Seminar Talk Series – 11

27 March 2024



Representation of some Infinite Group using some Diagrams


Dr. Claire Levaillant, Assistant Professor (RTPC) of Mathematics, University of Southern California, USA

Date and Time:

Wednesday, March 27, 2024 at 9:00 AM

Location of event:

Beirut Arab University, Debbieh Campus, A3 building, Meeting room


Talk Summary:

In this talk, I will build a representation of an analog of the infinite braid group. Some of the generators will be similar to those of the braid group but other elements in the group will satisfy some new relations. We will even work in a bigger mathematical structure, namely an algebra, which contains the group. We will further introduce some diagrams, involving strands in a quite similar way as those for the braid group in order to represent all the algebra elements that are involved, as well as relations on these diagrams, namely relations matching the defining relations from the algebra. We will show that we obtain a faithful linear representation of the group and that this generically irreducible representation becomes reducible when its two parameters satisfy certain relations which we provide.

Speaker Bio:

Dr. Claire Levaillant pursued her undergraduate studies at Ecole Normale Supérieure de Cachan in France. In 2003, she moved to the USA to become an Albert and Marguerite Ramond scholar at Caltech, where she received her Ph.D. in representation theory of algebras under Professor David Wales. Since then, she has held an academic position at the University of California at Santa Barbara and she currently serves on the faculty of the University of Southern California.