报告题目：Testing chirality in incidence geometry

报告人：Dimitri Leemans，布鲁塞尔自由大学（法语）

报告时间：2026年4月30日（周四），16:00-17:00

报告地点: 数学楼2-2会议室

报告摘要：In 1956, Jacques Tits introduced the concept of an incidence geometry as an object generalizing the notion of incidence. He also established its close relation with groups and showed how to construct incidence geometries starting from a group and some of its subgroups, inventing the concept of a coset geometry. Specific classes of incidence geometries have been studied in various contexts. For instance, thin residually connected and regular incidence geometries with a linear diagram give the family of abstract regular polytopes while thin residually connected and chiral incidence geometries with a linear diagram give the family of chiral polytopes.

In 2016, Maria Elisa Fernandes, Dimitri Leemans and Asia Weiss introduced the concept of hypertopes, that are thin and residually connected incidence geometry as a generalization of abstract polytopes, dropping the linearity condition that is imposed on polytopes. They studied in particular two families of hypertopes, namely the regular ones (where the automorphism group has a unique orbit on the set of chambers) and the chiral ones (where the automorphism group has two orbits on the set of chambers with adjacent chambers in distinct orbits). They showed among other things that the automorphism group of a regular hypertope has to be a C-group and that the automorphism group of a chiral hypertope has to be a C⁺-group.

In the regular case, given a C-group, one can easily construct a coset geometry, and then, results from Buekenhout, Hermand, Dehon and Leemans permit to translate the geometric properties of thinnness, residual connectedness and flag-transitivity in group-theoretical properties. Such tests are available in the computational algebra software Magma. In the chiral case, we recently managed to translate these geometric properties into group-theoretical properties. This talk will describe the work we did in that direction, joint with Wei-Juan Zhang.  

报告人简介：Dimitri Leemans is an internationally recognised leader in algebraic and geometric combinatorics, currently holding the highest academic rank of Full Professor at the Université libre de Bruxelles (ULB). He has research contributions in both theoretical and computational mathematics. He has authored over 120 peer-reviewed publications, received prestigious distinctions including the François Deruyts Prize and a Marsden Grant, and developed widely used computational tools in Magma that are now fundamental for research in group theory and incidence geometry. As a senior academic leader at ULB, he has played a major role in mentoring and supervising numerous PhD students and early-career researchers, making a decisive contribution to the training and development of the next generation of mathematicians.