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Generating Function of q- and Elliptic Multiple Polylogarithms of Hurwitz Type
Ohno and Zagier (Indag Math 12:483–487, 2001) found that a generating function of sums of multiple polylogarithms can be written in terms of the...
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Around spin Hurwitz numbers
We present a review of the spin Hurwitz numbers, which count the ramified coverings with spin structures. It is known that they are related to the...
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Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial...
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Hurwitz numbers from Feynman diagrams
AbstractTo obtain a generating function of the most general form for Hurwitz numbers with an arbitrary base surface and arbitrary ramification...
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Simple Maps, Hurwitz Numbers, and Topological Recursion
We introduce the notion of fully simple maps, which are maps with non self-intersecting disjoint boundaries. In contrast, maps where such a...
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Matrix and tensor witnesses of hidden symmetry algebras
Permutation group algebras, and their generalizations called permutation centralizer algebras (PCAs), play a central role as hidden symmetries in the...
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Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals
We consider the Laguerre partition function and derive explicit generating functions for connected correlators with arbitrary integer powers of...
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Hidden symmetries and large N factorisation for permutation invariant matrix observables
Permutation invariant polynomial functions of matrices have previously been studied as the observables in matrix models invariant under S N , the...
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Genus expansion of matrix models and ћ expansion of KP hierarchy
We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ -functions with natural genus...
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Cut-and-join structure and integrability for spin Hurwitz numbers
Spin Hurwitz numbers are related to characters of the Sergeev group, which are the expansion coefficients of the Q Schur functions, depending on odd...
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Polygon gluing and commuting bosonic operators
AbstractTwo families of commuting Hamiltonians are constructed, parameterized by a constant matrix. The first series is new and the second is...
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Superintegrability of Kontsevich matrix model
Many eigenvalue matrix models possess a peculiar basis of observables that have explicitly calculable averages. This explicit calculability is a...
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Riemann–Hilbert Problem and Fay's Identity
In Chap. 2 we have shown that the Ernst equation can be treated as the integrability condition of an overdetermined linear di.erential system for...
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Analytic solutions to the fractional kinetic equation involving the generalized Mittag-Leffler function using the degenerate Laplace type integral approach
Recently, several fractional kinetic equations involving various special functions have been widely and usefully used in describing and solving...
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Diffusive pattern formations in three-species nonlinear dynamics of cancer
We examine pattern formations of the spatiotemporal dynamics of tumor growth model. The system is modeled by three-species reaction–diffusion...
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Shannon information entropy, soliton clusters and Bose-Einstein condensation in log gravity
We give a probabilistic interpretation of the configurational partition function of the logarithmic sector of critical cosmological topologically...