Maîtresse de conférences -- Associate professor
Laboratoire Interdisciplinaire des Sciences du Numérique (LISN) -- Université Paris-Saclay
Viviane Pons is an expert of the Tamari lattice and the weak order on permutations. She studies combinatorial aspects, such as bijections, and more specifically the relations between the combinatorics and the algebraic and geometric structures that arise (Hopf algebras, polytopes).
In her work, she has introduced several combinatorial concepts such as Tamari interval-posets, combinatorial interpretations of \(m\)-Tamari lattices and intervals, Permutree lattices and Hopf algebras, \(s\)-weak order... These objects give new insights on the combinatorial, algebraic and geometric landscape surrounding the permutahedra and associahedra. For example, she used Tamari interval-posets to prove the conjecture on the equi-distribution of "rises" and "contacts" on intervals of the \(m\)-Tamari lattice. Tamari interval-posets have also been used in many different contexts outside her own work.
Viviane Pons is also a contributor and active promoter of the open-source software SageMath. She was the Paris-Saclay site lead and for the H2020 European infrastructure project OpenDreamKit, as well as the workpackage leader for the project dissemination. Through this project and her other commitments, talks, seminars, workshop organizations, editorial work, she is a well known member of the open-source scientific community at large. She is also committed to science popularization (talks, school projects and more) and more specifically to gender equity in science and women representations.