### Mathematics Colloquium

# Delaram Kahrobaei

### (University of York, U.K., New York University, U.S.A.)

## "Some applications of arithmetic and graph groups in cryptography"

** Date: ** |
February 14, 2019 |

** Time: ** |
17:15 |

** Place: ** |
Lecture Hall, **Research III** |

**Abstract:** In this talk we will give various examples of exponentially distorted subgroups in linear groups, including some new example of subgroups of \({\mathrm{SL}}_n( \mathbb{Z}[x])\) for \(n \ge 3\), and show how they can be used to construct symmetric-key cryptographic platforms. This is a joint work K. Mallahi-Karai to appear in the Journal of Groups Complexity, Cryptology, De Gruyter. In the second part of the talk we consider several classical and novel algorithmic problems for right-angled Artin groups (a.k.a. graph groups), some of which are closely related to graph theoretic problems, and study their computational complexity. We study these problems with a view towards applications to cryptography. This is joint work with Ramon Flores and Thomas Koberda, just published in Journal of Algebra, Elsevier.