LISMATH
Lisbon Mathematics PhD

The LisMath Seminar

The purpose of the LisMath seminar is to provide an initiation into research as well as to make students train their oral skills.  Each LisMath student will be asked to give a talk, based on research papers, chosen from a list covering a variety of research topics. The seminar should be comprehensible to everyone. The student will be asked to make an effort to explain why he/she finds the topic interesting, and how it fits into the broader research picture. The LisMath seminar will thus help broadening the students training.
 
The LisMath seminar takes place on a weekly basis in the Spring semester. Attendance is mandatory for LisMath students. Venue: Wednesday 17h-18h, alternating between FCUL (seminar room 6.2.33 of the Department of Mathematics) and IST (seminar room P9 of the Department of Mathematics) except for 26/6/2018 and 15/7/2019, LisMath Seminar Day, when all sessions will be held at the former location.

– Europe/Lisbon — Online

Inês Rodrigues, LisMath, Faculdade de Ciências, Universidade de Lisboa.
A cactus group action on shifted tableau crystals and a shifted Berenstein-Kirillov group.

Gillespie, Levinson and Purbhoo recently introduced a crystal-like structure for shifted tableaux, called the shifted tableau crystal. Following a similar approach as Halacheva, for crystals of finite Cartan type, we exhibit a natural internal action of the cactus group on this structure, realized by the restrictions of the shifted Schützenberger involution to all primed intervals of the underlying crystal alphabet. This includes the shifted crystal reflection operators, which agree with the restrictions of the shifted Schützenberger involution to single-coloured connected components, but unlike the case for type A crystals, these do not need to satisfy the braid relations of the symmetric group.

In addition, we define a shifted version of the Berenstein-Kirillov group, by considering shifted Bender-Knuth involutions. Paralleling the works of Halacheva and Chmutov, Glick and Pylyavskyy for type A semistandard tableaux of straight shape, we exhibit another occurrence of the cactus group action on shifted tableau crystals of straight shape via the action of the shifted Berenstein-Kirillov group. We also conclude that the shifted Berenstein-Kirillov group is isomorphic to a quotient of the cactus group. Not all known relations that hold in the classic Berenstein-Kirillov group need to be satisfied by the shifted Bender-Knuth involutions, namely the one equivalent to the braid relations of the type A crystal reflection operators, but the ones implying the relations of the cactus group are verified, thus we have another presentation for the cactus group in terms of shifted Bender-Knuth involutions.