I recently received my PhD in mathematics under the supervision of Prof. Sofia Lambropoulou, at National Technical University of Athens.
Prof. Louis H. Kauffman at UIC was my co-advisor.
I am interested in low dimensional topology, combinatorial knot theory, knot theories; classical&virtual knot theory, particularly knotoid theory and its applications in chemistry, biology and physics.
My PhD was mainly based on:
A study on knotoids of Turaev: With Kauffman, we worked on the height (or complexity) problem of knotoids, constructed new invariants for knotoids in relation with invariants of virtual knots. We showed that our invariants are useful in estimating the height of a knotoid! We also presented a geometric interpretation for (planar) knotoids , discussed briefly on virtual knotoids. See 1, 2 at the next page for details or my thesis below.
The theory of braidoids: With Lambropoulou, we initiated a "braided" counterpart theory to the theory of knotoids. We presented the notion of braidoid and developed algorithms to obtain analogous theorems to the classical Alexander and Markov theorem for knotoids and braidoids.
See 4 at the next page or my thesis below for details.
Applications of knotoids&braidoids: With colleagues in Center for Integrative Genomics at Universite de Lausanne, we analyzed topological structures of (linear) protein chains and also bonded protein chains through planar knotoids by utilizing our former geometric interpretation of knotoids. See 3 at the next page or again my thesis, for details.
I now work on construction of quantum invariants of knotoids and an algebraic theory for braidoids. Recently, with Sam Nelson we started a study on biquandle colorings of knotoids.
Here you can find my CV. Here is my PhD thesis.