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・Kurando Baba（Tokyo University of Science）slides
Title: Geometry of symmetric triad
Abstract: As an extension of the adjoint actions on compact connected Lie groups and the isotropy action on compact symmetric spaces, Hermann actions are defined on compact symmetric spaces. Robert Hermann (1960) proved that the Hermann action is variationally complete. After that, the geometry of orbits of this action has been studied intensively. Systematic studies of the adjoint actions and the isotropy actions can be given by root systems and restricted root systems. Osamu Ikawa (2011) introduced the notion of symmetric triad as an extension of root systems and restricted root systems, and investigated orbits of Hermann actions associated with commutative compact symmetric triads. It is also known that this notion is applied to study the intersection of two real forms in Hermitian symmetric space of compact type.
In this talk, we explain the theory of symmetric triads and concrete examples of symmetric triads which are given by commutative compact symmetric triads. This talk is based on a joint work with Osamu Ikawa (Kyoto Institute of Technology).
・Seonmi Choi（Kyungpook National University）slides
Title: On the triple point number and the length of a 3-cocycle of the 7-dihedral quandle
Abstract: The triple point number, a fundamental invariant for surface-knots analogous to the crossing number in classical knot theory, is defined as the minimum number of triple points across all possible diagrams of a surface-knot. Upper and lower bounds have been explored to estimate the triple point number of surface-knots. Satoh proposed a lower bound based on the length of a 3-cocycle of the 5-dihedral quandle. In this talk, we delve into the investigation of a lower bound for the triple point number of surface-knots, specifically focusing on the 7-dihedral quandle.
・Erika Kuno（Osaka University）
Title: A quasi-isometric embedding induced by the orientation double covering
Abstract: Classifying finitely generated groups by quasi-isometries is a key issue in geometric group theory. It is known that the mapping group of a nonorientable surface is a subgroup of the mapping group of the orientation double cover. We show that this injective homomorphism is a quasi-isometric embedding by using semihyperbolicity of the extended mapping class groups of orientable surfaces. This is a joint work with Takuya Katayama.
・Sam Nelson（Claremont McKenna College）slides
Title: Quiver Categorification of Quandle Invariants
Abstract: Quiver structures are naturally associated to subsets of the endomorphism sets of quandles and other knot-coloring structures, providing a natural form of categorification of homset invariants and their enhancements. In this talk we will survey recent work in this area.
・Shinji Ohno（Nihon University）slides
Title: Antipodal sets of generalized s-manifolds
Abstract: In this talk, I will introduce the notion of generalized s-manifold as a generalization of symmetric spaces. This notion is defined as a generalization of the point-symmetric structure of symmetric spaces.
We will give some typical examples and define the notion of antipodal sets.
・Koya Shimokawa（Ochanomizu University）
Title: Band surgery and its application
Abstract: Topological changes due to site-specific recombination of DNA and reconnection of a vortex are modeled by band surgery of knots and links. In this talk, we discuss untying pathways of the (2,2n)-torus link that appear in those phenomena.
・Masaki Taniguchi（Kyoto University）slides
Title: Knots, Floer theory, and Chern-Simons functional
Abstract: The Chern-Simons functional has been employed to derive numerous knot invariants. In this presentation, we explain the concept of instanton knot Floer homology, which can be regarded as an infinite-dimensional Morse homology with respect to the functional defined on the space of singular connections. The homology has several interesting topological applications to knot theory. We will discuss such applications and recent developments in this field.
・Masahito Yamazaki（Kavli IPMU）slides
Title: Quandles and Topological Quantum Field Theories
Abstract: Quandles are fascinating algebraic structures associated with knots. In this lecture, I will discuss recent attempts in incorporating the quandles into topological quantum field theories associated with supersymmetric quiver gauge theories.
・Kentaro Yonemura（Sumitomo Electric Industries, Ltd.）slides
Title: An embedding of a smooth quandle into a Lie group
Abstract: A quandle is an algebraic system closely related to knot theory. In this talk, we propose a conjecture that both the quandle and the manifold structure of smooth quandles may be embedded in Lie groups and show that it is correct in the case of spherical quandles.
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