Neslihan Gügümcü, Izmir University of Economics.
Date: 24th of October, 2018, Thursday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: A (classical) knot is basically a loop in 3-dimensional space with a possible entanglement. Understanding the entanglement type of a given knot; to distinguish it from other knots or to see if its entanglement can be resolved and the knot can be turned into just a simple loop, lies as a central problem of knot theory. Knot invariants are tools used for solving this problem. Recently, Turaev introduced knotoids which are a natural extension of knots giving rise to generalizations of many knot invariants and also many new concepts.
In this talk I firstly introduce basic notions of classical knot and knotoid theory. Then I present some generalized algebraic structures such as quandles and biquandles. Finally I show how to color a knot/knotoid diagram by using a biquandle, and how to derive invariants for them by this coloring.
This is a joint work with Sam Nelson at Claremont McKenna College, USA.