Presented by: 
Dr Arkadius Kalka
Tue 17 Apr, 3:00 pm - 4:00 pm
Room 442, Building 67

We review braid and Garside groups and the history of conjugacy in these groups. Then, we also consider the friends of the conjugacy problem like subgroup (subCP), shifted (ShCP) and simultaneous conjugacy (SCP) and the double coset problem (DCP). In particular, we present improved invariants for the SCP, first deterministic algorithms for ShCP and for subCP and DCP for parabolic subgroups of braid groups. This is based on joint work with several co-authors from the Bar-Ilan University, Israel.

Further motivation for these problems comes from non-commutative public key cryptography, and we discuss basic key agreement protocols. Dehornoy's shifted conjugacy leads us to left-self distributive (LD) systems, multi-LD systems, and our new idea of non-associative cryptography.