin classes and manifolds like projective planes |
We introduce and study the model of a logarithmic gas at arbitrary temperature on a smooth closed contour in the plane. This model generalizes Dyson’s gas on the unit circle. We compute the non-vanishing terms of the large N expansion of the free energy (N is the number of particles) by iterating the loop equation that is the Ward identity with respect to reparametrizations of the contour. Similarities with conformal field theory will be outlined. The leading and subleading contributions to the free energy are expressed through the conformal radius of the domain surrounded by the contour. The O(1)-contribution is expressed through the spectral determinant of the Neumann jump operator associated with the contour. It coincides with the Loewner energy of the contour as it was defined in the recent works by Y. Wang. This is the joint work with P. Wiegmann