Braid Parking Varieties

par Nathan Williams (UT Dallas)

mardi 25 juin 2024, 10:45 → 11:45 Europe/Paris

Salle Fokko du Cloux, Bât Braconnier (ICJ, Université Lyon 1)

By considering various preimages of projections of a certain braid variety and using the combinatorics of the center of the Hecke algebra, we find (or conjecture) subvarieties whose point counts recover parking numbers, Catalan numbers, HOMFLY coefficients and Kirkman numbers, Kreweras numbers, B-stable ideal numbers, and parabolic parking numbers.  The classical combinatorial objects associated to these numbers are obtained from suitable Deodhar decompositions. This is joint work with Minh-Tâm Trinh.