강연 초록

Title :  Optimization of links and spatial graphs on 3D lattice 

Abstract : This talk explores mathematical links and spatial graphs embedded in 3D space. It employs geometric models to simulate these graphs, with a particular emphasis on lattice links within a cubic lattice space. A central aspect of the research centers on the lattice stick number, which quantifies the minimum sticks required to represent a lattice link. The study includes quantitative analyses of links, Brunnian theta-curves, and handcuff graphs, which will be introduced during the talk. 

Title :  Alexander polynomial of twisted torus knots 

Abstract : Twisted torus knots are a generalization of torus knots obtained by introducing additional full twists to adjacent strands of torus knots. In this talk, we present an explicit formula for the Alexander polynomial of twisted torus knots. We use a presentation of the knot group of twisted torus knots and Fox’s free differential calculus. We further explore the applications of our computations, including a determination of the genus for certain families of twisted torus knots. This is joint work with Adnan. 

Title : Fundamental Concepts of Deep Learning and Our Research Team's Results  

Abstract : In this seminar, we will introduce the basic concepts of deep learning and share the research findings obtained by our research team. Deep learning has garnered significant interest in the field of artificial intelligence, bringing about transformative changes in various domains. During the seminar, we will start by providing a brief explanation of the fundamental concepts and operational principles of deep learning. We will offer an overview of deep neural network structures and learning algorithms to help you understand how deep learning processes data and makes predictions. In particular, we will delve into topics like `gradient descent’ and `backpropagation’. Additionally, we will present the research results from our research team. 

Title : Upper bound of folded ribbon length for arbitrary knots 

Abstract : The folded ribbonlength is a two dimensional version of ropelength for knots and links.

The upper bound of a folded ribbonlength is estimated to be a linear with respect to a minimal crossing number.

Several knot types are evidence of this problem, but there is no proof for general cases.

In this talk, we show that the upperbound folded ribbonlength of a knot or a non-split link is bounded above by 3c(K)+2. 

Title :  Signed mosaic graphs and alternating mosaic number of knots 

Abstract: Lomonaco and Kauffman introduced knot mosaics in their work on quantum knots. This definition is intended to represent an actual physical quantum system. A knot n-mosaic is an n by n matrix of 11 kinds of specific mosaic tiles representing a knot or a link. In this talk, we consider the alternating mosaic number of an alternating knot K which is defined as the smallest integer n for which K is representable as a reduced alternating knot n-mosaic. We define a signed mosaic graph and a diagonal grid graph and construct Hamiltonian cycles derived from the diagonal grid graphs. Using the cycles, we completely determine the alternating mosaic number of torus knots of type (2,q) for q>= 2, which grows in an order of q^{1/2}.

Title :  Crossing number and \Delta Y-move

Abstract:  We report a behavior of crossing number of graphs under \Delta Y-moves on the complete graph K_n. Concretely it is shown that for any k in N, there exists a natural number n and a sequence of \Detla Y-moves K_n -> G^(1) -> ... -> G^(k) which is decreasing with respect to the crossing number. We also discuss the decrease of crossing number for relatively small n. This is a joint work with Ryo Nikkuni (Tokyo Woman's Christian University).