|
・Hiroyuki Fuji（Kobe University）slides
Title: On analogues of Mirzakhani's recursion formula via minimal string theories
Abstract: Mirzakhani's recursion formula for the Weil-Petersson volume of the moduli space of bordered hyperbolic Riemann surfaces is well-known. On the other hand, recent studies in theoretical physics have made significant progress in analyzing the partition function of the two-dimensional gravity theory known as Jackiw-Teitelboim gravity based on this relation. By extending this correspondence to minimal string theory and using the framework of the topological recursion by Chekhov-Eynard-Orantin (CEO), we find an analogue of Mirzakhani's recursion formula.
This talk is based on joint work (SIGMA 20 (2024) 043) with Masahide Manabe (OCAMI and Osaka University).
・Shinobu Fujii（Chitose Institute of Science and Technology）
Title: Symmetric Clifford systems and maximal s-commutative sets in real oriented Grassmannian manifolds
Abstract: A symmetric Clifford system is a set of finite real symmetric matrices which correspond one-to-one with the representation of the Clifford algebra. In this talk, we explain that subquandles of the real oriented Grassmannian manifolds are generated from symmetric Clifford systems. In addition, we try to determine the maximal s-commutative subsets in the Grassmannian manifolds by using Tanaka--Tasaki's classification of maximal antipodal sets in them.
・Noboru Ito（Shinshu University）
Title: Twin commutators and higher Arnold strangeness invariants
Abstract: In this talk, we describe the relationship between higher Arnold strangeness invariants of plane curves and the lower central series of subgroups of the pure twin group. In particular, using commutators in the twin group, we explain how higher Arnold strangeness invariants vanish and have finite order under triple-point modifications. As an application, we construct infinite families of plane curves whose higher invariants coincide with those of a plane curve up to a specified order.
・Yewon Joung（Hanyang University）slides
Title: Bikei module invariants of unoriendted surface-links
Abstract: We introduced the biquandle module invariants of oriented surface-links in previous work.
In this talk, we introduce invariants of unoriented surface-links using bikei modules.
We also show that these invariants are more effective than the bikei homset cardinality invariant alone at distinguishing non-orientable surface-links. This is joint work with Sam Nelson.
・Ryoya Kai（Osaka Metropolitan University）slides
Title: On metrics for quandles
Abstract: In geometric group theory, finitely generated infinite groups are studied from the geometric perspective. We aim to construct geometric group theoretic analogue for quandles, and to provide geometric knowledges of infinite quandles. In this talk, we define two types of quasi-isometric classes of metrics for a quandle with a certain finiteness property. Additionally, we provide some examples of quandles that are quasi-isometric to typical metric spaces. This talk is based on a joint work with Kohei Iwamoto (Ritsumeikan Univ.) and Yuya Kodama (Kagoshima Univ.)
・Naoki Kimura（Tokyo University of Science）slides
Title: Invariants of Legendrian knots and rack colorings
Abstract: Legendrian knots are defined when the ambient 3-manifold is equipped with a contact structure. Legendrian knots are classified up to Legendrian isotopy and Legendrian isotopy classes are finer than knot types. In this talk, we present several invariants of Legendrian knots, including the classical invariants and rack coloring invariants.
・Hokuto Konno（The University of Tokyo）slides
Title: Symplectic structures and diffeomorphisms of 4-manifolds
Abstract: I will explain how to use families of symplectic forms and families Seiberg-Witten theory to study diffeomorphism groups of 4-manifolds. Concretely, we apply this technique to prove the infinite generation of homotopy groups of diffeomorphism groups and to compare diffeomorphism groups with symplectomorphism groups. This is joint work with Jun Li and Weiwei Wu.
・Dongsoo Lee（Korea Advanced Institute of Science and Technology）slides
Title: ON THE GROUP OF HOMOLOGY S1×S2’S
Abstract: Kawauchi defined a group Ω(S1×S2) on the set of homology S1×S2's under an equivalence relation called H-cobordism. This group receives a homomorphism from the knot concordance group, given by the operation of zero-surgery. We will talk about the kernel of the zero-surgery homomorphism and the 2-torsion subgroup of Ω(S1×S2).
・Sam Nelson（Claremont McKenna College）slides
Title: Quandle cohomology quiver representations
Abstract: Quandles are algebraic structures encoding the motion of knots through space. Quandle cocycle quivers categorify the quandle cocycle invariant. In this talk we will define a quiver representation associated to quandle cocycle quivers and use it to obtain new polynomial invariants of knots.
・Hiroshi Tamaru（Osaka Metropolitan University）slides
Title: On the Euler characteristics for quandles
Abstract: In this talk, we will define the Euler characteristic for quandles, and introduce some of its properties and computational results. In particular, when we consider compact symmetric spaces as quandles, the Euler characteristic we have defined coincides with the usual topological Euler characteristic.
Thanks to the pioneering work of Chen and Nagano, the Euler characteristics of compact symmetric spaces have been shown to relate to the notions of antipodal sets and 2-numbers. Our research aims to extend this framework to quandles.
The content of this talk is based on joint work with Ryoya Kai (arXiv:2411.08319).
| 