# IMath Seminar: Alfilgen Sebandal and Monika Kudlinska

You are all invited to a seminar featuring talks from two visiting PhD students, Ms. Alfilgen Sebandal and Ms. Monika Kudlinska. This is an in-person event and it will be held on **Monday, February 13, 2023, 1:00 – 3:00 PM** at the** Math Bldg Conference Room**.

** Ms. Alfilgen Sebandal** (MSU-IIT and Western Sydney University)

**Leavitt Path Algebra – Talented Monoid Finite Graded Classification Conjecture**

*Title:***Given a directed graph, one can associate two algebraic entities: the Leavitt path algebra and the talented monoid. The Graded Classification conjecture states that the talented monoid could be a graded invariant for the Leavitt path algebra, i.e. isomorphism in the talented monoids reflects as graded equivalence in the category of graded modules over the Leavitt path algebra of the corresponding directed graphs. In this talk, we shall see confirmations of this invariance in the ideal structure of the talented monoid with the so-called Gelfand-Kirillov Dimension of the Leavitt path algebra. The last part of the talk is an affirmation of the Graded classification conjecture in the finite-dimensional case. This is joint work with Roozbeh Hazrat (WSU Australia), Wolfgang Bock (TUK, Germany) and Jocelyn P. Vilela (MSU-IIT, Philippines).**

*Abstract:*** Ms. Monika Kudlinska** (University of Oxford)

**On profinite properties of free-by-cyclic groups**

*Title:***A central question in Geometric Group Theory is to determine how much algebraic information is encoded in the set of finite quotients of a given group. More precisely, we try to establish which properties of infinite discrete groups are preserved under isomorphisms of their profinite completions. In this talk, we will focus our attention on the family of groups known as free-by-cyclic groups, which have natural connections with 3-manifolds. We will give an overview of the state of the art, and discuss new results on the profinite rigidity of free-by-cyclic groups. This is joint work with Sam Hughes.**

*Abstract:*