分野別セミナー

One general principle in asymptotic combinatorics is that the siingularities of generating functions explain the asymptotics of their coefficients, leading to compact derivations for many phenomena like frozen regions in tiling models, or LDP in spin models.

Surprisingly, one observes sometime a discontinuous drop in the exponential growth rate for certain multivariate rational generating functions in a parametric family. The explanation of this phenomenon turned out to depend on the computations of homologies of the algebraic variety where the generating function has a pole. Our result is conceptually related to a thread of research in applications of complex algebraic geometry to hyperbolic PDEs, going back to Leray, Petrowski, Atiyah, Bott and Garding.

As a consequence, we give a topological explanation for certain asymptotic phenomenon appearing in the combinatorics and number theory literature.


※ このセミナーは九州確率論セミナーとの合同セミナーです。