Séminaires : Géométrie énumérative

Equipe(s) : aa,
Responsables :Penka Georgieva, Ilia Itenberg.
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Orateur(s) Ellena Moskovsky - Monash University,
Titre Generalising Narayana polynomials using topological recursion
Horaire14:00 à 15:00

Narayana polynomials arise in a number of combinatorial settings and have been proven to satisfy many properties, including symmetry, real-rootedness and interlacing of roots. Topological recursion, on the other hand, is a unifying mathematical framework that has been proven to govern a vast breadth of problems. One relatively unexplored feature of topological recursion is its ability to generalise existing combinatorial problems; one can use this feature of topological recursion to motivate a particular generalisation of Narayana polynomials. In ongoing work-in-progress with Norman Do and Xavier Coulter, we prove that the resultant generalised polynomials satisfy certain recursive and symmetry properties analogous to their original counterparts, while conjecturing that they also satisfy real-rootedness and interlacing.