Lecture 1 : Hwa Jeong Lee
Title : Minimal grid diagrams of the prime alternating knots with 12 crossings
Abstract : A grid diagram is a knot diagram with finitely many horizontal segments and the same number of vertical segments such that the vertical segments cross over the horizontal segments at all crossings. In this talk, we give a list of minimal grid diagrams of the 12 crossing prime alternating knots.
Lecture 2 : Sungjong No
Title : An upper bound on the simple hexagonal lattice stick number of a knot
Abstract : The simple hexagonal lattice(sh-lattice) is a lattice space based on four types of sticks: x=<1, 0, 0>, y=<1/2, √3/2, 0>, z=<1/2, √3/2, 0>, and w=<0, 0, 1>. In this talk, I introduce the relationships and distinctions between lattice stick knots and sh-lattice stick knots. Furthermore, I suggest an upper bound on the sh-lattice stick number of a given knot expressed in terms of its crossing number.
Lecture 3 : Hyoungjun Kim
Title : Introduction to the superhelical structure
Abstract : The ropelength of a knotted string with volume is defined as the ratio of the length of its central curve to the radius of its sectional disc. In a physical context, achieving minimal ropelength corresponds to a state of minimal potential energy, and geometrically, it signifies a tightly-packed conformation. The quest to establish a connection between the topological complexity of knotted strings and their minimal ropelength has persisted into recent years. In this talk, I introduce the superhelical structure and some results
Lecture 4 : Seungsang Oh
Title : Pure dimer system in 3-dimensional lattice
Abstract : A perfect matching in a graph is a set of independent edges of the graph covering all vertices. The exact enumeration of perfect matchings in the grid graph on the plane was obtained by Kasteleyn, Temperley and Fisher in 1961. The state matrix recursion method was developed by Oh for the enumeration of various 2-dimensional regular lattice models. In this talk, this method is extended into a 3-dimensional model. We investigate the perfect matching enumeration for a rectangular parallelepiped in the 3-dimensional simple cubic lattice.
Lecture 5 : Hyungkee Yoo
Title : Restricted arc-presentations of knots and links
Abstract : A knot is a simple closed curve in R³ (or S³). An arc presentation of a knot is an embedding into the open book decomposition of R³ such that each half plane contains a properly embedded single simple arc. In this talk, I limit the number of pages in the arc presentation to three and instead have multiple arcs on each page. This type of arc presentation is called a three-page presentation. Also I introduce the results of three-page presentation for torus knots and 2-bridge knots. These results induce the exact value of three-page index of trefoil knot.